DESCRIPTION Title of Invention: ENCODING DEVICE AND METHOD, DECODING DEVICE AND METHOD, AND PROGRAM Technical Field [0001] The present invention relates to an encoding device and method, a decoding device and method, and a program, and specifically relates to an encoding device and method, a decoding device and method, and a program which enable music signals to be played with high sound quality by expanding a frequency band. Background Art [0002] In recent years, music distribution service to distribute music data via the Internet or the like has been spreading. With this music distribution service, encoded data obtained by encoding music signals is distributed as music data. As a music signal encoding technique, an encoding technique has become the mainstream wherein a bit rate is lowered while suppressing file capacity of encoded data so as not to take time at the time of downloading. [0003] Such a music signal encoding techniques, are roughly - 2 - SP313141 divided into an encoding technique such as MP3 (MPEG (Moving Picture Experts Group) Audio Layer 3) (International Standards ISO/IEC 11172-3) and so forth, and an encoding technique such as HE-AAC (High Efficiency MPEG4 AAC) (International Standards ISO/IEC 14496-3) and so forth. [0004] With the encoding technique represented by MP3, of music signals, signal components in a high-frequency band (hereinafter, referred to as high-frequency) equal to or greater than around 15 kHz of hardly sensed by the human ear, are deleted, and signal components in the remaining lowfrequency band (hereinafter, referred to as low-frequency) are encoded. Such an encoding technique will be referred to as high-frequency deletion encoding technique. With this high-frequency deletion encoding technique, file capacity of encoded data may be suppressed. However, high-frequency sound may slightly be sensed by the human ear, and accordingly, at the time of generating and outputting sound from music signals after decoding obtained by decoding encoded data, there may be deterioration in sound quality such as loss of sense of presence that the original sound has, or the sound may seem to be muffled. [0005] On the other hand, with the encoding technique represented by HE-AAC, characteristic information is - 3 - SP313141 extracted from high-frequency signal components, and encoded along with low-frequency signal components. Herein after, such an encoding technique will be referred to as a highfrequency characteristic encoding technique. With this high-frequency characteristic encoding technique, only characteristic information of high-frequency signal components is encoded as information relating to the highfrequency signal components, and accordingly, encoding efficiency may be improved while suppressing deterioration in sound quality. [0006] With decoding of encoded data encoded by this highfrequency characteristic encoding technique, low-frequency signal components and characteristic information are decoded, and high-frequency signal components are generated from the low-frequency signal components and characteristic information after decoding. Thus, a technique to expand the frequency band of low-frequency signal components by generating high-frequency signal components from lowfrequency signal components will hereinafter be referred to as a band expanding technique. [0007] As one application of the band expanding technique, there is post-processing after decoding of encoded data by the above-mentioned high-frequency deletion encoding - 4 - SP313141 technique. With this post-processing, high-frequency signal components lost by encoding are generated from the lowfrequency signal components after decoding, thereby expanding the frequency band of the low-frequency signal components (see PTL 1). Note that the frequency band expanding technique according to PTL 1 will hereinafter be referred to as the band expanding technique according to PTL 1. [0008] With the band expanding technique according to PTL 1, a device takes low-frequency signal components after decoding as an input signal, estimates high-frequency power spectrum (hereinafter, referred to as high-frequency frequency envelopment as appropriate) from the power spectrum of the input signals, and generates high-frequency signal components having the high-frequency frequency envelopment from the low-frequency signal components. [0009] Fig. 1 illustrates an example of the low-frequency power spectrum after decoding, serving as the input signal, and the estimated high-frequency frequency envelopment. [0010] In Fig. 1, the vertical axis indicates power by a logarithm, and the horizontal axis indicates frequencies. [0011] - 5 - SP313141 The device determines the band of low-frequency end of high-frequency signal components (hereinafter, referred to as expanding start band) from information of the type of an encoding method relating to the input signal, sampling rate, bit rate, and so forth (hereinafter, referred to as side information). Next, the device divides the input signal serving as low-frequency signal components into multiple subband signals. The device obtains average for each group regarding a temporal direction of power (hereinafter, referred to as group power) of each of multiple subband signals following division, that is to say, the multiple subband signals on the lower frequency side than the expanding start band (hereinafter, simply referred to as low-frequency side). As illustrated in Fig. 1, the device takes a point with average of group power of each of the multiple subband signals on the low-frequency side as power, and also the frequency of the lower end of the expanding start band as the frequency, as the origin. The device performs estimation with a primary straight line having predetermined inclination passing through the origin thereof as frequency envelopment on higher frequency side than the expanding start band (hereinafter, simply referred to as high-frequency side). Note that a position regarding the power direction of the origin may be adjusted by a user. The device generates each of the multiple subband signals on - 6 - SP313141 the high-frequency side from the multiple subband signals on the low-frequency side so as to obtain the estimated frequency envelopment on the high-frequency side. The device adds the generated multiple subband signals on the high-frequency side to obtain high-frequency signal components, and further adds the low-frequency signal components thereto and output these. Thus, music signals after expanding the frequency band approximates to the original music signals. Accordingly, music signals with high sound quality may be played. [0012] The above-mentioned band expanding technique according to PTL 1 has a feature wherein, with regard to various highfrequency deletion encoding techniques and encoded data with various bit rates, the frequency band regarding music signals after decoding of the encoded data thereof can be expanded. Citation List Patent Literature [0013] PTL 1: Japanese Unexamined Patent Application Publication No. 2008-139844 Summary of Invention Technical Problem [0014] t3 - 7 - SP313141 However, with the band expanding technique according to PTL 1, there is room for improvement in that the estimated frequency envelopment on the high-frequency side becomes a primary straight line with predetermined inclination, i.e., in that the shape of the frequency envelopment is fixed. [0015] Specifically, the power spectrums of music signals have various shapes, there may be many cases to greatly deviate from the frequency envelopment on the high-frequency side estimated by the band expanding technique according to PTL 1, depending on the types of music signals. [0016] Fig. 2 illustrates an example of the original power spectrum of a music signal of attack nature (music signal with attack) accompanying temporal rapid change such as strongly hitting a drum once. [0017] Note that Fig. 2 also illustrates frequency envelopment on the high-frequency side estimated by the band expanding technique according to PTL 1 from signal components on the low-frequency side of a music signal with attack serving as an input signal. [0018] As illustrated in Fig. 2, the original power spectrum on the high-frequency side of the music signal with attack - 8 - SP313141 is generally flat. [0019] On the other hand, the estimated frequency envelopment on the high-frequency side has a predetermined negative inclination, and accordingly, even when adjusting the power at the origin approximate to the original power spectrum, as the frequency increases, difference with the original power spectrum increases. [0020] Thus, with the band expanding technique according to PTL 1, according to the estimated frequency envelopment on the high-frequency side, the original frequency envelopment on the high-frequency side cannot to be reproduced with high precision. As a result thereof, at the time of generating and outputting sound from a music signal after expanding the frequency band, clearness of sound has been lost as compared to the original sound on listenability. [0021] Also, with the above-mentioned high-frequency characteristic encoding technique such as HE-AAC or the like, though frequency envelopment on the high-frequency side is employed as characteristic information of high-frequency signal components to be encoded, it is demanded that the decoding side reproduces the frequency envelopment on the high-frequency side with high precision. - 9 - SP313141 [0022] The present invention has been made in the light of such situations, and enables music signals to be played with high sound quality by expanding the frequency band. Solution to Problem [0023] An encoding device according to a first aspect of the present invention includes: subband diving means configured to divide an input signal into multiple subbands, and to generate a low-frequency subband signal made up of multiple subbands on the low-frequency side, and a high-frequency subband signal made up of multiple subbands on the highfrequency side; feature amount calculating means configured to calculate feature amount that represents features of the input signal based on at least any one of the low-frequency subband signal and the input signal; smoothing means configured to subject the feature amount smoothing; pseudo high-frequency subband power calculating means configured to calculate pseudo high-frequency subband power that is an estimated value of power of the high-frequency subband signal based on the smoothed feature amount and a predetermined coefficient; selecting means configured to calculate high-frequency subband power that is power of the high-frequency subband signal from the high-frequency subband signal, and to compare the high-frequency subband - 10 - SP313141 power and the pseudo high-frequency subband power to select any of the multiple coefficients; high-frequency encoding means configured to encode coefficient information for obtaining the selected coefficient, and smoothing information relating to the smoothing to generate highfrequency encoded data; low-frequency encoding means configured to encode a low-frequency signal that is a lowfrequency signal of the input signal to generate lowfrequency encoded data; and multiplexing means configured to multiplex the low-frequency encoded data and the highfrequency encoded data to obtain an output code string. [0024] The smoothing means may subject the feature amount to smoothing by performing weighted averaging for the feature amount of a predetermined number of continuous frames of the input signal. [0025] The smoothing information may be information that indicates at least one of the number of the frames used for the weighted averaging, or weight used for the weighted averaging. [0026] The encoding device may include parameter determining means configured to determine at least one of one of the number of the frames used for the weighted averaging, or - 11 - SP313141 weight used for the weighted averaging based on the highfrequency subband signal. [0027] The coefficient may be generated by learning with the feature amount and the high-frequency subband power obtained from a broadband supervisory signal as an explanatory variable and an explained variable. [0028] The broadband supervisory signal may be a signal obtained by encoding a predetermined signal in accordance with an encoding method and encoding algorithm and decoding the encoded predetermined signal; with the coefficient being generated by the learning using the broadband supervisory signal for each of multiple different encoding methods and encoding algorithms. [0029] An encoding method or program according to the first aspect of the present invention includes the steps of: dividing an input signal into multiple subbands, and generating a low-frequency subband signal made up of multiple subbands on the low-frequency side, and a highfrequency subband signal made up of multiple subbands on the high-frequency side; calculating feature amount that represents features of the input signal based on at least any one of the low-frequency subband signal and the input - 12 - SP313141 signal; subjecting the feature amount smoothing; calculating pseudo high-frequency subband power that is an estimated value of power of the high-frequency subband signal based on the smoothed feature amount and a predetermined coefficient; calculating high-frequency subband power that is power of the high-frequency subband signal from the high-frequency subband signal, and comparing the high-frequency subband power and the pseudo high-frequency subband power to select any of the multiple coefficients; encoding coefficient information for obtaining the selected coefficient, and smoothing information relating to the smoothing to generate high-frequency encoded data; encoding a low-frequency signal that is a low-frequency signal of the input signal to generate low-frequency encoded data; and multiplexing the low-frequency encoded data and the high-frequency encoded data to obtain an output code string. [0030] With the first aspect of the present invention, an input signal is divided into multiple subbands, a lowfrequency subband signal made up of multiple subbands on the low-frequency side, and a high-frequency subband signal made up of multiple subbands on the high-frequency side are generated, feature amount that represents features of the input signal is calculated based on at least any one of the low-frequency subband signal and the input signal, the - 13 - SP313141 feature amount is subjected to smoothing, pseudo highfrequency subband power that is an estimated value of power of the high-frequency subband signal is calculated based on the smoothed feature amount and a predetermined coefficient, high-frequency subband power that is power of the highfrequency subband signal is calculated from the highfrequency subband signal, the high-frequency subband power and the pseudo high-frequency subband power are compared to select any of the multiple coefficients, coefficient information for obtaining the selected coefficient, and smoothing information relating to the smoothing to generate high-frequency encoded data are encoded, a low-frequency signal that is a low-frequency signal of the input signal is encoded to generate low-frequency encoded data, and the lowfrequency encoded data and the high-frequency encoded data are multiplexed to obtain an output code string. [0031] A decoding device according to a second aspect of the present invention includes: demultiplexing means configured to demultiplex input encoded data into low-frequency encoded data, coefficient information for obtaining a coefficient, and smoothing information relating to smoothing; lowfrequency decoding means configured to decode the lowfrequency encoded data to generate a low-frequency signal; subband dividing means configured to divide the low- 14 - SP313141 frequency signal into multiple subbands to generate a lowfrequency subband signal for each of the subbands; feature amount calculating means configured to calculate feature amount based on the low-frequency subband signals; smoothing means configured to subject the feature amount to smoothing based on the smoothing information; and generating means configured to generate a high-frequency signal based on the coefficient obtained from the coefficient information, the feature amount subjected to smoothing, and the low-frequency subband signals. [0032] The smoothing means may subject the feature amount to smoothing by performing weighted averaging on the feature amount of a predetermined number of continuous frames of the low-frequency signal. [0033] The smoothing information may be information indicating at least one of the number of frames used for the weighted averaging, or weight used for the weighted averaging. [0034] The generating means may include decoded high-frequency subband power calculating means configured to calculate decoded high-frequency subband power that is an estimated value of subband power making up the high-frequency signal based on the smoothed feature amount and the coefficient, - 15 - SP313141 and high-frequency signal generating means configured to generate the high-frequency signal based on the decoded high-frequency subband power and the low-frequency subband signal. [0035] The coefficient may be generated by learning with the feature amount obtained from a broadband supervisory signal, and power of the same subband as a subband making up the high-frequency signal of the broadband supervisory signal, as an explanatory variable and an explained variable. [0036] The broadband supervisory signal may be a signal obtained by encoding a predetermined signal in accordance with a predetermined encoding method and encoding algorithm and decoding the encoded predetermined signal; with the coefficient being generated by the learning using the broadband supervisory signal for each of multiple different encoding methods and encoding algorithms. [0037] A decoding method or program according to the second aspect of the present invention includes the steps of: demultiplexing input encoded data into low-frequency encoded data, coefficient information for obtaining a coefficient, and smoothing information relating to smoothing; decoding the low-frequency encoded data to generate a low-frequency - 16 - SP313141 signal; dividing the low-frequency signal into multiple subbands to generate a low-frequency subband signal for each of the subbands; calculating feature amount based on the low-frequency subband signals; subjecting the feature amount to smoothing based on the smoothing information; and generating a high-frequency signal based on the coefficient obtained from the coefficient information, the feature amount subjected to smoothing, and the low-frequency subband signals. [0038] With the second aspect of the present invention, input encoded data is demultiplexed into low-frequency encoded data, coefficient information for obtaining a coefficient, and smoothing information relating to smoothing, the lowfrequency encoded data is decoded to generate a lowfrequency signal, the low-frequency signal is divided into multiple subbands to generate a low-frequency subband signal for each of the subbands, feature amount is calculated based on the low-frequency subband signals, the feature amount is subjected to smoothing based on the smoothing information, and a high-frequency signal is generated based on the coefficient obtained from the coefficient information, the feature amount subjected to smoothing, and the low-frequency subband signals. Advantageous Effects of Invention - 17 - SP313141 [0039] According to the first aspect and second aspect of the present invention, music signals may be played with higher sound quality by expanding the frequency band. Brief Description of Drawings [0040] [Fig. 1] Fig. 1 is a diagram illustrating an example of low-frequency power spectrum after decoding serving as an input signal, and estimated high-frequency frequency envelopment. [Fig. 2] Fig. 2 is a diagram illustrating an example of the original power spectrum of a music signal with attack, accompanying temporal rapid change. [Fig. 3] Fig. 3 is a block diagram illustrating a functional configuration example of a frequency band expanding device according to a first embodiment of the present invention. [Fig. 4] Fig. 4 is a flowchart for describing frequency band expanding processing by the frequency band expanding device in Fig. 3. [Fig. 5] Fig. 5 is a diagram illustrating the power spectrum of a signal to be input to the frequency band expanding device in Fig. 3, and locations of band pass filters on the frequency axis. [Fig. 6] Fig. 6 is a diagram illustrating an example of - 18 - SP313141 frequency characteristic within a vocal section, and an estimated high-frequency power spectrum. [Fig. 7] Fig. 7 is a diagram illustrating an example of the power spectrum of a signal to be input to the frequency band expanding device in Fig. 3. [Fig. 8] Fig. 8 is a diagram illustrating an example of the power spectrum after liftering of the input signal in Fig. 7. [Fig. 9] Fig. 9 is a block diagram illustrating a functional configuration example of a coefficient learning device for performing learning of a coefficient to be used at a high-frequency signal generating circuit of the frequency band expanding device in Fig. 3. [Fig. 10] Fig. 10 is a flowchart for describing an example of coefficient learning processing by the coefficient learning device in Fig. 9. [Fig. 11] Fig. 11 is a block diagram illustrating a functional configuration example of an encoding device according to a second embodiment of the present invention. [Fig. 12] Fig. 12 is a flowchart for describing an example of encoding processing by the encoding device in Fig. 11. [Fig. 13] Fig. 13 is a block diagram illustrating a functional configuration example of a decoding device according to the second embodiment of the present invention. - 19 - SP313141 [Fig. 14] Fig. 14 is a flowchart for describing an example of decoding processing by the decoding device in Fig. 13. [Fig. 15] Fig. 15 is a block diagram illustrating a functional configuration example of a coefficient learning device for performing learning of a representative vector to be used at a high-frequency encoding circuit of the encoding device in Fig. 11, and a decoded high-frequency subband power estimating coefficient to be used at the highfrequency decoding circuit of the decoding device in Fig. 13. [Fig. 16] Fig. 16 is a flowchart for describing an example of coefficient learning processing by the coefficient learning device in Fig. 15. [Fig. 17] Fig. 17 is a diagram illustrating an example of a code string that the encoding device in Fig. 11 outputs. [Fig. 18] Fig. 18 is a block diagram illustrating a functional configuration example of an encoding device. [Fig. 19] Fig. 19 is a flowchart for describing encoding processing. [Fig. 20] Fig. 20 is a block diagram illustrating a functional configuration example of a decoding device. [Fig. 21] Fig. 21 is a flowchart for describing decoding processing. [Fig. 22] Fig. 22 is a flowchart for describing encoding processing. - 20 - SP313141 [Tig. 23] Fig. 23 is a flowchart for describing decoding processing. [Fig. 24] Fig. 24 is a flowchart for describing encoding processing. [Fig. 25] Fig. 25 is a flowchart for describing encoding processing. [Fig. 26] Fig. 26 is a flowchart for describing encoding processing. [Fig. 27] Fig. 27 is a flowchart for describing encoding processing. [Fig. 28] Fig. 28 is a diagram illustrating a configuration example of a coefficient learning processing. [Fig. 29] Fig. 29 is a flowchart for describing coefficient learning processing. [Fig. 30] Fig. 30 is a block diagram illustrating a functional configuration example of an encoding device. [Fig. 31] Fig. 31 is a flowchart for describing encoding processing. [Fig. 32] Fig. 32 is a block diagram illustrating a functional configuration example of a decoding device. [Fig. 33] Fig. 33 is a flowchart for describing decoding processing. [Fig. 34] Fig. 34 is a block diagram illustrating a configuration example of hardware of a computer which executes processing to which the present invention is - 21 - SP313141 applied using a program. Description of Embodiments [0041] Hereinafter, embodiments of the present invention will be described with reference to the drawings. Note that description will be made in accordance with the following order. 1. First Embodiment (Case of Having Applied Present Invention to Frequency Band Expanding Device) 2. Second Embodiment (Case of Having Applied Present Invention to Encoding Device and Decoding Device) 3. Third Embodiment (Case of Including Coefficient Index in High-frequency Encoded Data) 4. Fourth Embodiment (Case of Including Coefficient Index and Pseudo High-frequency Subband Power Difference in Highfrequency Encoded Data) 5. Fifth Embodiment (Case of Selecting Coefficient Index Using Evaluated Value) 6. Sixth Embodiment (Case of Sharing Part of Coefficients) 7. Seventh Embodiment (Case of Subjecting Feature Amount to Smoothing) [0042] <1. First Embodiment> With the first embodiment, low-frequency signal components after decoding to be obtained by decoding encoded - 22 - SP313141 data using the high-frequency deletion encoding technique is subjected to processing to expand the frequency band (hereinafter, referred to as frequency band expanding processing). [0043] [Functional Configuration Example of Frequency Band Expanding Device] Fig. 3 illustrates a functional configuration example of a frequency band expanding device to which the present invention has been applied. [0044] A frequency band expanding device 10 takes a lowfrequency signal component after decoding as an input signal, and subjects the input signal thereof to frequency band expanding processing, and outputs a signal after the frequency band expanding processing obtained as a result thereof as an output signal. [0045] The frequency band expanding device 10 is configured of a low-pass filter 11, a delay circuit 12, band pass filters 13, a feature amount calculating circuit 14, a highfrequency subband power estimating circuit 15, a highfrequency signal generating circuit 16, a high-pass filter 17, and a signal adder 18. [0046] - 23 - SP313141 The low-pass filter 11 performs filtering of an input signal with a predetermined cutoff frequency, and supplies a low-frequency signal component which is a signal component of low-frequency to the delay circuit 12 as a signal after filtering. [0047] In order to synchronize the time of adding a lowfrequency signal component from the low-pass filter 11 and a later-described high-frequency signal component, the delay circuit 12 delays the low-frequency signal component by fixed delay time to supply to the signal adder 18. [0048] The band pass filters 13 are configured of band pass filters 13-1 to 13-N each having a different passband. The band pass filter 13-i (1 < i < N) passes a predetermined passband signal of input signals, and supplies this to the feature amount calculating circuit 14 and high-frequency signal generating circuit 16 as one of the multiple subband signals. [0049] The feature amount calculating circuit 14 calculates a single or multiple feature amounts using at least any one of the multiple subband signals from the band pass filters 13 or the input signal to supply to the high-frequency subband power estimating circuit 15. Here, the feature amount is - 24 - SP313141 information representing features as a signal of the input signal. [0050] The high-frequency subband power estimating circuit 15 calculates a high-frequency subband power estimated value which is power of a high-frequency subband signal for each high-frequency subband based on a single or multiple feature amounts from the feature amount calculating circuit 14, and supplies these to the high-frequency signal generating circuit 16. [0051] The high-frequency signal generating circuit 16 generates a high-frequency signal component which is a highfrequency signal component based on the multiple subband signals from the band pass filters 13, and the multiple high-frequency subband power estimated values from the highfrequency subband power estimating circuit 15 to supply to the high-pass filter 17. [0052] The high-pass filter 17 subjects the high-frequency signal component from the high-frequency signal generating circuit 16 to filtering with a cutoff frequency corresponding to a cutoff frequency at the low-pass filter 11 to supply to the signal adder 18. [0053] - 25 - SP313141 The signal adder 18 adds the low-frequency signal component from the delay circuit 12 and the high-frequency signal component from the high-pass filter 17, and outputs this as an output signal. [0054] Note that, with the configuration in Fig. 3, in order to obtain a subband signal, the band pass filters 13 are applied, but not restricted to this, and a band dividing filter as described in PTL 1 may be applied, for example. [0055] Also, similarly, with the configuration in Fig. 3, in order to synthesize subband signals, the signal adder 18 is applied, but not restricted to this, a band synthetic filter as described in PTL 1 may be applied. [0056] [Frequency Band Expanding Processing of Frequency Band Expanding Device] Next, the frequency band expanding processing by the frequency band expanding device in Fig. 3 will be described with reference to the flowchart in Fig. 4. [0057] In step SI, the low-pass filter 11 subjects the input signal to filtering with a predetermined cutoff frequency, and supplies the low-frequency signal component serving as a signal after filtering to the delay circuit 12. - 26 - SP313141 [0058] The low-pass filter 11 may set an optional frequency as a cutoff frequency, but with the present embodiment, a predetermined band is taken as a later-described expanding start band, and a cutoff frequency is set corresponding to the lower end frequency of the expanding start band thereof. Accordingly, the low-pass filter 11 supplies a low-frequency signal component which is a lower frequency signal component than the expanding start band to the delay circuit 12 as a signal after filtering. [0059] Also, the low-pass filter 11 may also set the optimal frequency as a cutoff frequency according to the highfrequency deletion encoding technique of the input signal, and encoding parameters such as the bit rate and so forth. As the encoding parameters, side information employed by the band expanding technique according to PTL 1 may be used, for example. [0060] In step S2, the delay circuit 12 delays the lowfrequency signal component from the low-pass filter 11 by fixed delay time and supplies this to the signal adder 18. [0061] In step S3, the band pass filters 13 (band pass filters 13-1 to 13-N) divided the input signal to multiple subband - 27 - SP313141 signals, and supplies each of the multiple subband signals after division to the feature amount calculating circuit 14 and high-frequency signal generating circuit 16. Note that, with regard to input signal dividing processing by the band pass filters 13, details thereof will be described later. [0062] In step S4, the feature amount calculating circuit 14 calculates a single or multiple feature amounts using at least one of the multiple subband signals from the band pass filters 13, and the input signal to supply to the highfrequency subband power estimating circuit 15. Note that, with regard to feature amount calculating processing by the feature amount calculating circuit 14, details thereof will be described later. [0063] In step S5, the high-frequency subband power estimating circuit 15 calculates multiple high-frequency subband power estimated values based on a single or multiple feature amounts from the feature amount calculating circuit 14, and supplies these to the high-frequency signal generating circuit 16. Note that, with regard to processing to calculate high-frequency subband power estimated values by the high-frequency subband power estimating circuit 15, details thereof will be described later. [0064] - 28 - SP313141 In step S6, the high-frequency signal generating circuit 16 generates a high-frequency signal component based on the multiple subband signals from the band pass filters 13, and the multiple high-frequency subband power estimated values from the high-frequency subband power estimating circuit 15, and supplies this to the high-pass filter 17. The high-frequency signal component mentioned here is a higher frequency signal component than the expanding start band. Note that, with regard to high-frequency signal component generation processing by the high-frequency signal generating circuit 16, details thereof will be described later. [0065] In step S7, the high-pass filter 17 subjects the highfrequency signal component from the high-frequency signal generating circuit 16 to filtering, thereby removing noise such as aliasing components to a low frequency included in a high-frequency signal component, and supplying the highfrequency signal component thereof to the signal adder 18. [0066] In step S8, the signal adder 18 adds the low-frequency signal component from the delay circuit 12 and the highfrequency signal component from the high-pass filter 17 to supply this as an output signal. [0067] - 29 - SP313141 According to the above-mentioned processing, the frequency band may be expanded as to a low-frequency signal component after decoding. [0068] Next, details of each process in steps S3 to S6 in the flowchart in Fig. 4 will be described. [0069] [Details of Processing by Band Pass Filter] First, details of processing by the band pass filters 13 in step S3 in the flowchart in Fig. 4 will be described. [0070] Note that, for convenience of description, hereinafter, the number N of the band pass filters 13 will be taken as N = 4. [0071] For example, one of the 16 subbands obtained by equally dividing a Nyquist frequency of the input signal into 16 is taken as the expanding start band, four subbands of the 16 subbands of which the frequencies are lower than the expanding start band are taken as the passbands of the band pass filters 13-1 to 13-4, respectively. [0072] Fig. 5 illustrates locations on the frequency axis of the passbands of the band pass filters 13-1 to 13-4, respectively. - 30 - SP313141 [0073] As illustrated in Fig. 5, if we say that of frequencybands (subbands) which are lower than the expanding start band, the index of the first subband from the high-frequency is sb, the index of the second subband is sb-1, and the index of the first subband is sb - (I - 1), the band pass filters 13-1 to 13-4, assign of the subbands having a lower frequency than the expanding start band, the subbands of which the indexes are sb to sb-3, as passbands, respectively. [0074] Note that, with the present embodiment, the passbands of the band pass filters 13-1 to 13-4 are predetermined four subbands of 16 subbands obtained by equally dividing the Nyquist frequency of the input signal into 16, respectively, but not restricted to this, and may be predetermined four subbands of 256 subbands obtained by equally dividing the Nyquist frequency of the input signal into 256, respectively. Also, the bandwidths of the band pass filters 13-1 to 13-4 may differ. [0075] [Details of Processing by Feature Amount Calculating Circuit] Next, description will be made regarding details of processing by the feature amount calculating circuit 14 in step S4 in the flowchart in Fig. 4. m - 31 - SP313141 [0076] The feature amount calculating circuit 14 calculates a single or multiple feature amounts to be used for the highfrequency subband power estimating circuit 15 calculating a high-frequency subband power estimated value, using at least any one of the multiple subband signals from the band pass filters 13 and the input signal. [0077] More specifically, the feature amount calculating circuit 14 calculates, from four subband signals from the band pass filters 13, subband signal power (subband power (hereinafter, also referred to as low-frequency subband power)) for each subband as a feature amount to supply to the high-frequency subband power estimating circuit 15. [0078] Specifically, the feature amount calculating circuit 14 obtains low-frequency subband power power(ib, J) in a certain predetermined time frame J from four subband signals x(ib, n) supplied from the band pass filters 13, using the following Expression (1). Here, ib represents an index of a subband, and n represents an index of discrete time. Now, let us say that the number of samples in one frame is FSIZE, and power is represented by decibel. [0079] [Mathematical Expression 1] - 32 - SP313141 |7(J+1)FSIZE-1 \ "] power (ib, J) =10log10^ Z x( ib, n)2 /FSIZE [ \\ n=J*FSIZE / J (sb-3 standard deviation of the subband powers is powerstd/ a mean value of the dip is dipaVef and standard deviation of the dip is dipstd- [0137] The high-frequency subband power estimating circuit 15 converts the value dip(J) of the dip using these values such as the following Expression (12) to obtain a dip dips(J) after conversation. [0138] - 49 - SP313141 [Mathematical Expression 12] A- f i\ dip(J)-dipave d i p s ( J ) " .. powerstd+powerave a i Pstd • • • ( 1 2) [0139] According to conversion indicated in Expression (12) being performed, the high-frequency subband power estimating circuit 15 may convert the dip value dip(J) into a variable (dip) dips(J) statistically equal to the average and dispersion of the low-frequency subband powers, and accordingly, an average of a value that the dip has may be set generally equal to a range of a value that the subband powers have. [0140] With the frequency expanding band, an estimated value powerest (ib, J) of a subband power of which the index is ib is represented by the following Expression (13) using linear coupling between the four low-frequency subband powers power(id, J) from the feature amount calculating circuit 14, and the dip dips(J) indicated in Expression (12), for example. [0141] [Mathematical Expression 13] - 50 - SP313141 powerest(ib,J) = ( I {Cib(kb) power(kb,J)}|+Dibdips(J)+Eib \ kb=sb-3 / (J*FSIZE< n < (J+1) FSIZE-1, sb+1 < i b With the second embodiment, the input signal is subjected to encoding processing and decoding processing in the high-frequency characteristic encoding technique by an encoding device and a decoding device. [0175] [Functional Configuration Example of Encoding Device] Fig. 11 illustrates a functional configuration example of an encoding device to which the present invention has been applied. [0176] An encoding device 30 is configured of a low-pass filter 31/ a low-frequency encoding circuit 32, a subband dividing circuit 33, a feature amount calculating circuit 34, a pseudo high-frequency subband power calculating circuit 35, a pseudo high-frequency subband power difference calculating circuit 36, a high-frequency encoding circuit 37, a multiplexing circuit 38, and a low-frequency decoding circuit 39. [0177] # - 63 - SP313141 The low-pass filter 31 subjects an input signal to filtering with a predetermined cutoff frequency, and supplies a lower frequency signal (hereinafter, referred to as low-frequency signal) than the cutoff frequency to the low-frequency encoding circuit 32, subband dividing circuit 33 and feature amount calculating circuit 34 as a signal after filtering. [0178] The low-frequency encoding circuit 32 encodes the lowfrequency signal from the low-pass filter 31, and supplies low-frequency encoded data obtained as a result thereof to the multiplexing circuit 38 and low-frequency decoding circuit 39. [0179] The subband dividing circuit 33 equally divides the input signal and the low-frequency signal from the low-pass filter 31 into multiple subband signals having predetermined bandwidth to supply to the feature amount calculating circuit 34 or pseudo high-frequency subband power difference calculating circuit 36. More specifically, the subband dividing circuit 33 supplies multiple subband signals (hereinafter, referred to as low-frequency subband signals) obtained with the low-frequency signals as input to the feature amount calculating circuit 34. Also, the subband dividing circuit 33 supplies, of multiple subband signals - 64 - SP313141 obtained with the input signal as input, higher frequency subband signals (hereinafter, refereed to as high-frequency subband signals) than a cutoff frequency set at the low-pass filter 31 to the pseudo high-frequency subband power difference calculating circuit 36. [0180] The feature amount calculating circuit 34 calculates one or multiple feature amounts using at least any one of the multiple subband signals of the low-frequency subband signals from the subband dividing circuit 33, and the lowfrequency signal from the low-pass filter 31 to supply to the pseudo high-frequency subband power calculating circuit 35. [0181] The pseudo high-frequency subband power calculating circuit 35 generates a pseudo high-frequency subband power based on the one or multiple feature amounts from the feature amount calculating circuit 34 to supply to the pseudo high-frequency subband power difference calculating circuit 36. [0182] The pseudo high-frequency subband power difference calculating circuit 36 calculates later-described pseudo high-frequency subband power difference based on the highfrequency subband signal from the subband dividing circuit - 65 - SP313141 33, and the pseudo high-frequency subband power from the pseudo high-frequency subband power calculating circuit 35 to supply to the high-frequency encoding circuit 37. [0183] The high-frequency encoding circuit 37 encodes the pseudo high-frequency subband power difference from the pseudo high-frequency subband power difference calculating circuit 3 6 to supply high-frequency encoded data obtained as a result thereof to the multiplexing circuit 38. [0184] The multiplexing circuit 38 multiplexes the lowfrequency encoded data from the low-frequency encoding circuit 32, and the high-frequency encoded data from the high-frequency encoding circuit 37 to output as an output code string. [0185] The low-frequency decoding circuit 39 decodes the lowfrequency encoded data from the low-frequency encoding circuit 32 as appropriate to supply decoded data obtained as a result thereof to the subband dividing circuit 33 and feature amount calculating circuit 34. CLAIMS [Claim 1] An encoding device comprising: subband diving means configured to divide an input signal into a plurality of subbands, and to generate a lowfrequency subband signal made up of a plurality of subbands on the low-frequency side, and a high-frequency subband signal made up of a plurality of subbands on the highfrequency side; feature amount calculating means configured to calculate feature amount that represents features of the input signal based on at least any one of the low-frequency subband signal and the input signal; smoothing means configured to subject the feature amount smoothing; pseudo high-frequency subband power calculating means configured to calculate pseudo high-frequency subband power that is an estimated value of power of the high-frequency subband signal based on the smoothed feature amount and a predetermined coefficient; selecting means configured to calculate high-frequency subband power that is power of the high-frequency subband signal from the high-frequency subband signal, and to compare the high-frequency subband power and the pseudo high-frequency subband power to select any of a plurality of the coefficients; high-frequency encoding means configured to encode coefficient information for obtaining the selected coefficient, and smoothing information relating to the smoothing to generate high-frequency encoded data; low-frequency encoding means configured to encode a low-frequency signal that is a low-frequency signal of the input signal to generate low-frequency encoded data; and multiplexing means configured to multiplex the lowfrequency encoded data and the high-frequency encoded data to obtain an output code string. [Claim 2] The encoding device according to Claim 1, wherein the smoothing means subjects the feature amount to smoothing by performing weighted averaging for the feature amount of a predetermined number of continuous frames of the input signal. [Claim 3] The encoding device according to Claim 2, wherein the smoothing information is information that indicates at least one of the number of the frames used for the weighted averaging, or weight used for the weighted averaging. [Claim 4] The encoding device according to Claim 3, further comprising: parameter determining means configured to determine at least one of one of the number of the frames used for the weighted averaging, or weight used for the weighted averaging based on the high-frequency subband signal. [Claim 5] The encoding device according to Claim 1, wherein the coefficient is generated by learning with the feature amount and the high-frequency subband power obtained from a broadband supervisory signal as an explanatory variable and an explained variable. [Claim 6] The encoding device according to Claim 5, wherein the broadband supervisory signal is a signal obtained by encoding a predetermined signal in accordance with an encoding method and encoding algorithm and decoding the encoded predetermined signal; and wherein the coefficient is generated by the learning using the broadband supervisory signal for each of a plurality of different encoding methods and encoding algorithms. [Claim 7] An encoding method comprising the steps of: dividing an input signal into a plurality of subbands, and generating a low-frequency subband signal made up of a plurality of subbands on the low-frequency side, and a highL frequency subband signal made up of a plurality of subbands on the high-frequency side; calculating feature amount that represents features of the input signal based on at least any one of the lowfrequency subband signal and the input signal; subjecting the feature amount smoothing; calculating pseudo high-frequency subband power that is an estimated value of power of the high-frequency subband signal based on the smoothed feature amount and a predetermined coefficient; calculating high-frequency subband power that is power of the high-frequency subband signal from the high-frequency subband signal, and comparing the high-frequency subband power and the pseudo high-frequency subband power to select any of a plurality of the coefficients; encoding coefficient information for obtaining the selected coefficient, and smoothing information relating to the smoothing to generate high-frequency encoded data; encoding a low-frequency signal that is a low-frequency signal of the input signal to generate low-frequency encoded data; and multiplexing the low-frequency encoded data and the high-frequency encoded data to obtain an output code string. [Claim 8] A program causing a computer to execute processing comprising the steps of: dividing an input signal into a plurality of subbands, and generating a low-frequency subband signal made up of a plurality of subbands on the low-frequency side, and a highfrequency subband signal made up of a plurality of subbands on the high-frequency side; calculating feature amount that represents features of the input signal based on at least any one of the lowfrequency subband signal and the input signal; subjecting the feature amount smoothing; calculating pseudo high-frequency subband power that is an estimated value of power of the high-frequency subband signal based on the smoothed feature amount and a predetermined coefficient; calculating high-frequency subband power that is power of the high-frequency subband signal from the high-frequency subband signal, and comparing the high-frequency subband power and the pseudo high-frequency subband power to select any of a plurality of the coefficients; encoding coefficient information for obtaining the selected coefficient, and smoothing information relating to the smoothing to generate high-frequency encoded data; encoding a low-frequency signal that is a low-frequency signal of the input signal to generate low-frequency encoded data; and multiplexing the low-frequency encoded data and the high-frequency encoded data to obtain an output code string. [Claim 9] A decoding device comprising: demultiplexing means configured to demultiplex input encoded data into low-frequency encoded data, coefficient information for obtaining a coefficient, and smoothing information relating to smoothing; low-frequency decoding means configured to decode the low-frequency encoded data to generate a low-frequency signal; subband dividing means configured to divide the lowfrequency signal into a plurality of subbands to generate a low-frequency subband signal for each of the subbands; feature amount calculating means configured to calculate feature amount based on the low-frequency subband signals; smoothing means configured to subject the feature amount to smoothing based on the smoothing information; and generating means configured to generate a highfrequency signal based on the coefficient obtained from the coefficient information, the feature amount subjected to smoothing, and the low-frequency subband signals. [Claim 10] The decoding device according to Claim 9, wherein the smoothing means subjects the feature amount to smoothing by performing weighted averaging on the feature amount of a predetermined number of continuous frames of the lowfrequency signal. [Claim 11] The decoding device according to Claim 10, wherein the smoothing information is information indicating at least one of the number of frames used for the weighted averaging, or weight used for the weighted averaging. [Claim 12] The decoding device according to Claim 9, wherein the generating means include decoded high-frequency subband power calculating means configured to calculate decoded high-frequency subband power that is an estimated value of subband power making up the high-frequency signal based on the smoothed feature amount and the coefficient, and high-frequency signal generating means configured to generate the high-frequency signal based on the decoded high-frequency subband power and the low-frequency subband signal. [Claim 13] The decoding device according to Claim 9, wherein the coefficient is generated by learning with the feature amount obtained from a broadband supervisory signal, and power of the same subband as a subband making up the high-frequency signal of the broadband supervisory signal, as an explanatory variable and an explained variable. [Claim 14] The decoding device according to Claim 13, wherein the broadband supervisory signal is to be a signal obtained by encoding a predetermined signal in accordance with a predetermined encoding method and encoding algorithm and decoding the encoded predetermined signal; and wherein the coefficient is generated by the learning using the broadband supervisory signal for each of a plurality of different encoding methods and encoding algorithms. [Claim 15] A decoding method comprising the steps of: demultiplexing input encoded data into low-frequency encoded data, coefficient information for obtaining a coefficient, and smoothing information relating to smoothing; decoding the low-frequency encoded data to generate a low-frequency signal; dividing the low-frequency signal into a plurality of subbands to generate a low-frequency subband signal for each of the subbands; calculating feature amount based on the low-frequency subband signals; subjecting the feature amount to smoothing based on the smoothing information; and generating a high-frequency signal based on the coefficient obtained from the coefficient information, the feature amount subjected to smoothing, and the low-frequency subband signals. [Claim 16] A program causing a computer to execute processing comprising the steps of: demultiplexing input encoded data into low-frequency encoded data, coefficient information for obtaining a coefficient, and smoothing information relating to smoothing; decoding the low-frequency encoded data to generate a low-frequency signal; dividing the low-frequency signal into a plurality of subbands to generate a low-frequency subband signal for each of the subbands; calculating feature amount based on the low-frequency subband signals; subjecting the feature amount to smoothing based on the smoothing information; and generating a high-frequency signal based on the coefficient obtained from the coefficient information, the SP313141 feature amount subjected t o smoothing, and the low-frequency subband signals .