CLAIMS

1. Interpolator, for the interpolation by a ratio n of the sampling frequency of a signal called the input signal, the interpolator being characterized in that it comprises successively:

- a first interpolation stage (101) comprising an over-sampler configured to over-sample the input signal by a ratio of ¾, n x being a sub-multiple of n, and a filter to filter the over- sampled, and

- a second interpolation stage (102) comprising a linear interpolator configured to interpolate by a ratio n 2 the signal coming from the first interpolation stage, n 2 being a sub-multiple of n, and

- a third interpolation stage (103) comprising a blocking interpolator configured to interpolate by a ratio n 3 the signal coming from the second interpolation stage, n s being a sub-multiple of n ,

with n = nn 2 n 3 .

2. Interpolator according to claim 1, in which the filter used by the first interpolation stage (101) is a finite impulse response filter or an infinite impulse response filter.

3. Interpolator according to one of the preceding claims, in which the linear interpolator of the second interpolation stage (102) is configured to carry out a linear interpolation, said linear interpolation corresponding to the oversampling of the signal coming from the first stage of interpolation (101) of a ratio n 2 by inserting bad samples then filtering said over-sampled signal by a filter having a frequency response of ( sm(n. fe 2 )/(n. fe 2 )) 2 , with fe 2 the frequency

sampling of the signal at the output of the second interpolation stage (102), said frequency response at ( sm(.fe 2 )/( n.fe 2 )) 2 having (n 2 - 1) periodic zeros around each of which there is a frequency band whose attenuation is greater than a given minimum level, the interpolator being configured so that each of said frequency bands has a width greater than a useful band of the input signal.

4. Interpolator according to one of the preceding claims, in which the blocking interpolator of the third interpolation stage (103) is configured to carry out an interpolation by blocking, the said interpolation by blocking corresponding to the over-sampling of the signal coming from the second stage. interpolation (102) of a ratio n 3 by inserting bad samples then filtering said over-sampled signal by a filter having a frequency response in sin(n.fe 3 )/(n.fe 3 ), with fe 3 the sampling frequency of the signal at the output of the third interpolation stage (103), said frequency response in sin(n.fe 3 /(n.fe 3 having (n 3 - 1) periodic zeros around each of which there is a frequency band whose attenuation is greater than a given minimum level, the interpolator being configured so that each of said frequency bands has a width greater than a useful band of the signal d 'Entrance.

5. Method of interpolation by a ratio n of the sampling frequency of a signal called the input signal, the method being characterized in that it successively comprises:

- a first interpolation step (601) comprising the over-sampling of said input signal by a ratio n x, being a sub-multiple of n, and the filtering of the over-sampled signal, and

a second interpolation step (602) comprising the linear interpolation of the signal resulting from the first interpolation step by a ratio n 2 , n 2 being a sub-multiple of n, and

a third step (603) of interpolation by blocking interpolator of the signal resulting from the second interpolation step by a ratio n 3 , n 3 being a sub-multiple
with n = · h 2 - n 3 .

6. Method for dimensioning an interpolator such as that of one of claims 1 to 4, the method being characterized in that the dimensioning comprises:

- a first step (701) of determining the interpolation ratio of the first stage of the interpolator from a useful bandwidth of the input signal and a minimum attenuation of replicas of the signal entering the second stage of interpolation (102) due to the interpolation of a ratio n 2 ,

- a step (703) of determining the interpolation ratio n 2 of the second stage of the interpolator from a useful bandwidth of the signal to be transmitted and a minimum attenuation of replicas of the signal entering the third stage of interpolation (103) due to the interpolation of a ratio n 3 , and

- a step (702) of determining the interpolation ratio of the last stage of the interpolator from the interpolation ratio(s) of the stages preceding it.

The invention relates to the field of digital signal processing, and relates more particularly to the production of a high-rank interpolator allowing high-speed real-time processing.

The interpolation of a digital signal is a common operation in a digital signal processing chain. It consists of bringing the sampling frequency of a signal from a first frequency to a second, higher frequency, by calculating intermediate samples between each sample of the original signal. This is the case, for example, when a signal must be brought to a precise sampling frequency for processing purposes, or when two or more signals sampled at very different frequencies are processed together, which requires the prior harmonization of their sampling frequency. This second case occurs for example when a signal having a very high frequency band, and therefore sampled at a very high frequency, must be modulated by a modulating signal of narrow band and whose sampling frequency is optimized for this band. The two signals then have a high sampling frequency ratio. To carry out the modulation, that is to say the product of the two signals, it is necessary to bring the two signals beforehand to a common sampling frequency.

The interpolation of a signal is generally done in two steps:

- the signal is first over-sampled, that is to say that (n - 1) zeros are inserted between each original sample, n being the ratio of the sampling frequencies, to obtain a signal whose spectrum has n identical periods in the output spectral domain, and

- the over-sampled signal is filtered so as to attenuate the (n - 1) spurious periods of the spectrum to retain only the useful period,

but there are many other forms of interpolators.

Subsequently, when it comes to an interpolation, we will designate by "ratio" the value corresponding to the ratio of the output sampling frequency to the input sampling frequency of an interpolator or an interpolation stage. The term ratio is equivalent to the term "factor", "ratio" or "order", which can be found in the literature. In the context of the invention, the sampling frequency ratio is integer, factorizable and high (typically, of the order of one or several tens).

Effective interpolation has the following advantages:

- it maximizes the use of the useful band of the original signal. Although the useful band of the input signal is low compared to that of the output signal, the sampling frequency of the input signal must be as low as possible while respecting the Shannon criterion, in order to limit as much as possible the resources necessary for the development of the signal, whether:

calculation resources in the case of real-time calculation, these resources being less used the lower the sampling frequency, or

• memory resources in the event of a tabulated signal over a long period, the amount of storage required being proportional to the sampling frequency.

- it controls the spectral purity of the interpolated signal. One goal of interpolation is to attenuate, according to a specified template, the periodicities of the spectrum due to over-sampling, while modifying the spectrum of the useful part of the interpolated signal as little as possible,

- it maximizes the frequency of the interpolation output signal. This involves using a parallelizable calculation architecture so as to obtain a high output sampling frequency that can even be higher than the maximum clock frequency of the digital component used to implement the calculations,

- it minimizes the necessary computing resources. This involves minimizing the computational cost, in order to minimize the consumption of the digital component used for the implementation, and to make it possible to implement as many functions as possible in the digital component used.

The issue of interpolation is extensively covered in signal processing publications. Many calculation techniques exist. We know for example on this subject the article by Chao Cai et al. “A digital sampling rate synchronization scheme for fully digital relay protection”, Transmission and distribution conference and exhibition, 2010 IEEE PES, or US patent 5,732,107A

Depending on the technique used, interpolation can prove to be computationally expensive, and therefore difficult to implement on a software platform with limited computing power, such as a DSP (English acronym for Digital Signal Processor, or digital signal), an FPGA (English acronym for Field Programmable Gate Array, or programmable gate array), an ASIC (English acronym for Application-Specific Integrated Circuit, or integrated circuit specific to an application), or any hardware target making it possible to execute the necessary processing, such as a processor, in particular when the processing must be executed in real time and the interpolation ratio is high. It can also turn out to be inexpensive to implement but inefficient spectrally.

An objective that the invention seeks to solve consists in realizing an interpolation function in a digital signal processing chain which is both inexpensive to implement, which allows it to be carried by a real-time platform at a high output sampling frequency or even higher than the operating frequency of the device, while respecting spectral template constraints.

For this, the invention relates to a signal interpolator produced in the form of a structured cascade of interpolators of different types. Indeed, if cascaded interpolation structures are known from the state of the art in order to interpolate a signal of a high rank, these structures consist of interpolators of the same type, generally FIRs (acronym English for Finite Impulse Response or finite response filter), which can pose problems in particular for the last stages where the length of the filters depends on the sampling frequency and the desired spectral purity.

The invention starts from the principle that the cost of implementing the interpolation stages increases with the sampling frequency, and proposes using interpolators whose complexity decreases over the course of the interpolation. Advantageously, the interpolation ratios of the various stages take account of the spectral properties of the stage which follows them in order to limit their complexity and to respect a constraining spectral template.

To this end, the invention describes an interpolator, for the interpolation by a ratio n of the sampling frequency of a signal called the input signal. The interpolator according to the invention successively comprises:

- a first interpolation stage comprising an oversampler configured to oversample the input signal by a ratio of ¾, n x being a sub-multiple of n, and a filter to filter the oversampled signal, and

- a second interpolation stage comprising a linear interpolator configured to interpolate by a ratio n 2 the signal coming from the first interpolation stage, n 2 being a sub-multiple of n, and

- a third interpolation stage comprising a blocking interpolator configured to interpolate by a ratio n 3 the signal coming from the second interpolation stage, n 3 being a sub-multiple of n ,

with n = n 2 n 3 .

Advantageously, the filter used by the first interpolation stage is an Fl R filter or an 11 R filter (English acronym for Infinite Impulse Response, or infinite impulse response).

In the interpolator according to the invention, the linear interpolator of the second interpolation stage is configured to carry out a linear interpolation equivalent to the oversampling of the signal coming from the first interpolation stage by a ratio n 2 by inserting samples then filtering said over-sampled signal by a filter having a frequency response of (sin(7r. fe 2 )/ (p. /e 2 )) 2 , with fe 2 the sampling frequency of the signal at the output of the second interpolation stage, said frequency response at (sin(7r. fe 2 )/ (p. /e 2 )) 2 having (n 2- 1) periodic zeros around each of which there is a frequency band whose attenuation is greater than a given minimum level. The interpolator is configured so that each of these frequency bands has a width greater than the useful band of the input signal.

Indeed, linearly interpolating a signal amounts to over-sampling it by inserting harmful samples, then to filtering it by a filter whose frequency response is in (sin(7r.fe 2 )/(.fe 2 )) 2 . The over-sampling carried out by the second interpolation stage naturally creates n 2 periodic replicas of the spectrum of the signal coming from the first interpolation stage. The frequency response at (sin( . fe 2 )/( .fe 2 )) 2 includes (n 2- 1) periodic zeros (points of infinite theoretical attenuation) located at the level of the periodic replicas of the spectrum of the over-sampled signal. Around each zero is a frequency band in which the attenuation is greater than a given minimum attenuation. The interpolation ratios of the first two interpolation stages are chosen so that each of the frequency bands has a width greater than the useful band of the input signal. Thus, the replicas of the useful signal due to the over-sampling of a ratio n 2 in the linear interpolator are attenuated by a guaranteed minimum level. In other words, the ratio between the power of the useful signal replicas due to oversampling by a ratio n 2in the linear interpolator at the output of the equivalent filter whose frequency response is in ( sin(.fe 2 )/(.fe 2 )) 2 and the power of these same replicas at the input of the filter is less than a given ratio in any the frequency bands mentioned above.

In the interpolator according to the invention, the blocking interpolator of the third interpolation stage is configured to carry out an interpolation by blocking, equivalent to the oversampling of the signal coming from the second interpolation stage by a ratio n 3 by insertion samples then filtering said over-sampled signal by a filter having a frequency response in sin(n. fe 3 /(n. fe 3 , with fe 3 the sampling frequency of the signal at the output of the third stage of interpolation, said frequency response in sin(n.fe 3 /(n.fe 3 having (n 3- 1) periodic zeros around each of which there is a frequency band whose attenuation is greater than a given minimum level. The interpolator is configured so that each of these frequency bands has a width greater than the useful band of the input signal.

In fact, interpolating a signal by blocking amounts to over-sampling it by inserting harmful samples, then filtering it using a filter whose frequency response is in sin(n.fe 3 /(n.fe 3 . The over- sampling performed by the third interpolation stage naturally creates n 3 periodic replicas of the spectrum of the signal from the second interpolation stage. The frequency response is in sm(n. fe 3 /(n. fe 3 includes (n 3- 1) zeros (points of infinite theoretical attenuation) which are located at the level of the periodic replicas of the spectrum of the over-sampled signal. Around each zero is a frequency band in which the attenuation is greater than a given minimum attenuation. The interpolation ratios of the three stages of the interpolator are chosen so that each of these frequency bands has a width greater than or equal to the useful band of the input signal. Thus, the replicas of the useful signal due to the oversampling of a ratio n 3 in the blocking interpolator are attenuated by a guaranteed minimum level. In other words, the ratio between the power of the replicas of the useful signal due to the over-sampling of a ratio n 3in the linear interpolator at the output of the equivalent filter whose frequency response is in sin(n. fe 3 /(n. fe 3 and the power of these same replicas at the filter input is less than a given ratio in all the bands of frequencies mentioned above.

Advantageously, the interpolation ratio of at least one interpolation stage is a power of two, which gives the possibility of parallelizing the calculations as well as possible.

The invention also relates to a method of interpolation by a ratio n of the sampling frequency of a signal called an input signal. The process successively comprises:

a first interpolation step comprising oversampling said input signal by a ratio of ¾, where is a submultiple of n, and filtering the oversampled signal, and

a second interpolation step comprising the linear interpolation of the signal resulting from the first interpolation step by a ratio n 2 , where n 2 is a sub-multiple of n, and

a third interpolation step by blocking interpolator of the signal resulting from the second interpolation step by a ratio n 3 , where n 3 is a sub-multiple of n ,

with n n- n 2 n 3 .

Finally, the invention relates to a method for dimensioning an interpolator such as that described above. Interpolator sizing includes:

- a first step of determining the interpolation ratio n x of the first stage of the interpolator from a useful bandwidth of the input signal and a minimum attenuation of the replicas of the signal entering the second stage d ' interpolation due to the interpolation of an n 2 , and

- A step of determining the interpolation ratio n 2 of the second stage of the interpolator. This determination is made from a useful bandwidth of the signal to be transmitted and a minimum attenuation of replicas of the signal entering the third interpolation stage due to the interpolation of a ratio n 3 , and

- a step of determining the interpolation ratio of the last stage of the interpolator from the interpolation ratio(s) of the stages preceding it.

The invention will be better understood and other characteristics and advantages will appear better on reading the following description, given without limitation, and thanks to the appended figures, among which:

• Figure 1 shows an interpolator according to two embodiments of the invention;

• Figure 2 shows, by way of example, the normalized frequency response equivalent to a blocking interpolator interpolating the signal with a ratio of 8;

• Figure 3 shows, by way of example, the normalized frequency response equivalent to a linear interpolator interpolating the signal with a ratio of 8;

• Figure 4 shows three zoom levels of the normalized frequency response of a signal interpolated by an interpolator according to one embodiment of the invention;

• Figure 5 shows an embodiment of a device intended to modulate two signals having a different sampling frequency comprising two interpolators according to embodiments of the invention;

• Figure 6 shows the steps of a signal interpolation method according to the invention;

• Figure 7 shows the steps of a dimensioning method of an interpolator according to the invention.

FIG. 1 represents an interpolator according to two embodiments of the invention.

The interpolator takes as input a signal sampled at the frequency fe. It is composed of a plurality of cascaded interpolators whose last stages present a maximum simplification of the calculations, thus facilitating its realization at a very high output frequency which can even be higher than the maximum clock frequency of the digital component used to implement the interpolator, while controlling the spectral purity of the interpolated signal and maximizing the use of the input signal band. It takes as input a signal sampled at the frequency fe, and delivers the same signal sampled at the frequency Fe=n-fe.

The interpolator according to the invention comprises a first conventional interpolation stage 101, that is to say carrying out the over-sampling of the input signal by inserting (¾ - 1) zeros between each sample of this signal, n x being the oversampling ratio of the first stage of the interpolator. The sampling frequency after over-sampling being relatively low, an II R filter can be used in the case where the output frequency is compatible with the clock frequency of the digital component used. However, when it is desirable to have a linear phase or when the processing operations must be parallelized from the first stage of the interpolator, the use of an FIR filter proves to be advantageous.

The technique of interpolation by filtering makes it possible to control the spectral purity and to optimize the exploitation of the useful band of the original signal. However, when the frequency ratio is very high, the transition band of the filter is very narrow, which leads to a filter order that is too high and therefore too complex to implement (in the case of a low-pass filter, the transition band corresponds to the zone between the end of the pass band and the beginning of the rejected band). To minimize the complexity of this interpolation stage, the interpolation ratio n x must therefore be chosen as low as possible. It must also take into account the usable frequency domain of the next stage, as detailed below.

The signal leaving the first interpolation stage 101 is an interpolated signal sampled at the frequency fe 1 =n × fe.

The interpolator according to the invention also comprises a second interpolation stage 102 in the form of a linear interpolator. This is one of the simplest interpolation techniques, which consists in calculating the intermediate samples on a straight line which passes through two adjacent samples. One speaks sometimes of "blocker of order 1 on n cycles", but this term is not completely exact because there is no blocking of the signal strictly speaking. The second interpolation stage 102 performs the interpolation of the signal coming from the first interpolation stage by a ratio n 2 .

In the case where n 2 is of the form 2 W , the linear interpolator can be carried out very simply, by calculating the half-sum of the adjacent samples on N successive layers, until obtaining the (n 2 - 1) middle layers.

Thus, for each cycle at the input sampling frequency, samples i and i+1 correspond to samples n 2 i and n 2 (i+1) at the output sampling frequency. Subsequently, these output samples will be named m(0) and m(n 2 ). The calculation of the intermediate samples is as follows:

- layer 1: 1 calculation:

o 0.5

(m( 0) + m(n 2 ))

- layer 2: 2 calculations:

o 0.5 (m(0) +

m(n 2 /2))

o 0.5 (

m(n 2 /2 ) + m(n 2 ))

- layer 3: 4 calculations:

o 0.5 (m( 0) + 7n(n 2 /4))

o (¾ = 0.5 ' < ( 3 ¾/4) + m(n 2 ))

etc.,

layer /c: 2 (fc ^ calculations

The implementation complexity of a linear interpolator is lower than that of the so-called "conventional" interpolator of the first stage, which allows it to be implemented at higher sampling frequencies. Also, the structure of the linear interpolator, especially when n 2 is a power of 2, is highly parallelizable. Such an interpolator is therefore particularly suitable for generating and interpolating a signal in real time, and can make it possible to generate an output signal from the second interpolation stage at a sampling frequency higher than the maximum operating frequency of the component on which the interpolator is implemented. Advantageously,3 , the interpolation ratio n 2 is chosen as low as possible while respecting the usable frequency domain of the third stage. In this way, the interpolation ratio n 3 is the greatest possible, the interpolator of the third stage being the one whose implementation is the least complex. The spectral performances of the linear interpolation are very low and do not make it possible to maximize the use of the band of the original signal, which is why such an interpolation cannot be used by the first stage of the interpolator.

The signal leaving the second interpolation stage 102 is an interpolated signal sampled at the frequency fe 2 =h c · h 2 · fe.

According to one embodiment, the interpolator comprises only the first stage 101 of interpolation by over-sampling and filtering, and the second stage 102 of linear interpolation. In this case, h = h 1 · n 2 .

In another embodiment, the interpolator further comprises a third interpolation stage 103, making it possible to interpolate the signal leaving the second interpolation stage by a ratio n 3 .

This stage, placed last in the chain, does not require any calculation. The principle of the interpolator blocker is to repeat n 3 times the same sample, hence the name blocker. One sometimes speaks of "blocker of order 0 on n cycles". In terms of implementation, it is the simplest solution because it does not require calculations, which is why it can be implemented for very high sampling frequencies. On the other hand, the spectral performances are very limited.

The signal leaving the second interpolation stage is an interpolated signal sampled at the frequency Fe=h 1 · h 2 · h 3 · fe.

As regards the spectral performances of the different stages of the interpolator according to the invention, the blocking interpolator of the third stage 103 performs an interpolation equivalent to the oversampling of the signal by a ratio n 3 by the insertion of n 3 1 harmed samples between each sample, then its filtering by an FIR filter comprising n 3 coefficients equal to 1. Over-sampling in a ratio n 3 naturally generates (n 3 - 1). replicas of the signal entering the blocking interpolator. Those

(n 3 - 1). replicas have a high power level over a bandwidth which corresponds to the width of the useful signal to be interpolated. It is therefore necessary for the filtering of these replicas to strongly attenuate the (n 3 - 1). replicas.

The Fourier transform of a rectangular impulse response

(order 0 blocker) corresponds to a frequency response in sin(x) / x. FIG. 2 represents, by way of example, the normalized frequency response of a filter Fl R comprising n 3 coefficients equal to 1 when n 3 = 8. It can be seen that:

- the useful spectrum, around / = 0 or around Fe (either here for

/ = 8 with / the frequency normalized by Fe/n 3 and n 3 = 8), is slightly degraded because the top of the central lobe of sin( f)/( f) is flat and equal to 1,

- the periodic spectrum replicas linked to the over-sampling of the signal by n 3 (i.e. for / = 1, 2, ... , n 3 - 1.) are strongly attenuated because they fall at the level of the zeros of sin(7r/ )/(7r/), (here around / = k, with k integer from 1 to 7).

In order to guarantee the spectral purity of the interpolated signal, it is advisable to limit the usable band of the signal entering the blocking interpolator according to the attenuation provided by the function sin(f)/(f) around its zeros, so that periodic spectrum replicas related to oversampling by inserting zeros do not exceed a given maximum level. Thus, the usable frequency band of the signal entering the blocking interpolator is limited by the width of the narrowest frequency band for a given attenuation around the zeros of the function sin(7r/)/(7r/), i.e. in the example of figure 2 around / = 1.

Let / of the form f = 1 - e, with e being the usable band of the signal entering the blocking interpolation stage. When the value of n 3 is high (in the example, n 3 = 8), and for two minimum attenuation values ​​sought (40 dB and 50 dB), the usable relative band is equal to:

- e = 1% of Fe/n 3 usable for 40dB of attenuation;

- e = 0.3% of Fe/n 3 usable for 50dB of attenuation.

When n 3 is greater than 8, it can be seen that the variations in the template of the normalized sin(f)/(f) function are negligible. Thus, the width of the usable frequency band of the signal remains stable for values ​​of n 3 greater than 8.

When n 3 is low (for example for n 3 <8), the width of the useful frequency band guaranteeing a given attenuation around the zeros of the function sin(f)/(f) decreases. For n 3 = 2., the usable relative band is then:

- e = 0.6% of Fe/n 3 usable for 40dB of attenuation;

- e = 0.2% of Fe/n 3 usable for 50dB of attenuation.

By way of illustration, the points 202 and 203 of FIG. 2 correspond to the limits of a frequency band 304 in which the attenuation is greater than 20dB around the first zero 201 of the frequency response in sin(7r/)/ (7r/). The threshold value of 20dB is given here as an example.

The relative bandwidth of the useful signal that can be used with a blocking interpolator is therefore low (less than 1% of the frequency band of the blocking output signal). However, it is sufficient with the proposed architecture because the first two interpolation stages make it possible to limit the ratio of the usable band of the signal to be interpolated at the sampling frequency of the third interpolation stage to the maximum ratio authorized by this stage. for the chosen spectral purity. Furthermore, the very low attenuation around the useful spectrum makes it particularly suitable for implementation as the last stage of a high rank interpolator.

The linear interpolator of the second stage 102 carries out an interpolation equivalent to the over-sampling of the incoming signal by a ratio n 2 by inserting (n 2 - 1) null samples between each sample, then to its filtering by an FIR filter comprising ( 2 n 2 - 1) triangle coefficients. Oversampling in a ratio n 2 naturally generates (n 2 - 1) replicas of the signal entering the linear interpolator. These (n 2 - 1). replicas have a high power level over a bandwidth which corresponds to the width of the useful signal to be interpolated. It is therefore necessary that the filtering of these replicas strongly attenuates these (n 2- 1). replicas.

The triangle impulse response corresponds to the convolution of two identical rectangles of n 2 points. Thus, the Fourier transform of a triangle impulse response (blocker of order 1) corresponds to that of a rectangle impulse response squared, i.e. a frequency response in
Figure 3 represents, by way of example, the normalized frequency response of an FIR filter comprising (2n 2 - 1) triangle coefficients with n 2 =8 .

We find there the properties of the filter of figure 2, that is to say a flat impulse response around / = 0 (here we measure less than 0.25dB of gain variation in the passband), and zeros positioned at the center of the periods of the modulating signal. Thanks to the squaring of the weighting, the attenuation in dB is doubled compared to the blocking interpolator, hence a widening of the frequency band guaranteeing a given attenuation around the zeros, thus improving the band ratio usable with respect to the latter.

By way of illustration, the points 302 and 303 of FIG. 3 correspond to the limits of a frequency band 304 in which the attenuation is greater than 40dB around the first zero 301 of the frequency response in (sin(7r/) /(7r/)) 2 . The threshold value of 40dB is given here as an example.

In the same way as for FIG. 2, the usable band for the transmission of the useful signal is given by the width, for a given attenuation, of the narrowest frequency band around the zeros of the function (sin(nf)/ (nf)) 2 for a given attenuation, i.e. in the example of figure 3 around / = 1. For n 2 = 8, we have:

- e = 9% of fe 2 /n 2 usable for 40dB of attenuation, and

- e = 5% of fe 2 /n 2 usable for 50dB of attenuation.

We also note here that for n 2 ³ 8. , the normalized template in (sin(7r/)/ (p/)) 2 varies little. Thus the width of the usable frequency band of the signal remains stable for values ​​of n 2 greater than 8.

When n 2 is small, the width of the frequency bands guaranteeing a given attenuation around the zeros of the function (sin(7r/)/(7r/)) 2 decreases, which decreases the usable relative band. For n 2 = 2., obtains:

- e = 6.3% of fe 2 /n 2 usable for 40dB of attenuation, and

- e = 3.5% of fe 2 /n 2 usable for 50dB of attenuation.

With the proposed architecture, the first interpolation stage is sized to limit the ratio of the band of the useful signal to the sampling frequency fe 2 to the maximum ratio authorized by the second linear interpolation stage for the chosen spectral purity.

The cascaded interpolator according to the invention therefore allows the implementation at limited cost of a high rank interpolator on logic components (for example an FPGA), by using stages of decreasing complexity and highly parallelizable, which facilitate its implementation. work in real time at high speed. The interpolator according to the invention has the following characteristics: - a high and factorizable integer interpolation rank (preferably of the form 2 N ),

- control of the spectral purity of the interpolated signal,

- maximum use of the usable band of the original signal, and

- an output sampling frequency which may be greater than the maximum clock frequency of the digital component used.

For this, it combines, successively and in an optimized way, known interpolation techniques which are:

- over-sampling and filtering, by a filter which can be an Fl R or IIR filter,

- linear interpolation, and depending on the embodiment,

- blocking interpolation.

The interpolation ratio of each stage is determined to control the spectral purity taking into account the ratio of the usable band to the sampling frequency of the following stage.

By way of illustration, three embodiments are described in more detail later in the document.

A first exemplary embodiment has a high-rank interpolator (4096) comprising three cascaded interpolation stages.

1- interpolation stage 101. of over-sampling and filtering type:

To limit the order (that is to say the length) of the filter of the first interpolation stage, it is chosen to use 80% of the Nyquist band at the input sampling frequency (fe). Thus, the pass frequency Fpass of the filter must equal Fpass=0.4/e. To optimize folding, it is desirable to have a stop frequency Fstop symmetrical with respect to Fe/2, ie Fstop=0.6/e.

One purpose of the first interpolation stage is to raise the sampling frequency to the minimum value making it possible not to exceed the bandwidth usable by the second linear interpolation stage. As seen previously, and anticipating a high % value, to reach 50dB of minimum attenuation of the periodic replicas of the oversampled spectrum in the second interpolation stage, the useful band of the signal must be less than 5% of relative band tolerated by the next stage of linear interpolation.

Thus, Fpass must be less than or equal to 0.05% fe. We then deduce = 8.

The value of %, as well as the values ​​of Fpass and Fstop make it possible to determine the mask of the filter of the first interpolation stage, according to means known to those skilled in the art. Such a filter can be produced for example with 80 coefficients. The implementation of such a filter is inexpensive because it operates at low frequency (at the sampling frequency fe 1 =8 fe).

2— interpolation stage 102. of linear interpolator type:

Identically to the first stage of the interpolator, and in order to respect an attenuation constraint greater than 50dB of the periodic replicas of the spectrum due to the interpolation, the second stage of linear interpolation raises the sampling frequency to the value minimum so as not to exceed the 0.3% of relative band tolerated by the final interpolation stage by blocking interpolator.

Thus, by anticipating a high value of n 3 , the useful band Fpass of the signal to be interpolated must be less than or equal to 0.003%% fe, ie n 2 16.7. The second interpolation stage can be performed using a frequency ratio %=17. However, it is preferable to use a power of 2 to optimize the parallelization of the calculations in the component. We will therefore choose n 2 = 32, which is the first power of 2 greater than 16.7.

3— interpolation stage 103. blocker type:

This stage raises the sampling frequency to the final value Fe. Thus, for n = 4096, and with = 8 and n 2 = 32, we find n s = 16.

The high-rank interpolator according to this embodiment has the following characteristics:

- an interpolation ratio n = 2 12 = 4096 given by three interpolation stages 101 , 102 and 103 respectively having interpolation ratios equal to = 8, n 2 = 32 and n s = 16,

- 80% use of the input signal sampling band,

- an attenuation of the periodic replicas of the spectrum linked to oversampling of the signal greater than 50dB,

- ripple in the band less than 0.5dB, and

- a linear phase.

The interpolator proposed in this embodiment therefore meets all of the requirements, and can be implemented at low cost in a digital component. The use of an FIR in the first interpolation stage does not pose any implementation problems because the output sampling frequency of this stage is low. Compared to a "conventional" interpolator carrying out the interpolation by 4096 in a single step of oversampling and filtering, the complexity of the first stage of the interpolator according to the invention is divided by a ratio n 2 n s thanks to the presence of the next two floors. So, for the same band of

transition of the filter and the same attenuation, the order of the filter used, that is to say its number of coefficients, is divided approximately in the same ratio.

FIG. 4 represents three zoom levels of the normalized frequency response of an interpolator such as that described above, of order 4096. The value 1 corresponds to /e.

Representation 401 is the frequency response between frequency 0 and frequency Fe/2 (2048/e). We can see there in particular that the periodic replicas of the spectrum around points 256, 512, ..., 2048, which correspond to the over-sampling by n 3 carried out by the third interpolation stage, are well attenuated by more than 50dB after their filtering by a filter having a frequency response of (sin(7r/)/(7r/)) 2 .

The representation 402 is a zoom on the frequency response between the frequency 0 and the frequency 4 fe 1 (ie 32/e). We can see there in particular that the periodic replicas of the spectrum around points 8, 16, ... 32, which correspond to the effects of the over-sampling by n x and n 2 of the first two stages of interpolation, -are indeed attenuated by more than 50dB after being filtered by a filter having a frequency response
Finally, the representation 403 is a zoom on the frequency response between the frequency 0 and the frequency fe. It can be observed that in the band of interest of the input signal, which corresponds to 0.4/e, the signal is only very slightly attenuated, whereas it is attenuated by more than 50dB in the rejected band , which starts at 0.6/e.

A second embodiment, given by way of example, has an interpolator whose rank (32) is lower than that of the previous one. This interpolator includes only two cascaded interpolation stages.

1- interpolation stage 101. of over-sampling and filtering type:

As in the previous example, in order to limit the order of the first stage interpolation filter, 80% of the Nyquist band of the input signal is used, that is Fpass = 0.4/e. To optimize folding, Fstop=0.6/e is also chosen.

To respect the constraint of 50dB minimum attenuation of the periodic replicas of the spectrum generated by the oversampling of the signal in the second stage of linear interpolation, and by anticipating a high value of n 2 , it is necessary that Fpass £ 0.05 fe, which gives = 8.

As previously, this value determines the mask of the filter of the first interpolation stage, such as for example an FIR with 80 coefficients, which does not pose any particular implementation problems at the sampling frequency fe 1 .

2— interpolation stage 102. of linear interpolator type:

This stage raises the sampling frequency to the final value Fe. We therefore necessarily have n 2 4.

In this example, it is not possible to implement a blocker type stage because the useful band Fpass of the input signal would necessarily be greater than 0.3% of the final sampling frequency, and would therefore not respect the attenuation constraint of the periodic replicas of the spectrum of at least 50dB.

The interpolator given in this embodiment therefore has the following characteristics:

- an interpolation ratio n = 2 5 = 32 given by two interpolation stages 101 and 102 having respectively interpolation ratios equal to = 8 and n 2 = 4,

- 80% use of the input signal sampling band,

- an attenuation of the periodic replicas of the spectrum linked to oversampling of the signal greater than 50dB,

- ripple in the band less than 0.5dB, and

- a linear phase.

A third embodiment, given by way of example and represented in FIG. 5, presents a device intended to modulate a signal C sampled at the frequency Fe by the product of two modulating signals, a first signal at the frequency Fe/ 4096 ( modulating signal A) and a second at the frequency Fe/32 (modulating signal B). Multiplying signal A by signal B and using the product of these two signals to modulate signal C requires the prior harmonization of their respective sampling frequency. The embodiment described in FIG. 5 then corresponds to a combination of the two- and three-stage embodiments presented above.

One way of producing the product of the two modulating signals is represented in FIG. 5. It consists in bringing the modulating signal A to the frequency Fe/ 4 by means of a three-stage interpolator such as that described previously for a ratio 4096 , and which comprises a first stage 501 of interpolation of a ratio 8 by over-sampling and filtering, a second stage 502 of linear interpolation of a ratio 32 and a third stage 503 of interpolation by blocking interpolator. Such an interpolator complies with all the requirements given previously with regard to the preservation of the signal in its useful band and the attenuation of the periodic replicas of the spectrum generated by the over-sampling of the signal. The modulating signal B is also brought to the frequency of

The product 505 of the two signals interpolated at Fe/4 is then produced, and the resulting signal is brought to the sampling frequency Fe by a linear interpolation stage 506 with a ratio of 4. Such an interpolation stage is possible because the set 504-506 relates to the case of the two-stage interpolator described previously for a ratio 32. The useful band of the modulating signal A is much lower than that of B: it therefore necessarily respects the constraint on the band d sampling usable by the linear interpolation stage 506. Finally, the product of the two modulating signals is used to modulate 507 the signal C at the frequency Fe.

The invention also relates to a method of interpolation by a ratio n of the sampling frequency of a signal. This method performs the functions described by the device according to the invention, and all of the embodiments described in connection with the device can be applied mutatis mutandis to the method. FIG. 6 represents the different steps of this process. He understands :

- A first step 601 of interpolation of the input signal. This interpolation is performed by over-sampling the input signal by a ratio , n x being a sub-multiple of n, then by filtering the over-sampled signal, and

- A second step 602 of interpolation by linear interpolation of the signal resulting from the first interpolation step. The linear interpolation is of a ratio n 2 , n 2 being a sub-multiple of n.

According to the embodiment envisaged, the method according to the invention may comprise only these two steps. In this case, the total interpolation ratio n equals n = ■ n 2 .

In another embodiment, the method according to the invention comprises a third step 603 of interpolation of the signal resulting from the second interpolation step. The interpolation is done by interpolation by locking of a ratio n 3 , % being a sub-multiple of n. In this case, the total interpolation ratio n of the interpolator is equal to n=n 2 n 3 .

The invention finally relates to a method for dimensioning an interpolator comprising several cascaded interpolation stages such as that represented in FIG.

When the interpolator comprises only two stages, a stage 101 of interpolation by oversampling and filtering and a stage 102 of linear interpolation, the dimensioning method according to the invention comprises:

- A first step 701 of determining the interpolation ratio of the first stage. This determination is made from:

o a useful bandwidth of the input signal, i.e. the bandwidth Fpass of the input signal that must be preserved during the interpolation (for example, Fpass = 0.4/e ), and

o a capacity of the linear interpolator of the second stage to attenuate the periodic replicas of the spectrum linked to the interpolation by the ratio n 2 , that is to say the size of the (n 2 - 1) frequency bands positioned around the frequencies fe ,

2 fe , 3 fe , ..., (n 2 - 1 )fe 1 guaranteeing a given attenuation (for example, choosing so that Fpass £ 0.05 fe guarantees a minimum attenuation of 50dB of the replicas of the useful signal around of the zeros of the linear interpolator), and - a second step 702 of determining the interpolation ratio of the last stage of the interpolator from the interpolation ratio(s) of the stages preceding it, that is to say in the case of a two-stage interpolator, n 2 =n/n.

When the interpolator comprises three stages, a stage 101 of interpolation by oversampling and filtering, a stage 102 of linear interpolation, and a stage 103 of interpolation by blocking interpolator, the dimensioning method according to the invention comprises the two steps 701 and 702 described previously, as well as an intermediate step 703 of determining the interpolation ratio n 2 of the second stage from:

- a useful bandwidth of the input signal, i.e. the bandwidth Fpass of the input signal which must be preserved during the interpolation, and

- a capacity of the blocking interpolator of the third stage to attenuate the periodic replicas of the spectrum linked to the interpolation by the ratio n 3 , that is to say the width of the (n 3 - 1) frequency bands positioned around the frequencies fe 2 , 2 fe 2 , 3 fe 2 , ..., (n 3 - l)fe 2 guaranteeing a given attenuation (for example, choose n x and n 2 so that Fpass £ 0.003 · h 1 · h 2 · fe guarantees a minimum attenuation of 50dB of the replicas of the useful signal around the zeros of the blocking interpolator).

In this case, step 702 of determining the interpolation ratio is carried out by calculating the ratio n 3 =n/(nn 2 ).

Although certain specific embodiments have been described by means of precise examples comprising numerous details, in particular concerning the characteristics of the interpolation stages such as, for example, the interpolation ratios used or the width of the useful bandwidth of the signal whose replicas can be attenuated in precise proportions by the various interpolation stages, the invention is not limited to these embodiments, but covers all the embodiments that can be developed by those skilled in the art at the light of the explanations given earlier in this description.