JP2009038742A - Up-sampling device and up-sampling method, and program thereof - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce throughput in an up-sampling frequency domain. <P>SOLUTION: An up-sampling device samples an input signal sampled at a frequency f<SB>s</SB>again at a frequency of Lf<SB>s</SB>, where L is an integer of not less than 2. A frequency analysis section converts the input signal into a frequency domain signal and outputs an input signal frequency spectrum. An imaging calculating section generates an imaging component that is a folding spectrum obtained by copying the input signal frequency spectrum, according to a prescribed value of L to output a signal frequency spectrum, after imaging calculation. An interpolation filter section multiplies the signal frequency spectrum, after imaging calculation by a frequency domain interpolation filter coefficient and restrains the imaging components. A frequency combining section performs conversion on the time domain signal of the number of samples Lf<SB>s</SB>, which is larger than that in the frequency analysis and outputs, with the output signal of the interpolation filter section as input. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

The present invention, an input signal sampled at a certain frequency f _s, and up-sampling method for re-sampled at the frequency higher Lf _s, the up-sampling device for the program.

In digital signal processing, it may be desired to vary the sampling rate of a signal discretized at a certain sampling frequency f _s . For example, an upsampling device is used when an FM sound source with a sampling frequency f _s = 32 kHz is converted into a CD sound source with f _s = 48 kHz.

FIG. 9 is a diagram illustrating a functional configuration example of a conventional upsampling apparatus 100. The upsampling apparatus 100 includes an upsampling unit 102 and an interpolation filter unit 104. In the upsampling process in which L−1 zero values are inserted between samples of the input signal x (nT) and the sampling frequency is increased to L times to generate the output signal y _U (nT ′), the imaging that occurs in the upsampling In order to remove (quantization distortion), a method has been proposed so far in which the interpolation filter h (nT) is convoluted with the upsampled signal x _U (nT ′) to limit the band (Non-Patent Document 1). ). Here, n is a number (sample point number) indicating a discrete time of a predetermined interval obtained by sampling the continuous time signal at the sample interval T. The up-sampling unit 102 receives the input signal x (nT) as an input, and calculates the post-up-sampled signal x _U (nT ′) according to Expression (1).

ここで、Ｔ’はアップサンプリング後のサンプル間隔でＴ’＝Ｔ/Ｌとする。インターポレーションフィルタ部１０４は、入力信号ｘ_Ｕ（ｎＴ’）を入力とし、フィルタ後信号ｙ_Ｕ（ｎＴ’）を式（２）により算出する。

Here, T ′ is a sample interval after upsampling, and T ′ = T / L. The interpolation filter unit 104 receives the input signal x _U (nT ′) as an input, and calculates the filtered signal y _U (nT ′) by Expression (2).

ここで、ｈ（ｎＴ’）はインターポレーションフィルタ、Ｐはインターポレーションフィルタのサンプル数を表わす。
「シミュレーションで学ぶディジタル信号処理−ＭＡＴＬＡＢによる例題を使って身につける基礎から応用」、尾知博著、ＣＱ出版、東京、pp.143-146,2001

Here, h (nT ′) represents an interpolation filter, and P represents the number of samples of the interpolation filter.
"Digital signal processing learned by simulation-applied from the basics learned using examples by MATLAB", Tomohiro Ochi, CQ Publishing, Tokyo, pp.143-146, 2001

  The conventional upsampling method requires a large amount of processing because the interpolation filter is convolved with the post-upsampled signal in the time domain. To avoid convolution with a large amount of processing, a method of frequency analysis of the input signal and filtering in the frequency domain is conceivable. However, since the processing amount of frequency analysis itself is large, there is a problem that the processing amount cannot be reduced even in the frequency domain if the number of frequency analysis points is large.

  The present invention has been made in view of the above points, and an object thereof is to provide a method, an apparatus, and a program for performing upsampling in the frequency domain with a small number of frequency analysis points.

The upsampling device according to the present invention is an upsampling device that resamples an input signal sampled at a frequency f _s at a frequency of Lf _s of L that is an integer of 2 or more. The frequency analyzer converts the input signal into a frequency domain signal and outputs an input signal frequency spectrum. The imaging calculation unit generates an imaging component, which is a folded spectrum obtained by copying the input signal frequency spectrum, in accordance with a predetermined value of L, and outputs the signal frequency spectrum after the imaging calculation. The interpolation filter unit suppresses the imaging component by multiplying the signal frequency spectrum after the imaging calculation by a frequency domain interpolation filter coefficient. Frequency synthesizing unit receives the output signal of the interpolation filter unit, and outputs the converted to the time domain signal of more number of samples Lf _s than at said frequency analysis.

  The imaging calculation unit of the upsampling apparatus according to the present invention generates an imaging component, which is a folded spectrum obtained by copying the input signal frequency spectrum output from the frequency analysis unit, according to a predetermined L value. Then, the frequency synthesizer performs frequency synthesis with L times the frequency analysis score to obtain an upsampled output signal. According to this method, distortion due to a reduction in processing amount is not generated. Therefore, the same result as the conventional upsampling can be obtained by reducing the processing amount in the frequency analysis unit to 1 / L.

  Embodiments of the present invention will be described below with reference to the drawings. The same reference numerals are given to the same components in a plurality of drawings, and the description will not be repeated.

FIG. 1 shows a functional configuration example of Embodiment 1 of the upsampling apparatus of the present invention, and FIG. 2 shows an operation flow. The upsampling apparatus 10 includes a frequency analysis unit 12, an imaging calculation unit 14, an interpolation filter unit 16, and a frequency synthesis unit 18. The frequency analyzer 12 receives the input signal x (nT) as an input, and outputs the input signal frequency spectrum X (e ^jωT ) of the sampling frequency f _s (step S12). Here, the frequency ω is the number of the frequency value of the spectrum obtained at a predetermined frequency interval. The sampling frequency f _s is a value such as 16 kHz, for example, and the frequency analysis score is a value such as 1024 points, for example. The imaging calculation unit 14 uses the input signal frequency spectrum X (e ^jωT ) as an input, and calculates the post-imaging signal frequency spectrum X _U (e ^{jωT ′} ) using Equation (3) (step S14).

ここでＴ’＝Ｔ/Ｌである。したがって、Ｌ＝２とした場合では、イメージング計算後信号周波数スペクトルＸ_Ｕの周波数がπ（rad）変化する間に、入力信号周波数スペクトルＸ（ｅ^ｊωＴ）が２回繰り返される。つまり、イメージング計算後信号周波数スペクトルＸ_Ｕ（ｅ^ｊωＴ’）が、アップサンプリング後のサンプリング周波数の１周期内に２回複写された波形になる。詳しくは後述する。このように、アップサンプリング後の周波数スペクトルをアップサンプリング前のスペクトルを用いて計算するため、歪を伴うことなく周波数分析を行う処理量を１/Ｌに削減することが出来る。

Here, T ′ = T / L. Therefore, in the case of the L = 2, while the frequency of the imaging calculation signal after the frequency spectrum X _U is [pi (rad) is changed, the input signal frequency spectrum ^X (e ^jωT) is repeated twice. That is, the signal frequency spectrum X _U (e ^{jωT ′} ) after the imaging calculation becomes a waveform copied twice within one period of the sampling frequency after the upsampling. Details will be described later. Thus, since the frequency spectrum after upsampling is calculated using the spectrum before upsampling, the amount of processing for performing frequency analysis without distortion can be reduced to 1 / L.

The interpolation filter unit 16 receives the post-imaging signal frequency spectrum X _U (e ^{jωT ′} ) as an input, and calculates the post-filter signal frequency spectrum Y _U (e ^{jωT ′} ) using equation (4) (step S16).

ここで、Ｈ（ｅ^ｊωＴ’）は周波数領域インターポレーションフィルタ係数を表わす。周波数合成部１８は、サンプリング周波数Ｌｆ_ｓで再合成して時間領域の出力信号ｙ_Ｕ（ｎＴ’）を出力する（ステップＳ１８）。周波数合成の方法としては、例えば逆フーリエ変換が利用出来る。

Here, H (e ^{jωT ′} ) represents a frequency domain interpolation filter coefficient. Frequency synthesizer 18 outputs an output signal of the re-synthesized time domain _y U (nT ') at a sampling frequency Lf _s (step S18). As a method of frequency synthesis, for example, inverse Fourier transform can be used.

[Characteristics of imaging components and interpolation filter]
Here, the relationship between the imaging component and the filter characteristics of the interpolation filter will be described. For example, FIG. 3A schematically shows a result of frequency analysis of an analog signal having a discrete value at a sampling frequency f _s = 4 kHz, for example. The horizontal axis of Fig.3 (a) represents a frequency by angular frequency (omega) (rad). The vertical axis represents the amplitude of the frequency spectrum. In this example, since the sampling frequency f _s = 4 kHz, 2π (rad) corresponds to 4 kHz. The Nyquist frequency ω _n at the sampling frequency f _s = 4 kHz is π (rad) (2 kHz). A frequency component exceeding the Nyquist frequency ω _n becomes aliasing noise. This folding is an imaging component. A waveform of 0 to π in the low frequency range centering on the Nyquist frequency ω _n is folded back in a complex conjugate relationship to become a waveform of π to 2π (rad). The signal waveform in the time domain continues indefinitely with the horizontal axis as time. On the other hand, the signal converted into the frequency domain has a waveform in the range of 0 to 2π (rad) repeated as a harmonic component as shown in FIG.

Here, FIG. 3B shows a frequency spectrum when the signal shown in FIG. 3A is up-sampled with the rate conversion value L = 2. The horizontal and vertical axes are the same as in FIG. However, as a result of upsampling with L = 2, the sampling frequency f _s = 8 kHz, so the Nyquist frequency ω _n is 4 kHz (π). Then, the waveform in the range of 0 to 4π in FIG. 3A becomes a frequency spectrum compressed in the range of 0 to 2π (rad) in FIG. As shown in FIG. 3 (b), the Nyquist frequency omega _n following frequency domain imaging moiety (dull) becomes to include. When this imaging component shows a face as a signal, the original signal cannot be reproduced.

Therefore, in the first embodiment, the interpolation filter unit 16 performs filtering at a frequency equal to or lower than the Nyquist frequency ω _n = π / 2 (2 kHz) before the upsampling. This is schematically shown in FIG. The characteristics of the low-pass filter that passes through the range of 0 to π / 2 are indicated by broken lines. The characteristics of this low-pass filter are also folded around π (rad) due to the complex conjugate, so that the band-pass filter having −π / 2 to π / 2, 3π / 2 to 5π / 2,. Show properties. FIG. 4B shows a frequency spectrum in which the range of π / 2 to 3π / 2 (1 kHz to 3 kHz) is deleted by the interpolation filter unit 16. It can be seen that the imaging components shown in FIG. By frequency-synthesizing the frequency spectrum from which the imaging component has been removed by the frequency synthesizer 18, a signal that is not affected by the imaging component can be restored.

The filter characteristics shown in FIG. 4A are ideal characteristics. The cutoff characteristic of the actual filter has a slope as shown in FIG. In FIG. 5, the horizontal axis represents frequency, and the vertical axis represents amplitude. Ω _SB1 and ω _SB2 whose amplitude first intersects with the horizontal axis are the frequencies ω _SB at the stop band edge of the filter. The sharper cutoff characteristic indicated by the solid line has more ripples and a larger amplitude vibration width. That is, distortion increases. In order to reduce this distortion, it is necessary to make the slope of the cutoff characteristic of the filter gentle. As a result, the frequency ω _SB at the end of the stop band may exceed the Nyquist frequency ω _n . Even in that case, the processing of the above-described formula (4) is performed up to the frequency ω _SB at the stop band end. That is, the occurrence of distortion can be suppressed by making the characteristics of the interpolation filter unit 16 linear.

  In the first embodiment described above, an example in which the rate conversion value L is determined in advance has been described. The present invention is also applicable to an upsampling apparatus that performs upsampling corresponding to an arbitrary rate conversion value L. A functional configuration example of the upsampling device 60 is shown in FIG. The upsampling device 60 is obtained by adding an L value setting unit 62 to the upsampling device 10 of the first embodiment. Other configurations are the same as those of the first embodiment. In the L value setting unit 62, a value of the rate conversion value L is set by a switch or the like (not shown).

For example, when L = 4 is set for the input signal x (nT) discretized at the sampling frequency f _s = 4 kHz, the imaging calculation unit 14 sets the frequency range of the sampling frequency f _s = 16 kHz after upsampling. At (0 to 2π), a waveform is generated by repeating the frequency spectrum in the range of 0 to 2π before upsampling four times. This state is schematically shown in FIG. In FIG. 7, the horizontal axis represents frequency and the vertical axis represents amplitude. The frequency spectrum (FIG. 3A) up to the sampling frequency f _s = 2 kHz (2π) before the up-sampling is repeated four times within the range of the sampling frequency f _s = 16 kHz (2π) after the up-sampling. I understand.

  By providing such an imaging calculation unit 14, it is possible to realize an upsampling apparatus that can cope with an arbitrary rate conversion value L and that has a reduced processing amount in the frequency analysis unit.

  In the first embodiment or the second embodiment described above, an example in which the filter characteristic of the interpolation filter unit 16 is a low-pass filter has been described. However, the filter characteristic of the interpolation filter unit 16 is not limited to the low-pass filter. A band pass filter may be used.

For example, when the number of frequency analysis points at the sampling frequency f _s is 2N, the length P of the interpolation filter H (e ^{jωT ′} ) is set to P <N. The idea of setting the filter length P to P <N is schematically shown in FIG. In FIG. 8, the horizontal axis represents frequency, and the vertical axis represents amplitude. The horizontal axis N is π, and the same waveform as 0 to π is folded in a range of π to 2π (not shown). That is, the idea is to make the filter length of the interpolation filter unit 16 only the width of the passband. In this way, both hardware and software resources can be saved.
In this case, the filtered signal frequency spectrum Y _U (e ^{jωT ′} ) that is the output signal of the interpolation filter unit 16 is ^expressed by the above-described equation in the range of ω _A ≦ ω ≦ ω _{B in} the frequency range corresponding to the filter length P. Calculate in (4). Other processes are the same as those in the first or second embodiment.

Thus, by limiting the necessary frequency range ω _{A to} ω _B, it is possible to save hardware resources and software resources of the upsampling apparatus.

  In addition to the above examples, the apparatus and method according to the present invention are not limited to the above-described embodiments, and can be appropriately changed without departing from the spirit of the present invention. Further, the processes described in the above apparatus and method are not only executed in time series according to the order of description, but also may be executed in parallel or individually as required by the processing capability of the apparatus that executes the process. Good.

  Further, when the processing means in the above apparatus is realized by a computer, the processing contents of functions that each apparatus should have are described by a program. Then, by executing this program on the computer, the processing means in each apparatus is realized on the computer.

  The program describing the processing contents can be stored in a computer-readable storage medium. The computer-readable storage medium may be any medium such as a magnetic storage device, an optical disk, a magneto-optical storage medium, and a semiconductor memory. Specifically, for example, as a magnetic storage device, a hard disk device, a flexible disk, a magnetic tape, etc., and as an optical disk, a DVD (Digital Versatile Disc), a DVD-RAM (Random Access Memory), a CD-ROM (Compact Disc Read Only) Memory), CD-R (Recordable) / RW (ReWritable), etc., magneto-optical storage media, MO (Magneto Optical disc), etc., semiconductor memory, EEP-ROM (Electronically Erasable and Programmable-Read Only Memory), etc. Can be used.

  The program is distributed by selling, transferring, or lending a portable storage medium such as a DVD or CD-ROM storing the program, for example. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

  Each means may be configured by executing a predetermined program on a computer, or at least a part of these processing contents may be realized by hardware.

The figure which shows the function structural example of the upsampling apparatus 10 of Example 1 of this invention. The figure which shows the operation | movement flow of the upsampling apparatus. Are diagrams for explaining the relationship between the filter characteristics of the imaging components and interpolation filter, (a) represents a certain analog signal as a discrete value at the sampling frequency f _{s =} 4 kHz, the result of frequency analysis of the signal schematically (B) is a figure which shows the frequency spectrum at the time of up-sampling the signal shown to (a) as rate conversion value L = 2. Is a diagram illustrating an example of the frequency spectrum after upsampling, (a) shows the shows that filtering by upsampling before the Nyquist frequency _{ω n = π / 2 (1kHz} ) frequencies below schematically, (b) FIG. 4 is a diagram showing a frequency spectrum from which the imaging component of (a) has been removed. The figure which shows the example of the interruption | blocking characteristic of a low-pass filter. The figure which shows the function structural example of the upsampling apparatus 60 of Example 2 of this invention. The figure which shows the example of a frequency spectrum in case of L = 4. The figure which shows typically the idea which sets the filter length P to P <N. The figure which shows the function structural example of the conventional upsampling apparatus 100. FIG.

Claims (5)

The input signal sampled at a frequency f _s, Lf s _(where, L is an integer of 2 or more) an up-sampling device for re-sampled at the frequency of,
A frequency analyzer that converts the input signal into a frequency domain signal and outputs an input signal frequency spectrum;
An imaging calculation unit that generates an imaging component that is a folded spectrum obtained by copying the input signal frequency spectrum according to a predetermined value of L, and outputs a signal frequency spectrum after imaging calculation;
An interpolation filter unit that suppresses an imaging component by multiplying the signal frequency spectrum after the imaging calculation by a frequency domain interpolation filter coefficient;
A frequency synthesis unit receives the output signal of said interpolation filter unit, and outputs the converted to the time domain signal of more number of samples Lf _s than at said frequency analysis,
An upsampling apparatus comprising: The upsampling device according to claim 1,
The L value setting unit for setting the value of L is also
An upsampling apparatus comprising: In the upsampling device according to claim 1 or 2,
An upsampling apparatus, wherein the frequency length of the interpolation filter unit is P <N when the number of frequency analysis points at the sampling frequency f _s in the frequency analysis unit is 2N. The input signal sampled at a frequency f _s, Lf s _(where, L is an integer of 2 or more) A upsampling method of resampling at a frequency of,
A frequency analysis process in which the frequency analysis unit converts the input signal into a frequency domain signal and outputs an input signal frequency spectrum;
An imaging calculation process in which an imaging calculation unit generates an imaging component that is a folded spectrum obtained by copying the input signal frequency spectrum according to a predetermined value of L, and outputs a signal frequency spectrum after the imaging calculation;
An interpolation filter unit that multiplies the signal frequency spectrum after the imaging calculation by a frequency domain interpolation filter coefficient to suppress an imaging component;
Frequency synthesizer unit, receives the output signal of said interpolation filter unit, a frequency synthesis process that converts a time domain signal of more number of samples Lf _s than the frequency analysis process,
An upsampling method.   A program for causing a computer to function as the upsampling apparatus according to any one of claims 1 to 3.

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