CN101105787A - Method and use for calculating long sequence and infinite long sequence convolution using overlapping reservation method - Google Patents
Method and use for calculating long sequence and infinite long sequence convolution using overlapping reservation method Download PDFInfo
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- CN101105787A CN101105787A CNA200610052452XA CN200610052452A CN101105787A CN 101105787 A CN101105787 A CN 101105787A CN A200610052452X A CNA200610052452X A CN A200610052452XA CN 200610052452 A CN200610052452 A CN 200610052452A CN 101105787 A CN101105787 A CN 101105787A
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Abstract
The invention refers to a method and application of calculating long-sequence and infinite-sequence convolution with a cascade retaining method. The invention is applied to the case of limited long sequence. The invention has some systems, such as digital reverberation effectors, the impulse response thereof is long. The prior methods, including the cascade retaining method, require a great deal of storage space. Low-priced DSP chips only have 32k-below chip storage, but their speed indexes usually have margins. When the cascade retaining method is used to segment infinite input signals, the segmentation length is shortened greatly to make the segmented input signal slightly above the length of impulse response. In such a way the method can calculate the convolution of a long impulse response (limited length signal) and an infinite long input signal (another infinite sequence) with smaller storage. Although this would reduce the efficiency of calculation, the calculation speed of the current DSP chip can still meet the requirement for real-time process.
Description
Technical field
The present invention relates to a kind of new method and related application technical field that overlapping reservation method calculates long sequence and endless sequence convolution of using.
Background technology
As everyone knows, overlapping reservation method and overlapping additive process [the cold China that builds, Li Ping, Wang Lianghong, digital signal processing, National Defense Industry Press, 2002] be the main method of calculating a finite length sequence (normally impulse response) and another endless sequence convolution (normally input signal).In these methods, can adopt various fast transform algorithms such as fast fourier transform (FFT), Hart comes conversion (FHT) [Bracewell R N.The fast Hartley transform.Proc.IEEE fast, 1984,772 (8) .Pp.1832-1835] even arithmetic Fourier transform (AFT) [L.S.Reed et al., Fourier analysis and signal processingby use of the Mobius Inversion Formulas, IEEE Trans.ASSP, Vol.38, No3, Mar.1990] [Zhang Xianchao, Wu Jigang, Jiang Zengrong, Chen Guoliang, the arithmetic Fourier Transform Algorithm of discrete Fourier transformation, electronic letters, vol, 2000, and method [the Winograd S.On computing the discrete Fourier transform of various fast convolution algorithm such as Winograd (5)] based on the quick computation cycles convolution of Chinese remainder theorem and subscript mapping, Proc.Nat Acad.Sci.USA, 1976,73 (Apr): 1005-1006] and based on the method [Yang Jing that the one dimension convolution is mapped to two dimension, Xu Wei, Huang shows smooth, a kind of fast algorithm analysis of convolution, microelectronics and computing machine, 2003, (3)] etc., calculate sectional convolution.But this is generally used for finite length sequence is the short situation of impulse response sequence. for the long system of impulse response, as digital reverberation effect device, its typical impulse response reaches about 40000, directly adopts said method, the storage space that needs are a large amount of.And be that digital signal processing chip has only the sheet internal memory reserves below the 32k usually than the dsp chip of low price.It at number of patent application 200610051649.1 Chinese patent " a kind of digital acoustic field audio frequency signal processing method ", we are by being divided into impulse response low-and high-frequency two parts, and low frequency part adopts and extracts (sampling again), HFS adopts and blocks the data volume that (energy of HFS goes to zero when growing slightly in the time) reduces impulse response.But nonetheless, data volume is still quite big.Length such as impulse response reduces to 8000, and according to common overlapping additive process, the section length of input signal also wants 8000 at least.Also to respectively mend 8000 zero on this basis.The section length of so only storing impulse response and input signal just needs 32k.Common overlapping reservation method is also very nearly the same therewith.
Summary of the invention
Primary technical matters to be solved by this invention provides a kind of method of calculating long sequence and endless sequence convolution with overlapping reservation method, when it utilizes overlapping reservation method that input signal is carried out segmentation, section length original in this method is reduced, so just can calculate the convolution of longer impulse response and endless list entries with less memory space, lay the foundation for current dsp chip carries out reverberation processing in real time to digital audio and video signals, method is simple.
Another technical matters to be solved by this invention provides the new application of said method.
The present invention solves the technical scheme that above-mentioned primary technical matters adopts: a kind ofly calculate the method for long sequence and endless sequence convolution with overlapping reservation method, the steps include:
(1) degree of rectificating is that the quick Hart of the finite length sequence h (n) of N comes conversion H (k)=FHT[h (n)], the N+M point;
(2) to be divided into the N+M point be one section to endless list entries x (n), and the first batch data and a batch data subsequently have the N point overlapping, use x
i(n) (i=1,2,3 ... wait natural number in turn) list entries of expression after the segmentation;
(3) calculate N+M point x
i(n) FHTX
i(k)=FFT[x
i(n)];
(4) calculate Y
i(k)=X
i(k) [H (k)+H (M-k)]/2+X
i(M-k) [H (k)-H (M-k)]/2, the N+M point;
(5) calculate N+M point IFHT:y
i(n)=IFHT[Y
i(k)];
(6) will discard the y that front N is ordered
i(n) couple together in turn and obtain exporting y (n);
Wherein, described finite length sequence h (n) length is N, and the segmentation output length of endless list entries is M+N, and satisfies M+N=2
P, N, M, P are positive integers; And adopt quick Hart to come conversion FHT; It is characterized in that M is less than N.
Another aspect of the present invention content is, being provided with limit for length's sequence length is N, and the section length of endless list entries is N+M, 1) length M is very less than length N; 2) M+N=2
P, P is an integer; 3) be that the sound signal of 44kHz and sheet internal memory reserves are that 32K, arithmetic speed are the dsp chip of 80MIPS (Million Instruction PerSecond-1,000,000 instruction per seconds) for sample frequency, work as P=13, N gets about 7859, M gets about 333, can not have processing in real time under the condition of external memorizer, thereby can on the digital reverberation effect device that adopts above-mentioned dsp chip, use; 4) when P be any positive integer, particularly P＞13 o'clock, be f for sample frequency
sThe signal of Hz and sheet internal memory reserves are for being the dsp chip of V (IPS) more than or equal to 3 (M+N) byte, arithmetic speed, the ratio of M and N be N/M＜-1+V/6Pf
sPreferred N/M ≈ V/6Pf
sThereby, can not have processing in real time under the condition of external memorizer.
Length of the present invention is long sequences h (n) impulse response normally of N, and endless sequence x (n) input signal normally.
Another technical matters to be solved by this invention provides said method and is utilizing dsp chip not having under the condition of external memorizer digital audio and video signals is carried out simple application aspect the reverberation processing in real time.
Compared with prior art, the invention has the advantages that: when the endless signal that import is carried out segmentation, with section length compared with reducing significantly originally, make the list entries section length slightly greater than impulse response (finite length sequence) length, so just can calculate the convolution of longer impulse response and endless list entries with as far as possible little memory space, though this can cause counting yield to reduce, but the computing velocity of current dsp chip is enough high, can make full use of dsp chip speed, exchange for and carry out the needed storage space of this algorithm, making the dsp chip of current low price can carry out reverberation to digital audio and video signals handles in real time, method is simple, and is with low cost.
Embodiment
Below in conjunction with embodiment the present invention is described in further detail.
One. when the impulse response length N is 8000 left and right sides, the setting of list entries section length in the overlapping reservation method
(1) setting of original list entries section length and calculated amount memory space are analyzed in the overlap-save method
If impulse response h (n) length is N, the section length of list entries x (n) is N+M, adopts the overlapping reservation method calculating of FHT to have the step of limit for length's impulse response h (n) and endless list entries x (n) linear convolution to be:
1. ask the quick Hart of impulse response h (n) to come conversion H (k)=FHT[h (n)], the N+M point.
2. endless list entries x (n) being divided into the N+M point is one section, and the first batch data and a batch data subsequently have the N point overlapping, use x
i(n) (i=1,2,3 ... wait natural number in turn) list entries of expression after the segmentation.
3. calculate N+M point x
i(n) FHT:X
i(k)=FHT[x
i(n)].
4. calculate Y
i(k)=X
i(k) [H (k)+H (M-k)]]/2+X
i(M-k) [H (k)-H (M-k)]/2; The N+M point.
5. calculate N+M point IFHT.y
i(n)=IFHT[Y
i(k)].
6. will discard the y that front N is ordered
i(n) couple together in turn and obtain exporting y (n).
Adopt quick Hart to come conversion FHT to be because it saves the memory space of half than fast fourier transform FFT.Be not difficult to find out that the 1st, 2 steps needed storage space 2 (N+M); 3rd, 4,5 steps can original position calculate, and needed storage space N+M, needed storage space 3 (N+M) altogether.
Generally, get M 〉=N so that obtain to try one's best high efficient.When the impulse response length N is about 8000, calculate for ease of FHT, get N=8192=2
13Point, and establish M=N=8192, then overlapping reservation method calculates each time that sectional convolution needs storage space about 3 (N+M) ≈ 48k; On the other hand, owing to calculate N+M=2
14Point FHT needs multiplication 142
14-32
14+ 4=180228 time; Addition (3/2) 142
14-(3/2) 2
14+ 2=319490 time; Need 499718 of one-cycle instructions (typical dsp chip is carried out with an one-cycle instruction and once taken advantage of or addition) altogether.Therefore calculation procedure 3 and 5 needs one-cycle instruction 2499718=999436 altogether.In step 4, calculate each Y
i(k) need multiplication 2 times, addition 3 times for all k, needs one-cycle instruction 5 (N+M)=81920 altogether.Result's sectional convolution each time needs one-cycle instruction 999436+81920=1081356 time.Average each output sample needs 132 of one-cycle instruction 1081356/M=1081356/8192 ≈.And the arithmetic speed of the DSP of present low price is also more than 80MIPS.The sampling rate of sound signal is 44kHz, thus under real-time treatment conditions each sampling period can hold 8010
6The one-cycle instruction of/44k ≈ more than 1818.
For the voice applications of general dsp, speed index is had a surplus and storage space is tight slightly.Be significantly smaller than N if get M,, then can under the prerequisite that makes full use of DSP speed, required memory space obviously reduced as less than more than 5 times.
(2) the resetting and the analysis of calculated amount memory space of section length in the overlap-save method
For same length N is about 8000 impulse response h (n), and the section length of establishing list entries is N+M, makes N+M=8192=2
13So, need storage space 3 (N+M) ≈ 24k.Calculate N+M=2
13Point FHT needs multiplication 132
13-32
13+ 4=81924 time; Addition (3/2) 132
13-(3/2) 2
13+ 2=147458 time; Need 229380 of one-cycle instructions altogether. so calculation procedure 3 and 5 needs one-cycle instruction 2229380=458760 altogether. in step 4, need one-cycle instruction 5 (N+M)=40960 altogether.Result's sectional convolution each time needs one-cycle instruction 458760+40960=499720 time.Average each sampling point needs one-cycle instruction 499720/M.If M=1000, N=7192; Then every sampling point needs about 500 of fill order's cycles per instruction.If M=333, N=7859; Then every sampling point needs about 1500 of fill order's cycles per instruction.Can hold the capacity of 1818 above one-cycle instructions with each sampling period of this chip and compare, satisfy N+M=8192=2
13Condition under, get N=7859, can try one's best about M=333 and utilize the speed of DSP fully.
So, for essentially identical impulse response length (about 8000), same overlap-save method and the Hart of adopting comes conversion, when the M among the section length N+M that gets list entries is significantly smaller than the impulse response length N (the list entries section length is slightly greater than impulse response length), can make full use of dsp chip speed, exchange for and carry out the needed storage space of this algorithm.
Two. when impulse response h (n) length N is any positive integer, the setting of M among the section length N+M of list entries in the overlapping reservation method
If N+M=2
PAnd P＞13 (be N be about 16000 or more than) time, even if adopt above-mentioned principle, the memory capacity of this chip is also not enough.But for the big chip of other sheet internal memory reserves, it still can change the space with speed on the basis of above-mentioned principle.
If certain chip speed is V (Instruction Per Second), capacity is greater than 3 (N+M).If pending signal sampling frequency is f
s, then each sampling period can be held V/f under real-time treatment conditions
sIndividual one-cycle instruction.Calculate N+M=2
P(P can be any positive integer) some FHT needs multiplication P2
P-32
P+ 4 times; Addition (3/2) P2
P-(3/2) 2
P+ 2 times; Need one-cycle instruction (2.5P-4.5) 2 altogether
P+ 6 ≈ (2.5P-4.5) 2
PIndividual.Therefore calculation procedure 3 and 5 needs one-cycle instruction 2 (2.5P-4.5) 2 altogether
P=(5
P-9) 2
PIndividual; In step 4, need one-cycle instruction 52 altogether
PIndividual; Result's sectional convolution each time needs one-cycle instruction (5P-9) 2P+52
P=(5
P-4) 2
PInferior.Average each sampling point needs one-cycle instruction (5
P-4) 2P/M=(5P-4) (N+M)/M＜5P (N/M+1) is individual.Obviously 5P (N/M+1) must be less than V/f
s, promptly N/M＜-1+V/5Pf
sWe get 5P (N/M+1)=5V/6f
s, N/M=-1+V/6Pf then
s≈ V/6Pf
s
Overlapping reservation method is to calculate one of main method of limit for length's impulse response sequence and endless list entries convolution is arranged, and being generally used for finite length sequence is the short situation of impulse response sequence.In this case, people consider is computing velocity rather than calculates needed storage space, need not consider especially because short impulse response makes that needed storage space is quite limited.But for the long system of impulse response,, adopt the various existing method that comprises overlapping reservation method, all will need a large amount of storage spaces as digital reverberation effect device.And present widely used low price dsp chip has only the following sheet internal memory reserves of 32k usually, but its speed index often has affluence.The present invention proposes a kind of new application process, and the section length that makes list entries was compared with reducing significantly originally, and the section length of promptly getting list entries is slightly larger than impulse response length.Can make full use of dsp chip speed like this, exchange for and carry out the needed storage space of overlapping reservation method.
Claims (5)
1. the method with long sequence of overlapping reservation method calculating and endless sequence convolution the steps include:
(1) degree of rectificating is that the quick Hart of the finite length sequence h (n) of N comes conversion H (k)=FHT[h (n)], the N+M point;
(2) to be divided into the N+M point be one section to endless list entries x (n), and the first batch data and a batch data subsequently have the N point overlapping, use x
i(n) list entries of expression after the segmentation, i is natural number in turn;
(3) calculate N+M point x
i(n) FHT X
i(k)=FFT[x
i(n)];
(4) calculate Y
i(k)=X
i(k) [H (k)+H (M-k)]/2+X
i(M-k) [H (k)-H (M-k)]/2, the N+M point;
(5) calculate N+M point IFHT:y
i(n)=IFHT[Y
i(k)];
(6) will discard the y that front N is ordered
i(n) couple together in turn and obtain exporting y (n);
Wherein, described finite length sequence is impulse response normally, and length is N, and the segmentation output length of endless list entries is M+N, and satisfies M+N=2
P, N, M, P are positive integers; And adopt quick Hart to come conversion FHT; It is characterized in that M is less than N.
2. method according to claim 1 is characterized in that described P is any positive integer, particularly P＞13 o'clock, is f for sample frequency
sThe signal of Hz and sheet internal memory reserves are for being the dsp chip of V (IPS) greater than 3 (M+N) byte, arithmetic speed, the ratio of M and N be N/M＜-1+V/5Pf
s
3. method according to claim 2 is characterized in that the preferred V/6Pf of described N/M
sThereby, dsp chip is handled under the condition of external memorizer not in real time.
4. method according to claim 2, it is characterized in that described P is 13, N preferred 7859, M preferred 333, for sample frequency is that sound signal and the sheet internal memory reserves of 44kHz are that 32K, arithmetic speed are the dsp chip of 80MIPS, do not handle in real time under the condition of external memorizer having, thereby can on the digital reverberation effect device that adopts above-mentioned dsp chip, use.
5. the described method of claim 1 is characterized in that using on the digital reverberation effect device, and dsp chip is handled digital audio and video signals under the condition of external memorizer in real time not having.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103294646A (en) * | 2012-03-05 | 2013-09-11 | 中兴通讯股份有限公司 | Digital signal processing method and digital signal processor |
| CN109542837A (en) * | 2018-11-30 | 2019-03-29 | 上海寒武纪信息科技有限公司 | Operation method, device and Related product |
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2006
- 2006-07-12 CN CNA200610052452XA patent/CN101105787A/en active Pending
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103294646A (en) * | 2012-03-05 | 2013-09-11 | 中兴通讯股份有限公司 | Digital signal processing method and digital signal processor |
| CN103294646B (en) * | 2012-03-05 | 2017-12-05 | 山东比特智能科技股份有限公司 | Digital signal processing method and digital signal processor |
| CN109542837A (en) * | 2018-11-30 | 2019-03-29 | 上海寒武纪信息科技有限公司 | Operation method, device and Related product |
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