[SciPy-User] which FFT, convolve functions are the fastest one?
Thu Nov 11 02:40:23 CST 2010
> On 11/11/2010 10:10 AM, firstname.lastname@example.org wrote:
>> On Wed, Nov 10, 2010 at 7:53 PM, David<email@example.com> wrote:
>>> On 11/11/2010 08:41 AM, LittleBigBrain wrote:
>>>> Hi everyone,
>>>> I found lots of implement of FFT and convolve
>>>> scipy.signal.fft (from the source, it seems all import from scipy.fftpack?)
>>> scipy.fftpack is faster than numpy.fft, scipy.signal.fft is the same as
>>> scipy.fftpack as you noticed.
>>>>> From the source, it looks like fftpack.convolve and signal.fftconvolve
>>>> all based on fftpack, then what is the difference between them?
>>> Different APIs (mostly for historical reasons AFAIK)
>>>> I take a glance at the lfilter.c, surprisingly it is a completely
>>>> naive implement via polynomial function. I hope I am wrong about this.
>>> No, you're right, it is a straightforward implementation of time-domain
>> Signal.lfilter is an IIR filter and does convolution only as a special
>> case, and only with "same" mode. I'm very happy with it, and wish we
>> had a real nd version.
> By convolution, I meant the broad, signal processing kind of definition
> (with multiple boundary effects modes), not the mathematical definition
> which ignores boundary effects.
>> One difference in the speed I found in references and using it,
>> without real timing:
>> fftconvolve is only faster if you have two long arrays to convolve,
>> not if a long array is convolved with a short array.
> Yes, that's exactly right: convolution of 1d signals of size M and N is
> roughly O(MxN), whereas fft-based will be O(P log (P)) - which one is
> "best" depends on the ration M/N. There is also an issue with naive
> fft-based convolution: it uses a lot of memory (the whole fft has to be
> in memory).
Yes you are all right about this, that is why I asked "especially those
convolve() does not based on FFT". I just wanna use to for IIR filters,
which usually have an order far far less than 200.
> Certainly, one could think about implementing smarter strategies, like
> short-time fourier kind of techniques (OLA or OLS), which avoid taking
> the whole signal FFT, and as such avoid most usual issues associated
> with FFT-based convolution. I had such an implementation somwhere in the
> talkbox scikits, but I am not sure I ever committed something, and I
> don't really have time to work on it anymore...
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