[SciPy-User] which FFT, convolve functions are the fastest one?

[braingateway]

josef.pktd at gmail.com :
> On Thu, Nov 11, 2010 at 3:40 AM, braingateway <braingateway at gmail.com> wrote:
>   
>> David :
>>     
>>> On 11/11/2010 10:10 AM, josef.pktd at gmail.com wrote:
>>>
>>>       
>>>> On Wed, Nov 10, 2010 at 7:53 PM, David<david at silveregg.co.jp>  wrote:
>>>>
>>>>         
>>>>> On 11/11/2010 08:41 AM, LittleBigBrain wrote:
>>>>>
>>>>>           
>>>>>> Hi everyone,
>>>>>>
>>>>>> I found lots of implement of FFT and convolve
>>>>>> numpy.fft
>>>>>> scipy.fftpack
>>>>>> 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
>>>>> convolution.
>>>>>
>>>>>           
>>>> 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.
>>     
>
> How can you use (regular) convolve for IIR filters?
> I thought it only works for moving average filters.
>
> Josef
>   
FIR is actually a convolution. IIR can use Direct form II, which split 
into a feedback and a FIR. You can do it by maitainning a buffer and a 
convolution.

LittleBigBrain
>
>   
>>> 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...
>>>
>>> cheers,
>>>
>>> David
>>> _______________________________________________
>>> SciPy-User mailing list
>>> SciPy-User at scipy.org
>>> http://mail.scipy.org/mailman/listinfo/scipy-user
>>>
>>>       
>> Sincerely,
>>
>> LittleBigBrain
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>>     
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