frequency analysis without numpy

[debug]

Hi-

I've been using python now for about 2 months for plugin development
within Maya (a commercial 3d application). I'm currently in the
process of writing a sound analysis plugin for maya and have completed
a good portion of it including the ability to retrieve the amplitude
at certain intervals from a wav file.

The next part of the project however consists of analysing the wav
file and outputting the amplitude at certain frequencies. Due to the
need of distributing this to many computers after it has been finished
I'm reluctant to use an external python module for FFT'ing. Accuracy
and speed aren't really issues as just a generalisation of the
amplitude of low, medium and high frequencies is required.

Do you either know of any generic FFT functions written in python that
could just be inserted into my processing class (open source
licensed).

So far i've managed to put together a chunk of code but I'm not sure
its returning the right values, any ideas?

import wave
import sys
import array
import struct
from cmath import pi, exp


def nextpow2(i):
n = 2
while n < i: n = n * 2
return n

def bitrev(x):
N, x = len(x), x[:]
if N != nextpow2(N): raise ValueError, 'N is not power of 2'
for i in range(N):
k, b, a = 0, N>>1, 1
while b >= a:
if b & i: k = k | a
if a & i: k = k | b
b, a = b>>1, a<<1
if i < k: # important not to swap back
x, x[k] = x[k], x
return x



def fft(x, sign=-1):
N, W = len(x), []
for i in range(N): # exp(-j...) is default
W.append(exp(sign * 2j * pi * i / N))
x = bitrev(x)
m = 2
while m <= N:
for s in range(0, N, m):
for i in range(m/2):
n = i * N / m
a, b = s + i, s + i + m/2
x[a], x = x[a] + W[n % N] * x, x[a] - W[n % N] * x

m = m * 2
return x



def ifft(X):
N, x = len(X), fft(X, sign=1) # e^{j2\pi/N}
for i in range(N):
x = x / float(N)
return x




fp = wave.open("hankuncom.wav","rb")
sample_rate = fp.getframerate()
total_num_samps = fp.getnframes()
fft_length = 4096
num_fft = (total_num_samps / fft_length ) - 2


temp = []

for i in range(num_fft):
tempb = fp.readframes(fft_length)
moo = struct.unpack("%uh"%(fft_length),tempb)
temp.append(moo)


listed = list(temp[0])

freq_pwr = fft(listed)

print(freq_pwr)

fp.close()

Quick warning this code snippet does run slowly
Thanks!

The wav file referenced in the script is here: www.reality-debug.co.uk/hankuncom.zip

 

[sturlamolden]

So far i've managed to put together a chunk of code but I'm not sure
its returning the right values, any ideas?

Don't use the periodogram for frequency analysis; it is not a good
estimate of the power spectrum. According to the Wiener-Khintchin
theorem, the power spectrum is the Fourier transform of the
autocorrelation, not the Fourier transform of the signal. You don't
want to just FFT the signal. FFTs are used for spectral estimation,
but not to obtain the periodogram. The periodogrgam is full of noise
and spectral leakage. And even worse, the variance of the periodogram
is constant, not inversely proportional to the number of samples. This
is not how you want a spectrum estimator to behave.

Consider using Thompson's multitaper method, autoregression (maximum
entropy), or Welch method for your frequency estimates. Blackman-
Tuckey is also a possibility, but I see no reason to prefer that to
Welch. Multitaper and AR tends to be the better options though, but
they are not as fast as Welch' method.

You probably also want to use real FFTs instead of complex FFTs,
unless you are interested in estimating the negative frequencies as
well. For common spectral analysis, real FFTs are almost always what
you want (complex FFTs can be used, but the incur redundant work).

Apart from that, an FFT in pure python is going to be atrociously slow
for anything but the shortest signals. I cannot imagine why you want
to do this. There are many free FFT libraries around, including
FFTPACK (used by NumPy) and FFTW.

The easiest way to check your FFT is to compare with a verified
implementation. I'd use NumPy or Matlab for that.



S.M.

 

[sturlamolden]

Apart from that, an FFT in pure python is going to be atrociously slow
for anything but the shortest signals. I cannot imagine why you want
to do this.

Just to elaborate on this:

The whole purpose of using FFT is speed. That pretty much excludes the
use of Python.

If you don't care about speed, you could just as well compute the DFT
directly. The FFT is just a O(n lon n) algorithm for computing the
DFT. Here is a DFT with O(N**2) behavior:


from math import sin, cos, pi

def real_dft(x):
''' DFT for a real valued sequence x '''
r = []
N = len(x)
M = N//2 + 1 if N%2 else N//2
for n in range(M):
s = 0j
for k in range(N):
tmp = 2*pi*k*n/N
s += x[k] * (cos(tmp) - 1j*sin(tmp))
r.append(s)
return r



S.M.

 

[philbru]

Consider using Thompson's multitaper method, autoregression (maximum
entropy), or Welch method for your frequency estimates. Blackman-
Tuckey is also a possibility, but I see no reason to prefer that to
Welch. Multitaper and AR tends to be the better options though, but
they are not as fast as Welch' method.

There is a fortran program named rainbow that has some dozen of these
methods to compare with. Rainbow is located at
http://www.digitalCalculus.com/demo/rainbow.html. I recommend Burg's
method or AutoCorrelation but its data dependent for best choice.

Phil

 

[debug]

Apart from that, an FFT in pure python is going to be atrociously slow
for anything but the shortest signals. I cannot imagine why you want
to do this.

Just to elaborate on this:

The whole purpose of using FFT is speed. That pretty much excludes the
use of Python.

If you don't care about speed, you could just as well compute the DFT
directly. The FFT is just a O(n lon n) algorithm for computing the
DFT. Here is a DFT with O(N**2) behavior:

from math import sin, cos, pi

def real_dft(x):
   ''' DFT for a real valued sequence x '''
   r = []
   N = len(x)
   M = N//2 + 1 if N%2 else N//2
   for n in range(M):
      s = 0j
      for k in range(N):
         tmp = 2*pi*k*n/N
         s += x[k] * (cos(tmp) - 1j*sin(tmp))
      r.append(s)
   return r

S.M.

Thanks for the quick reply, so what do I pass the real_dft function
(obviously a list) but do I pass it the unpacked binary data?

Dom