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#!/usr/bin/env python
# Copyright (c) 2003-2010, Mark Borgerding. All rights reserved.
# This file is part of KISS FFT - https://github.com/mborgerding/kissfft
#
# SPDX-License-Identifier: BSD-3-Clause
# See COPYING file for more information.
import math
import sys
import random
pi=math.pi
e=math.e
j=complex(0,1)
def fft(f,inv):
n=len(f)
if n==1:
return f
for p in 2,3,5:
if n%p==0:
break
else:
raise Exception('%s not factorable ' % n)
m = n/p
Fout=[]
for q in range(p): # 0,1
fp = f[q::p] # every p'th time sample
Fp = fft( fp ,inv)
Fout.extend( Fp )
for u in range(m):
scratch = Fout[u::m] # u to end in strides of m
for q1 in range(p):
k = q1*m + u # indices to Fout above that became scratch
Fout[ k ] = scratch[0] # cuz e**0==1 in loop below
for q in range(1,p):
if inv:
t = e ** ( j*2*pi*k*q/n )
else:
t = e ** ( -j*2*pi*k*q/n )
Fout[ k ] += scratch[q] * t
return Fout
def rifft(F):
N = len(F) - 1
Z = [0] * (N)
for k in range(N):
Fek = ( F[k] + F[-k-1].conjugate() )
Fok = ( F[k] - F[-k-1].conjugate() ) * e ** (j*pi*k/N)
Z[k] = Fek + j*Fok
fp = fft(Z , 1)
f = []
for c in fp:
f.append(c.real)
f.append(c.imag)
return f
def real_fft( f,inv ):
if inv:
return rifft(f)
N = len(f) / 2
res = f[::2]
ims = f[1::2]
fp = [ complex(r,i) for r,i in zip(res,ims) ]
print 'fft input ', fp
Fp = fft( fp ,0 )
print 'fft output ', Fp
F = [ complex(0,0) ] * ( N+1 )
F[0] = complex( Fp[0].real + Fp[0].imag , 0 )
for k in range(1,N/2+1):
tw = e ** ( -j*pi*(.5+float(k)/N ) )
F1k = Fp[k] + Fp[N-k].conjugate()
F2k = Fp[k] - Fp[N-k].conjugate()
F2k *= tw
F[k] = ( F1k + F2k ) * .5
F[N-k] = ( F1k - F2k ).conjugate() * .5
#F[N-k] = ( F1kp + e ** ( -j*pi*(.5+float(N-k)/N ) ) * F2kp ) * .5
#F[N-k] = ( F1k.conjugate() - tw.conjugate() * F2k.conjugate() ) * .5
F[N] = complex( Fp[0].real - Fp[0].imag , 0 )
return F
def main():
#fft_func = fft
fft_func = real_fft
tvec = [0.309655,0.815653,0.768570,0.591841,0.404767,0.637617,0.007803,0.012665]
Ftvec = [ complex(r,i) for r,i in zip(
[3.548571,-0.378761,-0.061950,0.188537,-0.566981,0.188537,-0.061950,-0.378761],
[0.000000,-1.296198,-0.848764,0.225337,0.000000,-0.225337,0.848764,1.296198] ) ]
F = fft_func( tvec,0 )
nerrs= 0
for i in range(len(Ftvec)/2 + 1):
if abs( F[i] - Ftvec[i] )> 1e-5:
print 'F[%d]: %s != %s' % (i,F[i],Ftvec[i])
nerrs += 1
print '%d errors in forward fft' % nerrs
if nerrs:
return
trec = fft_func( F , 1 )
for i in range(len(trec) ):
trec[i] /= len(trec)
for i in range(len(tvec) ):
if abs( trec[i] - tvec[i] )> 1e-5:
print 't[%d]: %s != %s' % (i,tvec[i],trec[i])
nerrs += 1
print '%d errors in reverse fft' % nerrs
def make_random(dims=[1]):
import Numeric
res = []
for i in range(dims[0]):
if len(dims)==1:
r=random.uniform(-1,1)
i=random.uniform(-1,1)
res.append( complex(r,i) )
else:
res.append( make_random( dims[1:] ) )
return Numeric.array(res)
def flatten(x):
import Numeric
ntotal = Numeric.product(Numeric.shape(x))
return Numeric.reshape(x,(ntotal,))
def randmat( ndims ):
dims=[]
for i in range( ndims ):
curdim = int( random.uniform(2,4) )
dims.append( curdim )
return make_random(dims )
def test_fftnd(ndims=3):
import FFT
import Numeric
x=randmat( ndims )
print 'dimensions=%s' % str( Numeric.shape(x) )
#print 'x=%s' %str(x)
xver = FFT.fftnd(x)
x2=myfftnd(x)
err = xver - x2
errf = flatten(err)
xverf = flatten(xver)
errpow = Numeric.vdot(errf,errf)+1e-10
sigpow = Numeric.vdot(xverf,xverf)+1e-10
snr = 10*math.log10(abs(sigpow/errpow) )
if snr<80:
print xver
print x2
print 'SNR=%sdB' % str( snr )
def myfftnd(x):
import Numeric
xf = flatten(x)
Xf = fftndwork( xf , Numeric.shape(x) )
return Numeric.reshape(Xf,Numeric.shape(x) )
def fftndwork(x,dims):
import Numeric
dimprod=Numeric.product( dims )
for k in range( len(dims) ):
cur_dim=dims[ k ]
stride=dimprod/cur_dim
next_x = [complex(0,0)]*len(x)
for i in range(stride):
next_x[i*cur_dim:(i+1)*cur_dim] = fft(x[i:(i+cur_dim)*stride:stride],0)
x = next_x
return x
if __name__ == "__main__":
try:
nd = int(sys.argv[1])
except:
nd=None
if nd:
test_fftnd( nd )
else:
sys.exit(0)
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