kissfft/fft.py
2003-12-07 04:04:27 +00:00

118 lines
2.7 KiB
Python

#!/usr/local/bin/python2.3
import math
import sys
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]
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 = []
for k in range(N):
F1k = Fp[k] + Fp[-k].conjugate()
F2k = -j*(Fp[k] - Fp[-k].conjugate())
print 'F2k[%d]=%s' % (k,F2k)
F.append( ( F1k + e ** ( -j*pi*k/N ) * F2k ) * .5 )
F.append( 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
if __name__ == "__main__":
main()