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