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decimation in time split-radix FFT
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import numpy as np | |
def sfft(x): | |
n = len(x) | |
if n==1: | |
return x | |
elif n==2: | |
return np.r_[x[0]+x[1], x[0]-x[1]] | |
else: | |
w = np.exp(-2j*np.pi/n*np.arange(n//4)) | |
w3 = np.exp(-2j*np.pi/n*3*np.arange(n//4)) | |
x02 = sfft(x[0::2]) | |
x1 = sfft(x[1::4])*w | |
x3 = sfft(x[3::4])*w3 | |
x1_ = x1+x3 | |
x3_ = x1-x3 | |
return np.r_[x02[:n//4] + x1_, | |
x02[n//4:] - 1j*x3_, | |
x02[:n//4] - x1_, | |
x02[n//4:] + 1j*x3_] | |
if __name__=="__main__": | |
print(sfft(np.arange(32))) |
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