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jakevdp / nfft

Lightweight non-uniform Fast Fourier Transform in Python

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how to use

dtsonov opened this issue · comments

commented

Hello,
I installed NFFT and tried forward and backward transform, as is shown on the examples.
After backward transform the input data I got is very different from the original input data.
Probably I'm not using the transform correctly. Would some one help with it.
Here is my code:

import nfft
import numpy as np
import matplotlib.pyplot as plt

data = np.array([1.431,   1.4312,  1.4314,  1.4315,  1.4314,  1.4309,  1.4309,  1.4306,  1.4303,
  1.4299,  1.4299,  1.4297,  1.43,    1.4299,  1.4302,  1.4299,  1.4297,  1.4296,
  1.4299,  1.4298,  1.43,    1.4298,  1.4298,  1.43,    1.4301,  1.4301,  1.4304,
  1.43,    1.43,    1.4303,  1.4304,  1.4305,  1.4303,  1.4303,  1.4306, 1.4304,
  1.4309,  1.4305,  1.4306,  1.4306,  1.4296,  1.4283,  1.4288,  1.4295,  1.4298,
  1.4294,  1.4291,  1.4288,  1.4284,  1.4287,  1.4289,  1.4289,  1.429,   1.4288,
  1.4286,  1.4283,  1.4276,  1.4276,  1.4279,  1.428,   1.4279,  1.4281,  1.4274,
  1.4273])

x = -0.5 + data
f = np.sin(10 * 2 * np.pi * x)

k = -20 + np.arange(40)

#forward Fourier
f_hat = nfft.nfft_adjoint(x, f, len(k))
plt.title('fft transform')
plt.plot(k, f_hat.real, label='real')
plt.plot(k, f_hat.imag, label='imag')
plt.show()

#backward Fourier
recf = nfft.nfft(x, f_hat)
plt.title('backward transform')
plt.plot(np.abs(recf))
plt.show()
    
#input data
plt.title('input data')
plt.plot(data)
plt.show()
commented

Yes, the documentation is not great, and I'm not sure I'll have time to address that any time soon. One thing: it's strange that you're subtracting 0.5 from your data. The reason I do that in the example is to get data that lies in the range [-0.5, 0.5]. Your data don't lie between 0 and 1, so I can't see any reason why you'd want to subtract 0.5.

commented

Also, if you plot f vs x, you'll see that your data is effectively a straight line... I wouldn't expect an fft to pull out meaningful frequency information from a non-periodic signal.

commented

When you plot your input data, you use plot.plot(data). That is not your input data: your input data is plt.plot(x, f)

commented

Here's how you can approximate the input data for an NFFT by doing a round-trip: note that it takes a LOT of frequencies to get a close approximation: this is because the effective Nyquist frequency is very large when data are not equally spaced.

import nfft
import numpy as np
import matplotlib.pyplot as plt

x = 100 * np.random.rand(1000)
f = np.sin(x / 10)

N = 1000000
k = -N / 2 + np.arange(N)
f_hat = nfft.nfft_adjoint(x, f, N)

f_reconstructed = nfft.nfft(x, f_hat) / N
plt.plot(x, f, '.', color='blue')
plt.plot(x, f_reconstructed, '.', color='red')

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