1 | initial version |

Finally I decided to create a simple as a log hand-made FFT filter. The concept is as follows:

- Perform the direct Fourier transform.
- Zero out the coefficients corresponding to the target frequencies
- Perform the inverse Fourier transform.

I borrowed this idea described here and wrote the following function:

```
def fft_lowpass_filter(signal, min_period=2):
"""Applies a simple as a log FFT lowpass filter to a signal.
INPUT:
- ``signal`` -- a list of data representing the sampled signal;
- ``min_period`` -- a threshold for the lowpass filter (the minimal period
of the oscillations which should be left intact) expressed in a number of
samples per one full oscillation.
EXAMPLES:
If you have a sampling frequency equal to 1 Hz (one sample per second)
and want to filter out all the frequencies higher than 0.5 Hz (two samples
per one oscillation period) you should call this function like this::
sage: fft_lowpass_filter(signal, min_period=2)
If you, for example, have a sampling frequency of 1 kHz (1000 samples per
second) and wish to filter out all frequencies hihger than 50 Hz, you should
use the value of ``min_period`` = <sampling frequency> / <cutoff frequency> = 1000 Hz / 50 Hz = 20::
sage: fft_lowpass_filter(signal, min_period=20)
"""
import scipy
signal_fft = scipy.fft(signal)
spectrum_array_length = n(len(signal_fft))
i = 0 # This is used instead of ' for i in range()'
while i < spectrum_array_length: # because the 'signal' array can be rather long
if i >= spectrum_array_length/min_period :
signal_fft[i] = 0
i += 1
signal_filtered = scipy.ifft(signal_fft)
fft_filtered_signal = []
filtered_signal_length = n(len(signal_filtered))
i = 0
while i < filtered_signal_length:
fft_filtered_signal.append(float(signal_filtered[i]))
i += 1
norm = max(signal)/max(fft_filtered_signal) # In case we need
# to renormalize
fft_filtered_signal_length = n(len(fft_filtered_signal)) # the filtered signal
i = 0 # in order to obtain
while i < fft_filtered_signal_length: # the same amplitude
fft_filtered_signal[i] *= norm # as the inintial
i += 1 # signal had.
return fft_filtered_signal
```

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