Question

is there any prepared function in python to apply a filter (for example Butterworth filter) to a given signal?
I looking for such a function in ‘scipy.signal’ but I haven’t find any useful functions more than filter design ones.
actually I want this function to convolve a filter with the signal.

Answer 1

Yes! There are two:

scipy.signal.filtfilt
scipy.signal.lfilter

There are also methods for convolution (convolve and fftconvolve), but these are probably not appropriate for your application because it involves IIR filters.

Full code sample:

b, a = scipy.signal.butter(N, Wn, 'low')
output_signal = scipy.signal.filtfilt(b, a, input_signal)

You can read more about the arguments and usage in the documentation. One gotcha is that Wn is a fraction of the Nyquist frequency (half the sampling frequency). So if the sampling rate is 1000Hz and you want a cutoff of 250Hz, you should use Wn=0.5.

By the way, I highly recommend the use of filtfilt over lfilter (which is called just filter in Matlab) for most applications. As the documentation states:

This function applies a linear filter twice, once forward and once backwards. The combined filter has linear phase.

What this means is that each value of the output is a function of both “past” and “future” points in the input equally. Therefore it will not lag the input.

In contrast, lfilter uses only “past” values of the input. This inevitably introduces a time lag, which will be frequency-dependent. There are of course a few applications for which this is desirable (notably real-time filtering), but most users are far better off with filtfilt.