I applied Butterworth filters (
order=5) that have different cutoff frequencies to a simple signal composed of four sinusoidal oscillations and computed its PSD.
% Simulated signal data = np.zeros((27000, 62)) t = np.arange(data.shape) for ch in range(62): for f in [1.2, 12, 24, 36]: data[:, ch] += np.sin(2*np.pi*t*f/2500)
However, I noticed that the spectral power changes depending on how I set the cutoff frequencies. Here, the spectral power values at 12 and 24 Hz decreases if I use a filter with the low and high cutoffs of 0.25 and 125 Hz (compared to a bandpass filter of 1-45 Hz). I understand that power at 1.2 and 36 Hz can be affected by the transition band but am confused why there are differences in 12 and 24 Hz. It seems like the amount of power decreased at 1.2 and 36 Hz moved to the power values at 12 and 24 Hz.
Is there any mathematical reason behind this phenomenon?
Without frequencies near transition band, two filters give a near-identical result.
The filter profile of the Butterworth filter is as below: