Creating a composite signal
Build a signal by summing sine waves at different frequencies. This is the starting point for most frequency-domain analysis.Computing the FFT and finding frequency components
The FFT converts a time-domain signal into its frequency-domain representation, revealing which frequencies are present.Filtering frequencies and inverse FFT
Remove unwanted frequencies by zeroing out their components in the frequency domain, then transform back to the time domain.Using fftfreq and fftshift
fftfreq returns the frequency bins for each FFT output element. fftshift rearranges the output so that the zero-frequency component is at the center, which is the standard convention for visualization.
Convolution with a kernel
Convolution is fundamental to signal processing — it is used for smoothing, differentiation, edge detection, and more. numpy-ts providesconvolve for 1-D convolution.
The
'same' mode returns output with the same length as the input, 'full' returns the full convolution (length M+N-1), and 'valid' returns only the part computed without zero-padded edges.Real FFT for real-valued signals
When your input is purely real (no imaginary component),rfft is more efficient than fft because it exploits the conjugate symmetry of the spectrum.