Window function figures of merit — scalloping, sidelobes, and ENBW
Compare FFT windows by scalloping loss, sidelobe level, 3 dB bandwidth, and ENBW — and when to pick Hann vs Blackman-Harris vs flattop.
dft
ENBW of FFT windows — formula, table, Matlab & Python
Equivalent noise bandwidth (ENBW) of FFT windows: time-domain formula, table for common windows, Matlab/Python code, and noise-floor correction.
Parseval’s theorem — energy in time equals energy in frequency
Parseval’s theorem (Plancherel): sum/integral of |x|² equals sum/integral of |X|² (with consistent DFT scaling). Derivation intuition and FFT checks.
FFT magnitude and phase spectrum — how to interpret (and fix noisy phase)
How to get amplitude and phase from an FFT: |X[k]|, atan2, why phase looks noisy, the magnitude threshold fix, Matlab + Python, and links to bins/fftshift and the FFT calculator.
Interpret FFT results — complex DFT, frequency bins, and fftshift
How DFT bins map to Hz, what negative frequencies mean, when to use fftshift/ifftshift, and how this pairs with magnitude/phase plots.