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.
FFT
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.
Plot FFT using Python – FFT of sine wave & cosine wave
FFT Lab path:Complex DFT, bins & fftshift → Magnitude & phase → Spectral leakage → Plot: Matlab / PythonTool: FFT bin frequency & resolution calculator Key focus: Learn how to plot FFT of sine wave and cosine wave using Python. Understand FFTshift. Plot one-sided, double-sided and normalized spectrum using FFT. Introduction Numerous texts are available … Read more
Phase demodulation via Hilbert transform: Hands-on
Analytic Signal Lab (same on every page in this path) 1. Hilbert / FFT → 2. Envelope & IF → 3. Phase demodulation (you are here) Tools: Hilbert / analytic signal demo Key focus: Demodulation of phase modulated signal by extracting instantaneous phase can be done using Hilbert transform. Hands-on demo in Python & Matlab. … Read more
Envelope and instantaneous frequency from the Hilbert transform
Extract amplitude envelope, instantaneous phase, and instantaneous frequency via the analytic signal — practical Hilbert/FFT notes.
Analytic signal & Hilbert transform (FFT) — Matlab/Python envelope
Build the analytic signal with Hilbert or FFT, extract envelope and instantaneous phase/frequency — Matlab, Python, and an interactive Hilbert demo.
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.
Autocorrelation matrix in Matlab & Python — build R for Wiener / MVDR
Build the autocorrelation (covariance) matrix R from snapshots in Matlab or NumPy — including complex conjugate correlation — for Wiener, LMS, and MVDR beamformers.
Chirp signal spectrum — frequency sweep, FFT, and PSD (Matlab & Python)
Generate a linear chirp, view the spectrogram/FFT, and estimate PSD in Matlab or Python — how the instantaneous frequency sweep fills the spectrum.