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
Equivalent noise bandwidth (ENBW) of FFT windows — formula & table
What ENBW means for FFT windows, the time-domain formula used in code, ENBW in bins for common windows, Python (SciPy), and how it shifts the noise floor.
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, and FFT — envelope and instantaneous phase
How the analytic signal and Hilbert transform give envelope and instantaneous phase/frequency, FFT implementation tips, and links to the envelope follow-on.
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.
Construct autocorrelation Matrix in Matlab & Python
Auto-correlation, also called series correlation, is the correlation of a given sequence with itself as a function of time lag. Cross-correlation is a more generic term, which gives the correlation between two different sequences as a function of time lag. Given two sequences $latex x$ and $latex y$, the cross-correlation at times separated by lag … Read more
Chirp signals — frequency sweep, FFT, and power spectral density
Generate linear chirps, view their evolving frequency, and compute FFT/PSD in Matlab and Python — with links to basic FFT plotting posts.