Gaussian pulse and its PSD — generate, FFT, and spectrum shape
Generate a Gaussian pulse, compute its FFT/PSD, and see why a Gaussian time pulse has a Gaussian spectrum.
FFT
Generating Basic signals – Rectangular Pulse and Power Spectral Density using FFT
Numerous texts are available to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT). Often we are confronted with the need to generate simple, standard signals (sine, cosine, Gaussian pulse, square wave, isolated rectangular pulse, exponential decay, chirp signal) for simulation purpose. I intend to show (in a series of articles) … Read more
Square wave and its PSD — harmonics via FFT
Generate a square wave, take its FFT/PSD, and recognize the odd-harmonic 1/n envelope predicted by Fourier series.
Plot FFT of sine and cosine in Matlab — spectrum peaks done right
Matlab walk-through: sample a sinusoid, take FFT, build the frequency axis, and read peak locations — with Python twin link and FFT tool.
FFT spectral leakage — causes, scalloping, and how windows help
Why FFT bins leak when tones miss bin centers, what scalloping loss is, and how windowing + ENBW trade leakage against noise bandwidth.