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.
Tips & Tricks
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.
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.
Generate multiple sequences of correlated random variables
In the previous post, a method for generating two sequences of correlated random variables was discussed. Generation of multiple sequences of correlated random variables, given a correlation matrix is discussed here. Correlation Matrix Correlation matrix defines correlation among N variables. It is a symmetric $latex N \times N $ matrix with the $latex (ij)^{th} $ … Read more
Generate two correlated random sequences
This article discusses the method of generating two correlated random sequences using Matlab. If you are looking for the method on generating multiple sequences of correlated random numbers, I urge you to go here. Generating two vectors of correlated random numbers, given the correlation coefficient $latex \rho $, is implemented in two steps. The first … Read more
Methods to compute linear convolution
Mathematical details of convolution, its relationship to polynomial multiplication and the application of Toeplitz matrices in computing linear convolution are discussed in the previous article. A short survey of different techniques to compute discrete linear convolution (with Matlab code) is given here. Definition Given an LTI (Linear Time Invariant) system with impulse response \(h[n]\) and … Read more
Convolution: understand the mathematics
Convolution operation is ubiquitous in signal processing applications. The mathematics of convolution is strongly rooted in operation on polynomials. The intent of this text is to enhance the understanding on mathematical details of convolution. Polynomial functions: Polynomial functions are expressions consisting of sum of terms, where each term includes one or more variables raised to … Read more
Compute signal power in Matlab
Calculating the energy and power of a signal was discussed in one of the previous posts. Here, we will verify the calculation of signal power using Discrete Fourier Transform (DFT) in Matlab. Check here to know more on the concept of power and energy. The total power of a signal can be computed using the … Read more