Generate AWGN in Matlab/Octave without awgn() — variance from Eb/N0
Build AWGN from randn without Communications Toolbox: set noise variance from SNR or Eb/N0, generate real/complex noise, verify power.
Matlab Code
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.
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
Non-central chi-squared PDF — non-centrality λ, Matlab & Python
Non-central chi-squared distribution: PDF with non-centrality parameter λ, relation to Rician power / energy detection, and Matlab/Python sampling examples.
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