Signal Processing for Communication Systems
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
Key focus: Learn how to generate color noise using auto regressive (AR) model. Apply Yule Walker equations for generating power law noises: pink noise, Brownian noise. Auto-Regressive (AR) model An uncorrelated Gaussian random sequence \(x[n]\) can be transformed into a correlated Gaussian random sequence \(y[n]\) using an AR time-series model. If a time series random … Read more
The aim of this article is to demonstrate the application of spectral factorization method in generating colored noise having Jakes power spectral density. Before continuing, I urge the reader to go through this post: Introduction to generating correlated Gaussian sequences. In spectral factorization method, a filter is designed using the desired frequency domain characteristics (like … Read more
Key focus: Colored noise sequence (a.k.a correlated Gaussian sequence), is a non-white random sequence, with non-constant power spectral density across frequencies. Introduction Speaking of Gaussian random sequences such as Gaussian noise, we generally think that the power spectral density (PSD) of such Gaussian sequences is flat.We should understand that the PSD of a Gausssian sequence … Read more
Generate linear chirps, view their evolving frequency, and compute FFT/PSD in Matlab and Python — with links to basic FFT plotting posts.
Generate a Gaussian pulse, compute its FFT/PSD, and see why a Gaussian time pulse has a Gaussian spectrum.
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
Generate a square wave, take its FFT/PSD, and recognize the odd-harmonic 1/n envelope predicted by Fourier series.
Matlab walk-through: sample a sinusoid, take FFT, build the frequency axis, and read peak locations — with Python twin link and FFT tool.
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