Plot FFT using Python – FFT of sine wave & cosine wave

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 to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT).  Often we are confronted with the need … Read more

Generate color noise using Auto-Regressive (AR) model

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 can be transformed into a correlated Gaussian random sequence using an AR time-series model. If a time series random sequence is … Read more

Generating colored noise with Jakes PSD: Spectral factorization

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

Generate correlated Gaussian sequence (colored noise)

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

Chirp Signal – FFT & PSD in Matlab & Python

Key focus: Know how to generate a Chirp signal, compute its Fourier Transform using FFT and power spectral density (PSD) in Matlab & Python. Introduction All the signals discussed so far do not change in frequency over time. Obtaining a signal with time-varying frequency is of main focus here. A signal that varies in frequency … Read more

Gaussian Pulse – FFT & PSD in Matlab & Python

Key focus: Know how to generate a gaussian pulse, compute its Fourier Transform using FFT and power spectral density (PSD) in Matlab & Python. 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 … Read more

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

Generating Basic signals – Square Wave 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, squarewave, isolated rectangular pulse, exponential decay, chirp signal) for simulation purpose. I intend to show (in a series of articles) how … Read more

Plot FFT using Matlab – FFT of sine wave & cosine wave

Key focus: Learn how to plot FFT of sine wave and cosine wave using Matlab. Understand FFTshift. Plot one-sided, double-sided and normalized spectrum. Introduction 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 … 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