Signal Processing for Communication Systems
Key focus: Window function smooths the observed signal over the edges. Analysis of some important parameters to help select the window for an application. Spectral leakage As we know, the DFT operation can be viewed as processing a signal through a set of filter banks with bandwidth Δf centered on the bin (frequency) of interest … Read more
Key focus: Equivalent noise bandwidth (ENBW), is the bandwidth of a fictitious brick-wall filter that allows same amount of noise as a window function. Learn how to calculate ENBW in applications involving window functions and FFT operation. FFT and spectral leakage As we know, the DFT operation can be viewed as processing a signal through … Read more
Key focus: Simulate bit error rate performance of Binary Phase Shift Keying (BPSK) modulation over AWGN channel using complex baseband equivalent model in Python & Matlab. Why complex baseband equivalent model The passband model and equivalent baseband model are fundamental models for simulating a communication system. In the passband model, also called as waveform simulation … Read more
The phase transition properties of the different variants of QPSK schemes and MSK, are easily investigated using constellation diagram. Let’s demonstrate how to plot the signal space constellations, for the various modulations used in the transmitter. Typically, in practical applications, the baseband modulated waveforms are passed through a pulse shaping filter for combating the phenomenon … Read more
Key focus: Shown with examples: let’s estimate and plot the probability density function of a random variable using Python’s Matplotlib histogram function. Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability … Read more
Let’s see how to design a simple digital FIR filter to reject unwanted frequencies in an incoming signal. As a per-requisite, I urge you to read through this post: Introduction to digital filter design Background on transfer function The transfer function of a system provides the underlying support for ascertaining vital system response characteristics without … Read more
Key focus: Let’s demonstrate basics of univariate linear regression using Python SciPy functions. Train the model and use it for predictions. Linear regression model Regression is a framework for fitting models to data. At a fundamental level, a linear regression model assumes linear relationship between input variables () and the output variable (). The input … Read more
Key focus: Generating simulated dataset for regression problems using sklearn make_regression function (Python 3) is discussed in this article. Problem statement Suppose, a survey is conducted among the employees of a company. In that survey, the salary and the years of experience of the employees are collected. The aim of this data collection is to … Read more
Often the most basic step in signal processing of audio files, one would like to visualize an audio sample file as time-series data. Audio sounds can be thought of as an one-dimensional vector that stores numerical values corresponding to each sample. The time-series plot is a two dimensional plot of those sample values as a … Read more
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