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
The Parseval’s theorem (a.k.a Plancherel theorem) expresses the energy of a signal in time-domain in terms of the average energy in its frequency components. Suppose if the x[n] is a discrete-time sequence of complex numbers of length N : xn={x0,x1,…,xN-1}, its N-point discrete Fourier transform (DFT)[1] : Xk={X0,X1,…,XN-1} is given by The inverse discrete Fourier … Read more
Key focus: Discuss statistical measures for stochastic signals : mean, variance, skewness, kurtosis, histogram, scatterplot, cross-correlation and auto-correlation. Deterministic and stochastic signals A deterministic signal is exactly predictable for the given time span of interest. It could be expressed using analytic form (example: x(t) = sin (2 π fc t) ). Many of the signals … 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: Develop basic understanding of digital filter design. Learn about fundamentals of FIR and IIR filters and the design choices. Analog filters and digital filters are the two major classification of filters, depending on the type of signal signal they process. An analog filter, processes continuous-time signal analog signals. Whereas, digital filters process sampled, … 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
Key focus: Fundamentals of signal processing for machine learning. Speaker identification is taken as an example for introducing supervised learning concepts. Signal Processing A signal, mathematically a function, is a mechanism for conveying information. Audio, image, electrocardiograph (ECG) signal, radar signals, stock price movements, electrical current/voltages etc.., are some of the examples. Signal processing is … Read more
In the previous post on Single Input Multiple Output (SIMO) models for receive diversity, various receiver diversity techniques were outlined. One of them is maximum ratio combining, the focus of the topic here. Channel model Assuming flat slow fading channel, the received signal model is given by where, is the channel impulse response, is the … Read more