Articles | Page 11 of 36

Linear interpolation between pilot subcarriers

July 18, 2022 Wireless and SDR

Channel Estimation in OFDM Systems

Channel estimation in single-carrier systems has been described in a previous article. In OFDM systems, each subcarrier acts as an independent channel as long as there is no Inter-Carrier Interference (ICI) left in the synchronized signal. The options of both a training sequence and individual pilots are available for channel estimation and the choice between the two depends on time variation rate of the channel as well as the computational complexity. Many systems acquire the channel through the preamble while employ the pilots for channel tracking. The discussion in this article is mostly based on Ref. [1]. For a simplified

Time and frequency response of a lowpass FIR filter designed with Parks-McClellan algorithm for N=33

August 23, 2022 DSP

Why FIR Filters have Linear Phase

One of the most attractive properties of a Finite Impulse Response (FIR) filter is that a linear phase response is easier to achieve. Not all FIR filters have linear phase though. This is only possible when the coefficients or taps of the filter are symmetric or anti-symmetric around a point. Today I want to describe the reason behind this kind of phase response in an intuitive manner. We have described Finite Impulse Response (FIR) filters before. Moreover, we have also discussed that the Discrete Fourier Transform (DFT) of a signal is complex in general and therefore both magnitude and phase

May 2, 2021 DSP

Convolution and Fourier Transform

One question I am frequently asked is regarding the definition of Fourier Transform. A continuous-time Fourier Transform for time domain signal $x(t)$ is defined as \[ X(\Omega) = \int _{-\infty} ^{\infty} x(t) e^{-j\Omega t} dt \] where $\Omega$ is the continuous frequency. A corresponding definition for discrete-time Fourier Transform for a discrete-time signal $x[n]$ is given by \[ X(e^{j\omega}) = \sum _{n=-\infty} ^{\infty} x[n] e^{-j\omega n} \] where $\omega$ is the discrete frequency related to continuous frequency $\Omega$ through the relation $\omega = \Omega T_S$ if the sample time is denoted by $T_S$. Focusing on the discrete-time Fourier Transform for

December 21, 2021 Machine Learning

A Beginner’s Guide to Bayesian Methodology

Thomas Bayes was an English statistician and Presbyterian minister who came up with this theorem in 18th century during his investigation on how to update the understanding of a phenomenon as more evidence becomes available. At that time, he did not deem it worthy of publication and never submitted it to any journal. It was discovered in his notes after his death and published by his friend Richard Price. In the past, Bayesian theorem was associated with highly complicated mathematics (and rightly so), and hence it was generally a topic of interest for mathematicians, statisticians and similar professionals. However, as

July 12, 2021 DSP

Generating Signals and Viewing the Spectrum

One of the most common questions DSP beginners have is how to generate the signals (particularly, sinusoids) and view their spectrum. They have a rough idea what time domain and frequency domain are about but struggle to construct the first few lines of code that open the gates towards a deeper understanding of signals. For this reason, I produce below an Octave (or Matlab) code that you can simply copy and paste to view and modify the results. Keep in mind that the code has been written for an explanation purpose, not conciseness or optimization. As you progress towards developing