Articles | Page 23 of 35

Beat frequency sinusoid and its spectrum

October 31, 2023 DSP

Spectrum of a Sinusoid

In this article, we derive the spectrum of a complex sinusoid that acts as the basis for all spectra. In fact, the very definition of the Fourier Transform, whether continuous or discrete, comes from the perspective of a complex sinusoid. Therefore, exploring this derivation will be useful in everything else we learn about DSP. For an in-depth understanding of complex signals and I/Q processing, you can read the following two articles (the option of downloading them as PDF is available). The origin of complex numbers and signals I/Q signal processing Let us start with the continuous-time case. A Continuous-Time Sinusoid

December 2, 2016 DSP / Machine Learning

The Master Algorithm

Recently, I was reading the book The Master Algorithm by Pedro Domingos — a Professor at the University of Washington in machine learning. According to the description of his book, The Master Algorithm in Machine Learning A spell-binding quest for the one algorithm capable of deriving all knowledge from data, including a cure for cancer. Society is changing, one learning algorithm at a time, from search engines to online dating, personalized medicine to predicting the stock market. But learning algorithms are not just about Big Data – these algorithms take raw data and make it useful by creating more algorithms.

November 15, 2016 DSP

Sampling and the Mysterious Scaling Factor

This post treats the signals in continuous time which is different than the approach I adopted in my book. The book deals exclusively in discrete time. Some time ago, I came across an interesting problem. In the explanation of sampling process, a representation of impulse sampling shown in Figure below is illustrated in almost every textbook on DSP and communications. The question is: how is it possible that during sampling, the frequency axis gets scaled by $1/Ts$ — a very large number? For an ADC operating at 10 MHz for example, the amplitude of the desired spectrum and spectral replicas

August 15, 2022 DSP

Goertzel Algorithm – Evaluating DFT without DFT

The Discrete Fourier Transform (DFT) computes the contribution of $N$ sinusoids that come together to form any input signal. However, in some applications, we are only interested in contributions from one or a few sinusoids This is where the Goertzel algorithm, proposed by Gerald Goertzel in 1958, comes in. The Goertzel algorithm evaluates the individual terms of the DFT in an efficient manner. We explain its derivation and implementation with the help of DTMF signals. DTMF Signal Generation In the early days of telephone, you could not call anyone directly. Instead, a telephone operator used to sit on the other

A digital signal and its underlying continuous waveform

February 27, 2022 Wireless/SDR

Why Digital Communication is Superior to Analog Communication

At the beginning, the history of wireless communication revolved around analog communication systems for several decades. Amplitude Modulation (AM) and Frequency Modulation (FM) were the most widely used techniques during this time. Gradually, however, a transition towards digital transmission occurred in wireless systems as well, a phenomenon that was in sync with digital revolution in the society as a whole. So what are the main benefits of digital technology that made it much superior to its analog counterpart? Let us analyze some of them below [1]. Performance Analog signals suffer from distortion and noise, even if they are small. Although