DSP Archives | Page 12 of 15

A rectangular signal and its upsampled version in time and frequency domains

August 3, 2016 DSP

Sample Rate Conversion

In the discussion on sampling, the process of sampling a continuous-time signal was discussed in detail and subsequently sampling theorem was derived. In many applications, resampling an already digitized signal is mandatory for an efficient system design. In wireless communications, sample rate conversion is utilized for upconversion and downconversion to a desired frequency, filtering stages in the digital frontend and sometimes for carrier and timing synchronization during signal acquisition. See the Cascade Integrator Comb (CIC) filters for how to accomplish this task with minimal resources. In discrete domain, sample rate can be reduced by discarding intermediate samples periodically called downsampling

A signal broken down into scaled and shifted impulses

August 9, 2016 DSP

Convolution

Understanding convolution is the biggest test DSP learners face. After knowing about what a system is, its types and its impulse response, one wonders if there is any method through which an output signal of a system can be determined for a given input signal. Convolution is the answer to that question, provided that the system is linear and time-invariant (LTI). We start with real signals and LTI systems with real impulse responses. The case of complex signals and systems will be discussed later. Convolution of Real Signals Assume that we have an arbitrary signal $s[n]$. Then, $s[n]$ can be

A prism decomposes the white light into 7 colors

August 2, 2016 DSP

The Discrete Fourier Transform (DFT)

Learned in some other articles on this website, the following three important concepts take us to the core of the Discrete Fourier Transform (DFT) idea. Regardless of the signal shape, most signals of practical interest can be considered as a sum of complex sinusoids oscillating at different frequencies. A set of $N$ orthogonal complex sinusoids can be constructed within a span of $N$ time domain samples. Each `tick’ or bin on the discrete frequency axis denotes the discrete frequency $k/N$ of such a complex sinusoid. To understand how a set of sinusoids with $N$ discrete frequencies can sum up to

July 30, 2016 DSP

Correlation

Correlation is a foundation over which the whole structure of digital communications is built. In fact, correlation is the heart of a digital communication system, not only for data detection but for parameter estimation of various kinds as well. Throughout, we will find recurring reminders of this fact. As a start, consider from the article on Discrete Fourier Transform that each DFT output $S[k]$ is just a sum of term-by-term products between an input signal and a cosine/sine wave, which is actually a computation of correlation. Later, we will learn that to detect the transmitted bits at the receiver, correlation

An increasing degree of polynomial approximation takes the filter closer and closer to an ideal sinc impulse response

January 11, 2022 DSP / Wireless/SDR

Interpolation in Digital Communication Receivers

Timing synchronization in a digital receiver is about finding the right symbol peak and the symbol rate at which digital samples are taken for decisions purpose in a constellation diagram. In general, interpolation is the process of reproducing a missing sample at a desired location. In digital and wireless communications, the role of interpolation can be explained as follows. Background Imagine a Tx signal constructed from the upsampled and pulse shaped modulation symbols. The job of the Rx is to sample this waveform at optimal intervals, i.e., exactly at the middle of the eye diagram. In other words, the Rx