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

Continue reading# Category: DSP

Digital Signal Processing

## 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

Continue reading## Linear Systems

In wireless communications and other applications of digital signal processing, we often want to modify a generated or acquired signal. A device or algorithm that performs some prescribed operations on an input signal to generate an output signal is called a system. Amplifiers in communication receivers and filters in image processing applications are some systems that we interact with in daily lives. Our main focus in these articles will be on a particular class of systems which are linear and time-invariant. A linear system implies that if two inputs are scaled and summed together to form a new input, the

Continue reading## A Digital Signal

We have talked about obtaining a discrete-time signal through sampling the time-axis and obtaining a discrete frequency set through sampling the frequency axis. The same concept can be applied to the amplitude-axis, where the signal amplitude can be sampled to take only a finite set of discrete values. This discrete-time discrete-valued signal is called a digital signal, as opposed to an analog signal that is continuous in time and continuous in amplitude. The above figure shows how a digital signal having amplitudes over a fixed set of values can be obtained through slicing the underlying continuous amplitudes. For example, an

Continue reading## Some DFT Properties

The purpose of this article is to summarize some useful DFT properties in a table. My favorite property is the beautiful symmetry depicted by continuous and discrete Fourier transforms. However, if you feel that this particular content is not as descriptive as the other posts on this website are, you are right. As opposed to the rest of the content on the website, we do not intend to derive all the properties here. Instead, based on what we have learned, some important properties of the DFT are summarized in the table below with an expectation that the reader can derive

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