Discrete Fourier Transform (DFT) Archives | Page 4 of 4

July 29, 2016 DSP

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

July 21, 2016 DSP

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

July 9, 2016 DSP / Wireless/SDR

Digital Filter and Square Timing Recovery

We have seen before how a symbol timing offset severely impacts the constellation of the received symbols. Therefore, symbol timing recovery is one of the most crucial jobs of a digital communications receiver. In the days of analog clock recovery, a timing error detector provided the instant to sample the Rx waveform at 1 sample/symbol at the maximum eye opening. However, discrete-time processing opened the doors for better timing recovery schemes as an ever increasing number of transistors within the same area consistently keeps bringing the digital processing cost down. Consequently, the use of analog circuits to control the timing