Processing math: 100%
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Engineering LibreTexts

12: Discrete-Time Systems

( \newcommand{\kernel}{\mathrm{null}\,}\)

Learning Objectives
  • Discrete-time calculations are generally easier and more flexible than analog ones, allowing for practical calculation of Fourier transform.

When we developed analog systems, interconnecting the circuit elements provided a natural starting place for constructing useful devices. In discrete-time signal processing, we are not limited by hardware considerations but by what can be constructed in software.

Exercise 12.1

One of the first analog systems we described was the amplifier. We found that implementing an amplifier was difficult in analog systems, requiring an op-amp at least. What is the discrete-time implementation of an amplifier? Is this especially hard or easy?

Solution

In discrete-time signal processing, an amplifier amounts to a multiplication, a very easy operation to perform.

In fact, we will discover that frequency-domain implementation of systems, wherein we multiply the input signal's Fourier transform by a frequency response, is not only a viable alternative, but also a computationally efficient one. We begin with discussing the underlying mathematical structure of linear, shift-invariant systems, and devise how software filters can be constructed.


This page titled 12: Discrete-Time Systems is shared under a CC BY 1.0 license and was authored, remixed, and/or curated by Don H. Johnson via source content that was edited to the style and standards of the LibreTexts platform.

Support Center

How can we help?