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Lecture 1: Intro

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Schedule :: Intro :: Signal Models for Discrete-Time :: Signal Operations :: Difference Equations :: Zero-Input :: Zero-State :: Natural & Forced :: System Stability

To learn about discrete-time systems. To learn about numeric solution of difference equations. To learn about analytical solution of difference equations, including the zero-input response and the zero-state response. To investigates stability issues for discrete-time systems.

pp. 540-616

Now we are ready to make a change of direction. Up till now we have focused on continuous time systems. Now we will look at discrete-time systems. This (I hope) will reinforce some of the stuff we have seen.

Where do these things come from? (C/D, discrete-time system, D/C). There is a sample interval $T$ . Many systems have an intrinsically defined period: days, weeks, months, etc. It is common to write $y(kT) = y[k]$ . (I may get sloppy on the parentheses and the brackets.)
\begin{example}
A sampled signal. suppose $f(t) = A \cos(\omega_0 t + \theta_0)...
...
\par
Now let $T = \frac{1}{1000} - \frac{1}{4000}$. What happens?
\end{example}

\begin{example}An example of a discrete-time
Bank deposit = $f[k]$. Bank balanc...
...est, plus any new deposits). Draw the
block diagram (realization).
\end{example}

\begin{example}If $y(t) = \frac{df}{dt}$, then
\begin{displaymath}y(kT) = \frac{...
...splaymath}y[k] \approx \frac{1}{T}(f[k] - f[k-1]) \end{displaymath}\end{example}

Instead of using RLC, the elements in discrete-time systems are delays, adders, and multipliers.

Comment on advantages: precision, stability, flexibility, variety, size, storage reliability, sophistication, sharing, cost.

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 16). Lecture 1: Intro. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/1_0lecture1.html. This work is licensed under a Creative Commons License Creative Commons License