DR. TAREK TUTUNJI PHILADELPHIA UNIVERSITY, JORDAN 2014 Discrete Time Signals and Systems
D R . T A R E K T U T U N J I
P H I L A D E L P H I A U N I V E R S I T Y , J O R D A N
2 0 1 4
Discrete Time Signals and Systems
Introduction
The basic theory of discrete-time signals and systems is similar to continuous-time signals and systems. However, there are some differences:
Discrete-time signals result from sampling of continuous-time signals and are only available at uniform times determined by the sampling period
Discrete-time signals depend on an integer variable n
The radian discrete frequency cannot be measured and depends on the sampling period
Introduction
Discrete-time periodic signals must have integer periods.
This imposes some restrictions for example it is possible to have discrete-time sinusoids that are not periodic, even if they resulted from the uniform sampling of continuous-time sinusoids.
Basic math operations:
Integrals are replaced by sums
Derivatives are replaced by finite differences
Differential equations are replaced by difference equations
Discrete Time Signals
A sampled signal x(nTs) = x(t)|t=nTs is a discrete-time signal x[n] that is a function of n only.
Once the value of Ts is known, the sampled signal only depends on n, the sample index.
Nyquist sampling rate condition
Conclusion
Discrete-Time signals are the result of sampling continuous-time signals
Discrete-time signals have discrete radian frequency that
varies between -p and p
Discrete-Time systems properties are similar to continuous-time systems: Linear, time-invariant, causal, and stable
Convolution operation is used in the time-domain Auto Regressive Moving Average (ARMA) represent a class of
linear discrete-time systems