discrete time signals and systems - philadelphia
TRANSCRIPT
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
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Discrete Time Signals and Systems
Discrete Time Signals
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
Example
Periodic Signals
Periodic Signals
Example
Periodic Discrete Sinusoid
Finite Energy and Finite Power
Example
Time Shift
Time Shift
Time Reflection
Odd and Even Signals
Discrete Time Exponential Signal
Discrete Time Exponentials
Discrete Frequency
Discrete Time Sinusoidal Signals
Unit Step and Impulse
Examples
Discrete Time Systems
Difference Equations
Recursive and Non-recursive Systems
Properties
Linearity
Time invariance
Stability
Causality
Linearity and Time-invariant
Example
Example
Causality and Stability
Convolution
Example
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
References
Chapter 8. Signals and Systems using MATLAB by Luis Chaparro. Elsevier Publisher 2011.