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