2/17/2007 DSP Course-IUST-Spring Semester 1

Digital Signal Processing

Electrical Engineering Department

Iran University of Science & Tech.

DSP Course-IUST-Spring Semester 22/17/2007

Digital Signal ProcessingTopic 1: Time Domain

1. Discrete-time systems

2. Convolution

3. Linear Constant-Coefficient Difference

Equations (LCCDEs)

4. Correlation

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1. Discrete-time systems

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Moving Average (MA)

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MA Smoother

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Accumulator

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Accumulator

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Classes of DT systems

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Linearity: Example 1

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Linearity Example 2:

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Linearity Example 3:

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Property: Shift (time) invariance

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Shift-invariance counterexample

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Another counterexample

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Linear Shift Invariant (LSI)

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Causality

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Causality example

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Impulse response (IR)

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Impulse response example

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2. Convolution

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Convolution sum

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Convolution properties

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Interpreting convolution

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Convolution interpretation 1

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Convolution interpretation 2

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Matrix interpretation

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Convolution notes

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Convolution in MATLAB

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Connected systems

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Inverse systems

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Inverse systems

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Inverse system example

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Parallel connection

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3. Linear Constant-CoefficientDifference Equation (LCCDE)

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Solving LCCDEs

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Complementary Solution

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Complementary Solution

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Complementary Solution

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Particular Solution

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LCCDE example

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LCCDE example

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LCCDE example

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LCCDE example

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LCCDE example

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LCCDE solving summary

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LCCDEs: zero input/zero state

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Impulse response of LCCDEs

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LCCDE IR example

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System property: Stability

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Stability

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Stability example

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Stability & LCCDEs

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4. Correlation

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Correlation and convolution

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Autocorrelation

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Correlation maxima

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AC of a periodic sequence

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AC of a periodic sequence

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What correlations look like

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What correlation looks like