Spring 1990

Professor Sergio Verdú

1. Discrete-time signals

Introduction Transformation of independent variable Basic signals Condition for periodicity of a sinusoid Recursive definition of sequences

2. Discrete-time Systems

Introduction Properties: memoryless, causal, stable, linear, time-invariant Impulse response Impulse response of LTI systems Convolution sum Conditions for memorylessness, causality and stability for LTI systems Convolution: graphical and analytical evaluation Impulse response of interconnected LTI systems LTI systems described by difference equations Zero-input response Frequency response of LTI systems Transfer function of LTI systems described by difference equations Magnitude and phase frequency response Properties of frequency response: periodic, even magnitude, odd phase Response of LTI systems to sinusoids Transfer function of interconnected systems

3. Fourier Analysis of Signals and Systems

Representation of Periodic Signals: Discrete Fourier Series Properties of the Discrete Fourier Series Discrete Fourier Transform of Finite Duration Sequences Properties of the DFT Fourier Transform Response of LTI Systems: nonperiodic and periodic inputs

4. Transforms

Definition and Region of Convergence Elementary signals Properties Inverse z-transform --power series --partial fraction expansion Response of LTI systems described by difference equations Properties of LTI systems via poles/zeros of transfer functions Frequency Response from Pole-Zero Pattern

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