Description: To teach the fundamentals of Digital Signal Processing.
Course Contents :
Discrete-Time Signals and Systems: Discrete time complex exponentials and other basic signals?scaling of the independent axis?system properties?LTI systems described by linear constant coefficient difference equations (LCCDE)?impulse response and convolution. Discrete-Time Fourier Transform (DTFT): Complex exponentials as eigensignals of LTI systems?DTFT definition?inversion formula?properties?relationship to continuous-time Fourier series (CTFS). Z-Transform: Generalized complex exponentials as eigensignals of LTI systems?z-transform definition?region of convergence (RoC)?properties of RoC?properties of the z-transform?inverse z-transform methods?pole-zero plots?time-domain responses of simple pole-zero plots?RoC implications of causality and stability. Frequency Domain Analysis of LTI Systems: Frequency response of systems with rational transfer function?definitions of magnitude and phase response?magnitude response of single complex zero/pole?magnitude response of simple configurations?phase response?definition of principal phase?zero-phase response?group delay?phase response of single complex zero/pole?extension to higher order systems?effect of a unit circle zero on the phase response?zero-phase response representation of systems with rational transfer function?minimum phase and allpass systems?constant group delay and its consequences?generalized linear phase?conditions that have to be met for a filter to have generalized linear phase?Type I through Type IV FIR filters. Sampling: Impulse train sampling?relationship between impulse trained sampled continuous-time signal spectrum and the DTFT of its discrete-time counterpart?relationship between true frequency and digital frequency?reconstruction through sinc interpolation?effects of oversampling?discrete-time processing of continuous-time signals. Discrete Fourier Transform (DFT): Definition of the DFT and inverse DFT?relationship to discrete-time Fourier series?matrix representation?DFT as the samples of the DTFT?recovering the DTFT from the DFT?properties of the DFT?effect of zero padding?introduction to the Fast Fourier Transform (FFT) algorithm?decimation-in-time and decimation-in-frequency algorithms.
(1) Digital Signal Processing by John G. Proakis and Dimitris K. Manolakis, 4th edition, 2007, Prentice Hall, Upper Saddle River, NJ.
(2) Digital Signal Processing by Sanjit Mitra, 4th edition, 2011, McGraw-Hill, New York, NY.