Course Details

Course details of EE5131
Course NoEE5131
Course TitleSelected Topics in Digital Signal Processing
Course ContentStructures for Discrete-Time Systems: IIR filter structures (direct form, cascade form, parallel form)—FIR filter structures (direct form for linear phase systems, frequency sampling structure)—signal flow graphs—lattice structures for FIR and all-pole IIR systems—state-space representation—introduction to coefficient quantization.Introduction to Fourier Analysis of Signals: Fourier analysis of continuous-time signals using the DFT—stationary and non-stationary signals—spectrogram analysis of non-stationary signals—effect of windowing on the spectrum—properties of the Dirichlet kernel—commonly used data winodws (Bartlett, Hann, Hamming, Blackman, Kaiser, Dolph)—frequency measurement of a single complex sinusoid—two complex exponentials case—chirp Fourier transform—discrete cosine transform (DCT).Cepstrum Analysis and Homomorphic Deconvolution: Definition of the cepstrum—definition of the complex cepstrum—alternative expressions for the complex cepstrum—complex cepstrum of exponential and minimum-phase sequences—relationship between the real cepstrum and the complex cepstrum—computation of the complex cepstrum—phase unwrapping—computation of the complex cepstrum using the logarithmic derivative—minimum-phase realizations for minimum-phase sequences—recursive computation of the complex cepstrum for minimum-phase sequences—computation of the complex cepstrum using polynomial roots—deconvolution using the complex cepstrum—minimum-phase/allpass homomorphic deconvolution—minimum-phase/maximum-phase homomorphic deconvolution—the complex cepstrum of a simple multipath model (computation of the complex cepstrum by z-transform analysis and using the DFT)—homomorphic deconvolution for the multipath model—applications to speech processing.Hilbert Transform: Continuous-time bandpass signal representation—pre-envelope and analytic signal—continuous-time Hilbert transform—complex envelope—in-phase (I) and quadrature signal (Q) representation—block-diagram for generating I and Q components (real-signal and complex-signal versions)—Bedrosian product theorem—Hilbert transform for causal discrete-time sequences—relationship between real and imaginary parts of a sequence whose spectrum is "periodically causal"—relationship between the real and imaginary parts of the spectrum corresponding to a "periodically causal" sequence—discrete-time Hilbert transformer design using Type III and Type IV filters (window-based design method).
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