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Prerequisite: |
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1.The student must be conversant with frequency domain analysis of discrete time signals and systems.
2.They will be familiar with the various kind of adaptive filter design technique.
3.Multirate Signal Processing fundamentals and applications of Wavelet Transforms will be covered.
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Syllabus: |
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Frequency Domain Analysis of Discrete Time Domain Signals and Systems: 6L
The concept of frequency in continuous time and discrete time signals. Fourier series for discrete periodic signals, Fourier Transform of discrete aperiodic signals, Power spectral densities of discrete aperiodic signals, Relationship between Fourier Transform and Z-Transform. Properties of Fourier Transform in discrete time domain; Time reversal, convolution, correlation, Wiener-Khintchine theorem, frequency shifting, modulation, windowing theorem, differentiation in digital frequency domain. Symmetry property for various types of signals.
[Reference PPT available in google class]
Frequency Domain Characteristics of LTI Systems: 6L
Response to complex exponential signals, steady state and transient response to sinusoidal signals, steady state response to periodic signals, response to aperiodic signals. Relation between system function H (z) and frequency response function h (w). Input-output correlation function and spectra, correlation functions and power spectra for random input signals. Invertibility of LTI systems, minimum/maximum/mixed phase systems, homomorphic systems and homomorphic deconvolution.
DFT & FFT: 2L
Computation of DFT and it’s properties, computation of DFT via FFT, chirp z-transform.[Google class]
Design of Digital Filters: 6L
Design of FIR filters, Effect of various windows, Effect of finite register length, frequency sampling, Optimization Algorithm. Adaptive Filters design, State-Space Kalman Filter, Extended Kalman Filter, Unscented Kalman Filter Sample-Adaptive Filters, Recursive Least Square (RLS) Adaptive Filters, The Steepest-Descent Method, LMS Filter.
Power Spectrum: 6L
Estimation of Power Spectrum and Correlation, Non-parametric and Parametric methods, Minimum Variation Estimation methods, Eigen Analysis algorithm, Power Spectrum analysis using DFT, Maximum Entropy Spectral Estimation, Model-Based Power Spectral Estimation.
Multirate Signal Processing: 6L
Sampling Rate Conversion; Decimation and Interpolation; Time and Frequency Domain Characterization; Filters in Sampling Rate Alteration Systems; Multi-rate Design of Decimator and Interpolator; Poly-phase Techniques; Poly-phase Down-sampler and Interpolator; Poly-phase Filter Design; Two-channel QMF Banks. Alias free FIR and IIR QMF Banks; Perfect Reconstruction Two-channel FIR Filter Banks; M-Channel Filter Banks Design; Cosine-Modulated M-channel Filter Banks Design;
Wavelet Transforms: 6L
Fourier Transform and its limitations, Short Time Fourier Transform, Continuous Wavelet Transform, Discretization of the Continuous Wavelet Transform, Multiresolution Approximations; Wavelet and Scaling Function Coefficients, Orthonormality of Compactly Supported Wavelets, Bi-orthogonal Decomposition, Harr Wavelets, The Daubechies Wavelets Construction, Fast Wavelet Transform and Image Compression, Denoising using Wavelets, Perfect Reconstruction Filter bank design using Wavelets.
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MODULE 1-Lec-1 -Lec-6 |
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Lecture-1:
The concept of frequency in continuous time and discrete time signals,Symmetry property for various types of signals, Fourier series for discrete periodic signals
Lecture-2:
Fourier Transform of discrete aperiodic signals, Power spectral densities of discrete aperiodic signals, Relationship between Fourier Transform and Z-Transform.
Lecture-3:
Z-Transform, ROC Calculations.
Lecture-4:
Properties of Fourier Transform in discrete time domain; Time reversal, convolution, correlation.
Lecture-5:
Wiener-Khintchine theorem, frequency shifting, modulation, windowing theorem.
Lecture-6:
Differentiation in digital frequency domain.
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MODULE 2-Lec-7 -Lec-12 |
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References:
1.Discrete – Time Signal Processing by A.V. Oppenheim and R. W. Schafer, with J. R. Buck ( Prentice- Hall, 1998)
2.Digital Signal Processing Using MATLAB by V. K. Ingle and J. G. Prokis (Books/Cole,2000)
3.Digital Signal Processing: A Computer Based Approach by S.K. Mitra ( Second edition , McGraw-Hill, 2001)
4.Digital Signal Processing: Principles, Algorithms and Applications by J. G. Proakis and D. G. Manolakis.
Some web resource/tutorial:
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