Unit 1 Overview of transformation techniques (Fourier Series, Fourier Transform,

2 lecture hours

• Laplace Transform
• Discrete-Time Fourier Transform
• Z-Transform, and DFT)
• Discrete-Time Signals & Systems
• Implementation of Discrete-Time Systems

Unit 2 Discrete random processes – Ensemble averages – Wide sense stationary

4 lecture hours

• process – Properties - Ergodic process – Sample mean & variance - Auto- correlation and Auto-correlation matricesProperties – White noise process – Weiner Khitchine relation - Power spectral Density – Filtering random process – Spectral Factorization Theorem – Special types of Random Processes – AR, MA, ARMA Processes – Yule-Walker equations

Unit 3 Design of Digital Filters

6 lecture hours

• General Consideration
• Design of FIR Filters – symmetric and antisymmetric FIR Filters
• design of linear phase FIR filters using Windows method
• the frequency-sampling method, and Chebyshev approximation
• design of FIR Differentiators, and Hilbert Transformers
• comparison of design methods for linear-phase FIR filters

Unit 4 Multirate Digital Signal Processing

8 lecture hours

• Decimation by a factor D, Interpolation by a factor I, Sampling rate conversation by a rational factor
• Implementation of sampling rate conversion
• multistage implementation of sampling rate conversion
• sampling rate conversion of bandpass signals
• sampling rate conversion by an arbitrary factor
• application of multi-rate signal processing
• digital filter banks
• two-channel quadrature mirror filter bank

Unit 5 Linear Prediction and optimum linear filters

8 lecture hours

• Forward and backward linear prediction
• solution of the normal equations
• properties of the linear prediction- error filters
• AR lattices and ARMA Lattice-Laddar filters
• Wiener filters for filtering and prediction

Unit 6 Adaptive Filters

• Applications of adaptive filters
• Adaptive Direct-Form FIR filters using the LMS algorithm
• RLS algorithm
• Adaptive Lattice-Ladder filter. 08 20

Unit 7 Power Spectrum Estimation

6 lecture hours

• Estimation of spectra from finite duration observations of signals
• Nonparametric methods – the Barlett method
• the Welch method, and the Blackman and Teky method
• Parametric methods – relationships between the autocorrelation and the model parameters
• AR model parameters using the Yuke-Walker method
• the Burg method, and unconstrained least-square method
• sequential estimation method