Digital Signal Processing

• The main objective of this course is to give an improved understanding of digital signal processing principles, tools and algorithms.

• Another objective of this course is to enable students to apply the DSP skills to solve a practical signal analysis problem.

• Apply the z-transform for analysis of discrete signals and systems

• Perform frequency domain analysis of linear systems

• Utilize the knowledge of Discrete Fourier Transform and its properties

• Demonstrate understanding of the Fast Fourier Transform and implement the algorithm for various applications

• Design, implement and analyze FIR and IIR digital filters for discrete time signals

• The Z- Transform (8 hrs )

  • The Z- Transform - Direct transform, inverse transform, Properties, Rational Transforms - poles & zeros, pole location and time domain behavior, system function, Inversion of z-transform - contour integration, power series expansion, partial fraction expansion, Analysis of LTI systems - System responses, transient and steady state, Causality and Stability

• Frequency Domain Analysis of LTI Systems (6 hrs)

  • Frequency Domain Characteristics of LTI Systems - Response to complex exponential and sinusoids, steady-state and transient analysis, steady state response to periodic signals, Frequency Response of LTI Systems - Frequency response of a system with rational transfer function, Correlation functions and spectra - input & output correlation functions, correlation functions and power spectra

• Discrete Fourier Transform (8 hrs )

  • Discrete Fourier Transform - Frequency domain sampling, Definition, Linear transformation, Properties - periodicity, linearity, symmetry, multiplication and circular convolution, Linear filtering methods - use of DFT, long data sequences

• Fast Fourier Transform algorithms (8 hrs)

  • Efficient computation of DFT - Direct computation, Divide and conquer, radix-2 FFT FFT Applications - Efficient computation of DFT of two real sequences, 2N point real sequence, Quantization Effects - Errors in FFT

• Design of FIR filters (9 hrs)

  • Design of FIR filters: FIR Structures - Direct form, cascade form, Frequency sampling, FIR Design methods - General considerations, symmetric and asymmetric FIR filters, linear phase FIR filters frequency sampling methods, equiripple method.

• Design of IIR Filters (9 hrs)

  • Structures - direct forms, signal flow graphs, cascade forms, IIR Design methods - approximation of derivatives, impulse invariance method, Bilinear transformation, frequency transformations in digital domain

Texts:

1. Digital Signal Processing, Proakis and Manolakis 4^th Edition, Pearson (Prentice Hall)

2. Discrete Time Signal Processing, 2^nd ed., Alan Oppenheim, Ronald Schafer and John, Buck, Prentice Hall, 1999.

References:

1. DSP using matlab (V. Ingle and J. Proakis)

2. Essential Matlab for Engineers and Scientists (B. Hahn, D. Valentine)

Scheduled Quizzes

Computer Assignments

Lab examination

In-class examinations