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Syllabus of Digital Signal Processing EG773EX of IOE, TU

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Digital Signal Processing EG773EX

Lecture: 3, Practical: 3, Year: 4, Part: B

Course Objectives: To introduce digital signal processing techniques and applications

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1.0 Introduction to Discrete Signals and Systems:

1.1   Discrete signal – unit impulse, unit step, exponential sequences

1.2   Linearity, shift invariance, causality

1.3   Convolution summation and discrete systems, response to discrete inputs

1.4   Stability, sum and convergence of power series

1.5   Sampling continuous signals – spectral properties of sampled signals

2.0 Difference Equation and Frequency Response:

2.1   General form of the linear, shift-invariant constant coefficient difference equation – signal flow graph representation

2.2   Steady state sinusoidal frequency response derived directly from the difference equation by assuming a form of the solution as a function of EXP (jwT)

2.3   Pole-zero diagrams, frequency response relationships

2.4   Design of a notch filter from the pole-zero diagram, finite impulse response (FIR) and infinite impulse response (IIR) filters

3.0 Z-Transform:

3.1   Definition of the Z-transform, relationship to convolution summation, one-sided and two-sided transforms

3.2   Left-sided, right-sided and two-sided sequences, region of convergence, relationship to causality

3.3   Inverse Z-transform – by long division, by partial fraction expansion

3.4   System response

3.5   Z-transform properties –delay, advance, convolution, Parseval’s theorem

3.6   Z-transform transfer function H(z) – transient and steady state sinusoidal response, pole-zero relationships, stability

4.0 Discrete Filters:

4.1   Discrete filter structures, second order sections, ladder and wave filters, frequency response

4.2   Sampling continuous signals, spectral properties of continuous signals, aliasing

4.3   Anti-aliasing and reconstruction analog filters, effects of sample and hold at filter input and output

4.4   Digital filters, finite precision implementations of discrete filters

4.5   Scaling and noise in digital filters, finite quantized signals, quantization error, linear models

5.0 IIR Filter Design:

5.1   Classical filter design using polynomial approximations – Butterworth, Chebyshev, Elliptic and Bessel forms

5.2   IIR filter design by transformation – matched Z-transform, impulse-invariant transform and bilinear transformation

5.3   Application of the bilinear transformation

5.4   Application of the bilinear transformation to IIR low pass discrete filter design

5.5   Spectral transformations, highpass, bandpass and notch filters

6.0 FIR Filter Design:

6.1   FIR filter design by Fourier approximation, the complex Fourier series

6.2   Gibbs phenomena in FIR filter design approximations, applications of windows functions to frequency response smoothing

6.3   Windows functions, rectangular, Hanning, Hamming and Kaiser Windows

6.4   FIR filter design by the frequency sampling method

6.5   FIR filter design using the Remez exchange algorithm

6.6   Linear phase FIR filters, unit sample response symmetry, group delay

7.0 Digital Filter Implementation:

7.1   Implementations using special purpose DSP processors, the Texas Instruments TMS320, the Motorola 5600

7.2   Bit-serial arithmetic, pipelined implementations

7.3   Distributed arithmetic implementations

8.0 The Discrete Fourier Transform:

8.1   The discrete Fourier transform (DFT) derivation

8.2   Properties of the DFT

8.3   DFT of non-periodic data, use of windows function

8.4   Introduction of the Fast Fourier Transform (FFT)

8.5   Power spectral density using DFT/FFT algorithms

Laboratory:

1.0   Introduction to digital signal – sampling properties, aliasing, simple digital notch filter behavior

2.0   Response of a recursive (IIR) digital filter – comparision to ideal unit sample and frequency response, coefficient quantization effects

3.0   Scaling, dynamic range and noise behavior of a recursive digital filter, observation of nonlinear finite precision effects

4.0   Response of non-recursive (FIR) digital filter order bandpass filters implemented using cascade second order sections and wave or ladder filters, comparision of implementations

5.0   Use of DFT and FFT transforms

 

References:

1.0   A. V. Oppenhen, “Discrete- Time Signal Processing”, Prentice Hall, 1990

2.0   John G Proakis, Dimitris G. Manolakis, “Digital Signal Processing, Principles, Algorithms, and Applications”, Prentice Hall, 2008

 

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