Digital Signal Processing
Course Objectives:
- To introduce digital signal processing techniques and applications.
- To design and implement IIR and FIR digital filter.
- Introduction(4 hours)
- Basic elements of Digital Signal Processing,
- Need of Digital Signal Processing over Analog Signal Processing,
- A/D and D/A conversion,
- Sampling continuous signals and spectral properties of sampled signals
- Discrete-time Signals and System(6 hours)
- Elementary discrete-time signals,
- Linearity, Shift invariance, Causality of discrete systems,
- Recursive and Non-recursive discrete-time systems,
- Convolution sum and impulse response,
- Linear Time-invariant systems characterized by constant coefficient difference equations,
- Stability of LTI systems, Implementation of LTI system.
- Z-Transform(6 hours)
- Definition of the z-transform,
- One-side and two-side transforms, ROC, Left-side, Right-sided and two-sided sequences, Region of convergence, Relationship to causality,
- Inverse z-transform-by long division, by partial fraction expansion,
- Z-transform properties-delay advance, Convolution, Parseval's theorem,
- Z-transform function H(z)-transient and steady state sinusoidal response, pole-zero relationship stability.
- Discrete Fourier Transform(7 hours)
- Definition and applications, Frequency domain sampling and for reconstruction, Forward and Reverse transforms, Relationship of the DFT to other transforms,
- Properties of the Discrete Fourier Transform: Periodicity, Linearity and Symmetry Properties, Multiplication of two DFTs and Circular Convolution, Time reversal, Circular time shift and Multiplication of two sequences circular frequency shift, Circular correlation and Parseval's Theorem,
- Efficient computation of the DFT: Algorithm, applications, Applications of FFT Algorithms.
- Implementation of Discrete-time System(8 hours)
- Structures for FIR and IIR, Direct Form, Cascaded and parallel form, Lattice for FIR,
- Conversion between direct form and lattice and vice verse, Lattice and lattice-ladder for IIR,
- Frequency response,
- Digital filters, finite precision implementations of discrete filters,
- Representation of Numbers; fixed point and floating binary point, Effect of Rounding and truncation; Limit cycle oscillations effect,
- Quantization of filter coefficients and effects on location of poles, and zeros; pole perturbation, Overflow and underflow error, Scaling to prevent overflow and underflow.
- IIR Filter Design (5 hours)
- IIR Filter Design: IIR filter design by classical filter design using low pass approximations Butterworth, Chebychev, Inverse Chebyshev, Elliptic and Bessel-Thompson filters,
- IIR filter design by Impulse-invariant method, Bilinear Transformation Method, Matched z-transform method,
- IIR lowpass discrete filter design using bilinear transformation,
- Spectral transformations, Highpass, Bandpass and Notch filters.
- FIR Filter Design(5 hours)
- FIR filter design by Fourier approximation,
- Gibbs phenomena in FIR filter design, Design of Linear Phase FIR filters using window function, Applications of window functions to frequency response smoothing,
- Window functions, Rectangular, Hamming, Blackman and Kaiser windows,
- Design of linear phase FIR filter by the frequency sampling method,
- FIR filter design using the Remez exchange algorithm,
- Design of optimum equiripple linear-phase FIR filters.
- Digital Filter Implementation(4 hours)
- Implementations using special purpose DSP processors,
- Bit-serial arithmetic, pipelined implementations,
- Distributed arithmetic implementations.
Practical:
- Study the behavior of a simple digital notch filter.
- Response of a recursive digital.
- Scaling, dynamic range and noise behavior of a recursive digital filter, observation of nonlinear finite precision effects.
- Response of a non-recursive digital filter, Implementation in Impulse Invariant and Bilinear Transformation.
- Band pass filters implemented using cascade second order sections and wave or ladder filters, Comparison of implementations.
- Design of FIR filter using window method, Comparison of FIR filter for different windowing method.
References:
- J.G. Proakis and D.G. Manolakis, Digital Signal Processing, Prentice Hall of India. 2009
- A.V. Oppenheim, Discrete-Time Signal Processing, Prentice Hall, 2009.
- S.K. Mitra, Digital Signal Processing, A Computer-based Approach, McGraw Hill, 2008
Evaluation Scheme:
Unit |
Hour |
Marks Distribution* |
1 |
4 |
7 |
2 |
6 |
11 |
3 |
6 |
11 |
4 |
7 |
13 |
5 |
8 |
14 |
6 |
5 |
9 |
7 |
5 |
9 |
8 |
4 |
6 |
Total |
45 |
80 |
*Note: There may be minor deviation in marks distribution.
|