Digital Signal Processing

EC3492

DIGITAL SIGNAL PROCESSING

COURSE OBJECTIVES:

i. To learn discrete fourier transform, properties of DFT and its application to linear filtering

ii. To understand the characteristics of digital filters, design digital IIR and FIR filters and apply these filters to filter undesirable signals in various frequency bands

iii. To understand the effects of finite precision representation on digital filters

iv. To understand the fundamental concepts of multi rate signal processing and its applications

v. To introduce the concepts of adaptive filters and its application to communication engineering

UNIT I

DISCRETE FOURIER TRANSFORM

Sampling Theorem, concept of frequency in discrete-time signals, summary of analysis & synthesis equations for FT & DTFT, frequency domain sampling, Discrete Fourier transform (DFT) - deriving DFT from DTFT, properties of DFT - periodicity, symmetry, circular convolution. Linear filtering using DFT. Filtering long data sequences - overlap save and overlap add method. Fast computation of DFT - Radix-2 Decimation-in-time (DIT) Fast Fourier transform (FFT), Decimation-in-frequency (DIF) Fast Fourier transform (FFT). Linear filtering using FFT.

UNIT II

INFINITE IMPULSE RESPONSE FILTERS

Characteristics of practical frequency selective filters. characteristics of commonly used analog filters - Butterworth filters, Chebyshev filters. Design of IIR filters from analog filters (LPF, HPF, BPF, BRF) - Approximation of derivatives, Impulse invariance method, Bilinear transformation. Frequency transformation in the analog domain. Structure of IIR filter - direct form I, direct form II, Cascade, parallel realizations.

UNIT III

FINITE IMPULSE RESPONSE FILTERS

Design of FIR filters - symmetric and Anti-symmetric FIR filters - design of linear phase FIR filters using Fourier series method - FIR filter design using windows (Rectangular, Hamming and Hanning window), Frequency sampling method. FIR filter structures - linear phase structure, direct form realizations

UNIT IV

FINITE WORD LENGTH EFFECTS

Fixed point and floating point number representation - ADC - quantization - truncation and rounding

- quantization noise - input / output quantization - coefficient quantization error - product quantization error - overflow error - limit cycle oscillations due to product quantization and summation - scaling to prevent overflow.

UNIT V

DSP APPLICATIONS

Multirate signal processing: Decimation, Interpolation, Sampling rate conversion by a rational factor

– Adaptive Filters: Introduction, Applications of adaptive filtering to equalization-DSP Architecture- Fixed and Floating point architecture principles

45 PERIODS

PRACTICAL EXERCISES: 30 PERIODS

MATLAB / EQUIVALENT SOFTWARE PACKAGE/ DSP PROCESSOR BASED IMPLEMENTATION

i. Generation of elementary Discrete-Time sequences

ii. Linear and Circular convolutions

iii. Auto correlation and Cross Correlation

iv. Frequency Analysis using DFT

v. Design of FIR filters (LPF/HPF/BPF/BSF) and demonstrates the filtering operation

vi. Design of Butterworth and Chebyshev IIR filters (LPF/HPF/BPF/BSF) and demonstrate the filtering operations

vii. Study of architecture of Digital Signal Processor

viii. Perform MAC operation using various addressing modes

ix. Generation of various signals and random noise

x. Design and demonstration of FIR Filter for Low pass, High pass, Band pass and Band stop filtering

xi. Design and demonstration of Butter worth and Chebyshev IIR Filters for Low pass, High pass, Band pass and Band stop filtering

xii. Implement an Up-sampling and Down-sampling operation in DSP Processor

COURSE OUTCOMES:

At the end of the course students will be able to:

CO1: Apply DFT for the analysis of digital signals and systems

CO2: Design IIR and FIR filters

CO3: Characterize the effects of finite precision representation on digital filters

CO4: Design multirate filters

CO5: Apply adaptive filters appropriately in communication systems

TOTAL:75 PERIODS

TEXT BOOKS:

i. John G. Proakis and Dimitris G.Manolakis, Digital Signal Processing – Principles, Algorithms and Applications, Fourth Edition, Pearson Education / Prentice Hall, 2007.

ii. A. V. Oppenheim, R.W. Schafer and J.R. Buck, ―Discrete-Time Signal Processing”, 8th Indian Reprint, Pearson, 2004.

REFERENCES

i. Emmanuel C. Ifeachor& Barrie. W. Jervis, “Digital Signal Processing”, Second Edition, Pearson Education / Prentice Hall, 2002.

ii. Sanjit K. Mitra, “Digital Signal Processing – A Computer Based Approach”, Tata Mc Graw Hill, 2007.

iii. Andreas Antoniou, “Digital Signal Processing”, Tata Mc Graw Hill, 2006.