## 21TOCEC06 : SIGNAL PROCESSING

##### COURSE OBJECTIVES

Discrete Time Signal Processing is concerned with the representation, transformation and manipulation of signals and the information they contain. Signal Processing has developed rapidly over the past few decades and has numerous applications in the field of Audio and Speech Processing, Radar, Sonar, Robotics, Big data, Bio medical and many more. In this course, we begin with the review of Signals and Systems including the summary of analysis and synthesis equation for Fourier Transforms tools and z-transform. An in-depth computation of DFT and FFT algorithms in spectral analysis and filtering applications is presented. This course develops different methods of filter design in both IIR and FIR and the corresponding structures. The effect of quantization is analyzed in digital filters using finite precision arithmetic. This includes the effects on the filter frequency response characteristics resulting from quantization and round-off noise effects inherent in the digital implementation of discrete time systems.

##### COURSE DURATION: 5 Weeks COURSE OUTCOMES:

By the end of this course, the learners will be able to
Compute DFT and IDFT coefficients of a given discrete time sequence using Fast Fourier Transform algorithms
Design Linear phase FIR digital filters using windowing and frequency sampling methods
Design IIR digital filters from analog filters namely Butterworth, and Chebyshev for a given specification
Draw the implementation structure of FIR and IIR discrete time systems using block diagram and signal flow graph representation.
Interpret the effects of finite precision representation on digital filters

##### COURSE CONTENTS:

Module 1: Review of signals and systems:
Concept of frequency in discrete-time signals, summary of analysis & synthesis equations for FT & DTFT, frequency domain sampling and z-transform

Module 2:  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

Module 3: 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

Module 4: Infinite Impulse Response
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.

Module 5: Finite World 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.