Syllabus

Introduction to DSP

Digital signals and systems: Operations in digital signal processing, the scope of DSP, analog to digital conversion, frequency Domain Effects of Sampling: Periodic repetitions in frequency domain due to sampling in time domain, recovery of continuous-time signal from its samples (reconstruction), role of anti-aliasing and reconstruction filters, examples of aliased signals (show how waveform is distorted), impulse response, finite impulse response (FIR) and infinite impulse response (IIR) of discrete-time systems, difference equation.

Discrete Transformations

Discrete Fourier series, the Discrete-Time Fourier Transform, discrete Fourier transform (DFT) and fast Fourier transform (FFT): Forward and inverse transforms; coefficient ordering; time and frequency resolution; periodic extension, zero padding and modulo-M reduction; properties of the DFT, circular convolution; Cooley-Tukey decomposition, recursive application, radix-2 FFTs ,FFTs, time and frequency decimation, computational complexity.

Z-Transforms

Regions of convergence, convolution property and graphical interpretation of the convolution operation, z-transforms of cascaded systems, stability and causality.

Realization and Ffrequency Response

Frequency response (Magnitude and Phase), representation of LTI systems with rational polynomials, block-form implementations of a rational polynomial transfer function.

Digital Filters

FIR filters- linear phase filters, specifications, design using window, optimal and frequency sampling methods; IIR filters- specifications, design using impulse invariant, bi-linear z-transformation, least-square methods, linear phase, Butterworth, Chebychev, Inverse Chebychev , Bessel and elliptic filters, finite precision effects in implementing digital filters.

Implementing Digital Filters

Block-diagram representations; direct forms; cascade forms, first and second-order factors; parallel forms; feedback loops transposed forms; linear-phase FIR structures.

Wavelets

Short time Fourier transform; fundamentals of wavelets, wavelet transform (continuous and discrete), time – frequency density and orthogonal bases.