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SYLLABUS

Unit-1:

Discrete Fourier Transform Review of signals and systems, 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-InTime (DIT) Fast Fourier Transform (FFT), Decimation-In-Frequency (DIF) Fast Fourier Transform (FFT). Linear filtering using FFT.

Unit-2:

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-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.

Unit-4:

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-5:

Introduction to Digital Signal Processors DSP functionalities - Circular buffering - DSP architecture - Fixed and Floating point architecture principles - Programming - Application examples.