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 81 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 ArchitectureFixed and Floating point architecture principles