Discrete Fourier Transforms (DFT): Frequency domain sampling and reconstruction of discrete time signals. DFT as a linear transformation, its relationship with other transforms. Properties of DFT, multiplication of two DFTs- the circular convolution
Additional DFT properties, use of DFT in linear filtering, overlap-save and overlap-add method. Fast-Fourier-Transform (FFT) algorithms: Direct computation of DFT, need for efficient computation of the DFT (FFT algorithms).
Radix-2 FFT algorithm for the computation of DFT and IDFT–decimation-in-time anddecimation-in-frequency algorithms. Goertzel algorithm, and chirp-z transform.
Structure for IIR Systems: Direct form, Cascade form, Parallel form structures.IIR filter design: Characteristics of commonly used analog filter – Butterworth andChebyshev filters, analog to analog frequency transformations.Design of IIR Filters from analog filter using Butterworth filter: Impulse invariance, Bilineartransformation.
Structure for FIR Systems: Direct form, Linear Phase, Frequency sampling structure,Lattice structure.
FIR filter design: Introduction to FIR filters, design of FIR filters using - Rectangular,Hamming, Hanning and Bartlett windows.
The question paper will have ten questions
Each full question consists of 16 marks.
There will be 2 full questions (with a maximum of four sub questions) from each module.
Each full question will have sub questions covering all the topics under a module
The students will have to answer 5 full questions, selecting one full question fromeach module