Module-1 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. Module-2 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). Module-3 Radix-2 FFT algorithm for the computation of DFT and IDFT–decimation-in-time and decimation-in-frequency algorithms. Goertzel algorithm and chirp-z transform. Module-4 Structure for IIR Systems : Direct form, Cascade form, Parallel form structures. IIR filter design : Characteristics of commonly used analog filter - Butterworth and Chebyshev filters, analog to analog frequency transformations. Design of IIR filters from analog filter using Butterworth filter : Impulse invariance, Bilinear transformation. Module-5 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.