Signals, systems and signal processing, classification of signals, Basic Operations on Signals, Basic Elementary Signals, properties of systems. concept of frequency in continuous and Discrete time signals, sampling of analog signals, the sampling theorem , quantization of continuous amplitude and sinusoidal signals , coding of quantized samples, digital to analog conversion

Time-domain representations for LTI systems: Convolution, impulse response representation, Convolution Sum and Convolution Integral, properties of impulse response representation, solution of difference equations.

Discrete Fourier Transforms (DFT): Introduction to DFT, definition of DFT and its inverse, matrix relation to find DFT and IDFT ,Properties of DFT, linearity, circular time shift, circular frequency shift, circular folding, symmetry of : real valued sequences, real even and odd sequences, DFT of complex conjugate sequence, multiplication of two DFTs- the circular convolution, Parseval’s theorem, circular correlation, Digital linear filtering using DFT. Signal segmentation , overlap-save and overlap-add method.

Fast-Fourier-Transform (FFT) algorithms: Direct computation of DFT, need for efficient computation of the DFT (FFT algorithms)., speed improvement factor, Radix-2 FFT algorithm for the computation of DFT and IDFT–decimation-in-time and Decimation-in-frequency algorithms , calculation of DFT when N is not a power of 2.

IIR filter design: Classification of analog filters, generation of Butterworth polynomials, frequency transformations. Design of Butterworth filters, low pass, high pass, band pass and band stop filters, Generation of Chebyshev polynomials, design of Chebyshev filters, design of Butterworth and Chebyshev filters using bilinear transformation and Impulse invariance method, representation of IIR filters using direct form one and two, series form and parallel form.

FIR filter design: Introduction to FIR filters, symmetriv and antisymmetric FIR filters, design of linear phase FIR filters using – Rectangular, Bartlett, Hamming, Hanning and Blackman windows, design of FIR differentiators and Hilbert transformers, FIR filter design using frequency sampling Technique. Representation of FIR filters using direct form and lattice structure.