Digital Signal Processing

Discrete-time signals and sequences; classification of discrete-time systems; Stability and invertibility of LTI systems; response of LTI systems to arbitrary inputs; Solution of linear constant coefficient difference equations; frequency domain representation; Review of Z-transforms; solution of difference equations using Z-transforms; system function

Discrete Fourier series representation of periodic sequences and properties; Discrete Fourier transform and its properties; Linear filtering methods based on the DFT; Fast Fourier transform (FFT): radix-2 decimation in time and frequency; inverse FFT

Analog filter approximations: Butterworth and Chebyshev filters; Design of IIR digital filters from analog filters; Analog and digital frequency transformations; Basic structures of IIR systems: direct, transposed, cascade, parallel, lattice and lattice-ladder

Characteristics of FIR filters with linear phase; frequency response of linear phase FIR filters; Design of FIR filters using window and frequency sampling techniques; Comparison of IIR and FIR filters; Basic structures of FIR systems: direct, cascade, linear phase and lattice structures

Decimation and interpolation; Sampling rate conversion by a rational factor; Implementation of sampling rate converters; Applications of multirate signal processing; digital filter banks