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• Real Time Signals India

Digital Signal Processing begins with a discussion of the analysis and representation of discrete-time signal systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. Emphasis is placed on the similarities and distinctions between discrete-time. The course proceeds to cover digital network and nonrecursive (finite impulse response) digital filters. Digital Signal Processing concludes with digital filter design and a discussion of the fast Fourier transform algorithm for computation of the discrete Fourier transform.

Prerequisites

Students are expected to have the following background: Knowledge of basic computer science principles and skills, at a level sufficient to write a reasonably non-trivial computer program. Familiarity with linear algebra.

##### What you'll learn

Introduction to discrete linear systems

• Discrete time signals

• Special sequences

• Shift invariance

• Stability and causality

• Impulse response

• Difference equations

Discrete-Time Fourier Transform and Linear Time Invariant Systems

• Transform definitions

• Theorems

• Frequency response of linear time invariant systems

• Phase and group delays

• Matlab computations

The Z transform

• Z-transforms by summation of left, right, and two-sided sequences

• Regions of convergence and Z-transform properties

• Inverse Z-transform

Properties of digital filters

• Averaging filter

• Recursive smoother

• First-order notch filter

• Second-order unity gain resonator

• All-pass filters

• Comb filters

• Equalization filters

• Group delay, linear phase, all-pass, minimum phase

• Fourier transforms, sampling

• Fourier transform review

• Sampling continuous-time signals: the sampling theorem

• Aliasing

• Re-sampling digital signalss

Fourier transforms, sampling

• A/D conversion and quantization

• D/A conversion

• Polyphase decomposition

• Polyphase DFT filterbanks

• Bandpass sampling

The discrete Fourier transform

• Definition of DFT and relation to Z-transform

• Properties of the DFT

• Linear and periodic convolution using the DFT

• Zero padding, spectral leakage, resolution and windowing in the DFT

The fast Fourier transform

• Decimation in time FFT

• Decimation in frequency FFT

Digital filter design

Finite impulse response (FIR) filters

• Window design techniques

• Kaiser window design technique

• Equiripple approximations

Infinite impulse response (IIR) filters

• Bilinear transform method

• Examples of bilinear transform method

Structures and properties of FIR and IIR filters and review

• IIR - Direct, parallel and cascaded realizations

• FIR - Direct and cascaded realizations

• Coefficient quantization effects in digital filters