Dr. Hedaya Mahmood Alasooly - Some Case Studies on Signal, Audio and Image Processing Using Matlab

2.Theory Related To Project:

2.1 What is the signal Processing Toolbox in Matlab:

The Signal Processing Toolbox is a collection of tools built on the MATLAB numeric computing environment. The toolbox supports a wide range of signal processing operations, from waveform generation to filter design and implementation, parametric modeling, and spectral analysis. The toolbox provides two categories of tools: Command line functions in the following categories:

• Analog and digital filter analysis
• Digital filter implementation
• FIR and IIR digital filter design
• Analog filter design Filter discretization
• Spectral Windows Transforms Cepstral analysis
• Statistical signal processing and spectral analysis
• Parametric modeling
• Linear Prediction
• Waveform generation

A suite of interactive graphical user interfaces for

• Filter design and analysis Window design and analysis
• Signal plotting and analysis
• Spectral analysis Filtering signals

2.2 Signal and Linear System Models:

The Signal Processing Toolbox provides a broad range of models for representing signals and linear time-invariant systems, including representations for transfer functions, state space, and zero-pole gain. The toolbox also includes functions for transforming models from one representation to another.

2.3 Filter Implementation and Analysis

This section describes how to filter discrete signals using the MATLAB filter function and other Signal Processing Toolbox functions. It also discusses how to use the toolbox functions to analyze filter characteristics, including impulse response, magnitude and phase response, group delay, and zero-pole locations.

• Convolution and Filtering

The mathematical foundation of filtering is convolution. The MATLAB conv function performs standard one-dimensional convolution, convolving one vector with another:

conv([1 1 1],[1 1 1])

ans =

1 2 3 2 1

A digital filter's output y(k) is related to its input x(k) by convolution with its impulse response h(k).

If a digital filter's impulse response h(k) is finite in length, and the input x(k) is also of finite length, you can implement the filter using conv. Store x(k) in a vector x, h(k) in a vector h, and convolve the two:

x = randn(5,1); % A random vector of length 5