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Some Case Studies on Signal, Audio and Image Processing Using Matlab

Some Case Studies on Signal, Audio and Image Processing Using Matlab

Dr. Hedaya Mahmood Alasooly

Some Case Studies on Signal, Audio and Image Processing Using Matlab

Supervised By

Dr. Hedaya Mahmood Alasooly

Diploma Project

Done by:

20073986: Mohameed Abdl Elah

20072601: Khalil Ebrahim Ahmed

20070618: Hasan Makki Mahdi

20073359: Ameen Ebrahim Ahmed

Abstract

This project shows some selected signal techniques, including image and audio processing, using the Matlab digital signal processing and image processing toolboxes. The project is divided to 3 parts.

Part I includes design and implementation of different types of filters for filtering signal that has different sinusoidal frequency components or noise. The comparison was made between FIR low pass flter, butterworth filter, Chebycheve Type I low pass filter and Chebycheve Type II low pass filter. Then different types of IIR Butterworth filters were designed and implemented to filter a signal that has many harmonics components, including low pass filter, high pass filter, stop band filter and band pass filter.

Part II examined audio filtering in the sense of specific frequency suppression and extraction. There are many different types of filters available for the construction of filters. We will specifically use the Butterworth filter. An audio signal was read and different types of filters, including low pass filter, high pass filter, stop band filter and band pass filter, were designed and implemented in order to filter the audio signal from some frequency bands. Then the discrete cosine transform compression examined on the audio signal at different compression rates: 50%, 75% , 87.5%

Part III deals with image processing; the project shows examples in smoothing, sharpening, and edge detection. Other useful operations on the image were tested, including image cropping, image resizing, image, histogram equalization and altering image brightness

Table of Contents

1. Introduction

2. Theory Related To Project

2.1 What is the signal Processing Toolbox in Matlab

2.2 Signal and Linear System Models

2.3 Filter Implementation and Analysis

2.4 Digital Filter Design Methods

2.5 Transforms

2.6 Frequency Response

2.7 GUIs for Filter Design, Analysis, and Visualization……………18

3. Descrption of Project and Results and Analysis

3.1 Part I: Design different filters for filtering sinusoidal signal

3.2 Part II: Audio Processing

3.2.2 Audio Compressing

3.3 Part III: Image Processing

3.3.1 Filtering

3.3.2 Other operations: Image cropping, sizing and histogram equalization, changing brightness

4. Conclusion

5. References

1. Introduction:

1. Introduction:

This project shows some selected signal techniques, including image and audio processing, using the Matlab digital signal processing and image processing toolboxes. The project is divided to 3 parts

Then the discrete cosine transform compression examined on the audio signal at different compression rates: 50%, 75% , 87.5%

2.Theory Related To Project:

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

h = [1 1 1 1]/4; % Length 4 averaging filter

y = conv(h,x);

The length of the output is the sum of the finite-length input vectors minus 1.

Filters and Transfer Functions

In general, the z-transform Y(z) of a discrete-time filter's output y(n) is related to the z-transform X(z) of the input by

where H(z) is the filter's transfer function. Here, the constants b(i) and a(i) are the filter coefficients and the order of the filter is the maximum of n and m.

MATLAB filter functions store the coefficients in two vectors, one for the numerator and one for the denominator. By convention, it uses row vectors for filter coefficients.

Filter Coefficients and Filter Names

Many standard names for filters reflect the number of a and b coefficients present:

When n = 0 (that is, b is a scalar), the filter is an Infinite Impulse Response (IIR), all-pole, recursive, or autoregressive (AR) filter.
When m = 0 (that is, a is a scalar), the filter is a Finite Impulse Response (FIR), all-zero, nonrecursive, or moving-average (MA) filter.
If both n and m are greater than zero, the filter is an IIR, pole-zero, recursive, or autoregressive moving-average (ARMA) filter.

The acronyms AR, MA, and ARMA are usually applied to filters associated with filtered stochastic processes.

Filtering with the filter Function

It is simple to work back to a difference equation from the z-transform relation shown earlier. Assume that a(1) = 1. Move the denominator to the left-hand side and take the inverse z-transform.

In terms of current and past inputs, and past outputs, y(k) is

Impressum

Verlag: BookRix GmbH & Co. KG

Tag der Veröffentlichung: 30.05.2020
ISBN: 978-3-7487-4380-4

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