LINEAR CONVOLUTIONUSING GUI

PROJECT BY:> Priyanka G > Pranita> Nikita Kumar> Pallavi Manjunath> Ramya Mallya

convolution

Convolution is an integral concatenation of two signals.

It has many applications in numerous areas of signal processing. The most popular application is the determination of the output signal of a linear time-invariant system by convolving the input signal with the impulse response of the system.

The linear convolution of two continuous time signals x(t) and h(t) is given by:

For discrete time signals x(n) and h(n), the integration is replaced by a summation as follows:

Convolution mathematical expression

dthxthtxty )()()()()(

k

knhkxnhnxny )()()()()(

Convolution Graphical implementation

Changing the variable from n to k.

FOLDING h(k) resulting in h(-k)

SHIFTING h(-k) by n, resulting in h(n-k)

Element-wise MULTIPLICATION of the sequences x(k) and h(n-k)

SUMMATION of the product sequence resulting in the convolution value for x(n)*h(n)

Input:x(n)=[1,1,1]

Impulse Response:h(n)=[1,1,1]

Output:y(n)=x(n)*h(n) =[1,2,3,2,1]

Graphical user interfacegui

GUI  is a program interface that takes advantage of the computer's graphics capabilities to make the program easier to use.

Well-designed graphical user interfaces can free the user from learning complex command languages.  

It uses windows, icons, buttons and menus which can be manipulated by a mouse and a keyboard.

GUI can be created in Matlab, using the GUIDE.

>> guide

This will open the ‘Quick Start’ window.

Select the fist option: ‘Blank GUI (Default)’.

imPLEMENTING LINEAR CONVOLUTION USING GUI

Then, an untitled figurewill pop-up. You havesome components on

theleft menu, which youcan drag onto yourinterface.Here we need 4 editboxes.

1. Input x(n)2. Starting point of x(n)3. Input h(n)4. Starting point of h(n)

The static text boxes areused for naming.

We need 3 axes plots forx(n),h(n) and output,

andone push button toperform convolutionoperation.

Drag and drop the components on the MATLAB GUI. The size of your interface window can be reduced or increased by dragging its lower-right corner, as it’s done in other drawing programs.

When you double click on your components, the ‘Property Inspector’ window will appear and you can make necessary adjustments. Background color can also be changed.

You’ll be taken to the Matlab code (in the editor window) that will drive your interface. Matlab has automatically created functions related to your components.

The ‘Callback’ functions are the instructions that will be executed when the user pushes the buttons or does something with the components that you have included in your Matlab GUI. Here ‘CONVOLVE’ is the push button included so v need to program the push button with convolution code.

function varargout = pushbutton1_Callback(h, eventdata, handles, varargin) x = str2num(get(handles.input_x,'String'));ox = str2double(get(handles.input_ox,'String')); h1 = str2num(get(handles.input_h,'String'));oh = str2double(get(handles.input_oh,'String')); x1=x;h2=h1; lx=length(x);lh=length(h1);ex=ox+lx-1;eh=oh+lh-1;st=ox; hf=fliplr(h1); n1=[ox:ex];y3=[];

matlab code

for k=0:1:(lx+lh-2) n2=[(st-lh+1):st]; n=min(min(n1),min(n2)):max(max(n1),max(n2));y1=zeros(1,length(n));y2=y1;y1(find((n>=min(n1))&(n<=max(n1))==1))=x1;y2(find((n>=min(n2))&(n<=max(n2))==1))=hf;a2=sum(y1.*y2); y3=[y3,a2];st=st+1; end y=y3;

matlab code

axes(handles.axes_x)nnx=[ox:ex];stem(nnx,x)xlabel('n'); ylabel('x(n)');title('INPUT SIGNAL'); axes(handles.axes_h)nnh=[oh:eh];stem(nnh,h1)xlabel('n'); ylabel('h(n)');title('SYSTEM RESPONSE'); axes(handles.axes_y)nny=[(ox+oh):(ox+oh+lx+lh-2)];stem(nny,y)xlabel('n'); ylabel('y(n)');title('OUTPUT SIGNAL');msgbox(num2str(y));

matlab code

After entering the program save it and go to ‘Debug’ option. Then select ‘Run’.

execution

Enter the values of x(n) and h(n) and their starting points.

Press ‘CONVOLVE’ push button.

execution

When push button is pressed we get the convolved output

y(n) = x(n) * h(n)

and the input plots, and a message box that displays the values of the samples of the output signal.

execution

Applications of convolution

•In electronics engineering, the convolution of one function (the input signal) with a second function (the impulse response) gives the output of a linear time-invariant system (LTI). At any given moment, the output is an accumulated effect of all the prior values of the input function, with the most recent values typically having the most influence (expressed as a multiplicative factor). The impulse response function provides that factor as a function of the elapsed time since each input value occurred.

•In probability theory, the probability distribution of the sum of two independent random variables is the convolution of their individual distributions.

•In optics, many kinds of "blur" are described by convolutions. A shadow (e.g., the shadow on the table when you hold your hand between the table and a light source) is the convolution of the shape of the light source that is casting the shadow and the object whose shadow is being cast. An out-of-focus photograph is the convolution of the sharp image with the shape of the iris diaphragm.

Applications of convolution

•In linear acoustics, an echo is the convolution of the original sound with a function representing the various objects that are reflecting it.

•In artificial reverberation (digital signal processing, pro audio), convolution is used to map the impulse response of a real room on a digital audio signal (see previous and next point for additional information).

•In radiotherapy treatment planning systems, most part of all modern codes of calculation applies a convolution-superposition algorithm.In physics, wherever there is a linear system with a "superposition principle", a convolution operation makes an appearance.

We would like to thank our teacherand guide Mr. C.G. Raghavendra forgiving us the opportunity to work on

this project, and also for all his supportand his valuable inputs.

acknowledgements