## Aim

To perform the Circular Convolution of two given discrete sequence in TMS320F2812 KIT.

☞CCS v3.3

☞ USB Cable

## Theory

The circular convolution is also known as cyclic convolution. A convolution operation that contains a circular shift is called circular convolutionCircular convolution of two sequences x1[n] and x2[n] is given by

x1[n]*x2[n] = εk x1[k] x2((n-k))N, 0≤ n ≤N-1

Where k ranges between 0 and N-1

One of the methods to find circular convolution….

In circular convolution the length of the output sequence will be equal to length of the input sequence ie. length(y)=length(x)

So first perform linear convolution using any of the methods u find easier.

If m is the length of ‘x’ and n is the length of the ‘h’ then length of ‘yl’ from linear conv is m+n-1.

Since length of output from circular conv is m, we will bring the last n-1 terms from ‘yl’ and add them to first n-1 terms. So the obtained output is circularly convoluted output.

For eg. if x= 1, 2, 3, 4 and h= 2,3,1 lin conv op ie. yl= 2,7,13,19,15,4

bring last two (n-1) terms to first two terms so circularly convoluted op is yc= 17, 11,13,19

## Procedure for build a project on Circular Convolution using TMS320F2812 DSP

Note: Once you install the Code Composer Studio v 3.3 software, the two icons will display in desktop

I. Setup Code Composer Studio v3.3 II. Code Composer Studio

1.Open Setup Code Composer Studio v3.3.

2.In System Configuration, select the board then >> Remove all >> yes.

a.In family, select C28xx.

b.In platform, select xds100 usb emulator.

c.In Endianness, select little.

d.Select F2812 XDS100 USB Emulator >> add >> save & quit >>no.

Note: The above two steps only for first time to setup the processor in CCS.

3.Open Code Composer Studio v3.3.

4.Project >> New.

a.Project name: type the project name.

b.Location: Browse, select the project location.

c.Project Type: Executable(.out)

d.Target: TMS320C28XX. >> Finish.

5. File >> New >> Source file.

a.Type the program in untitled window.

6. File >> Save.

a. Browse our project location then type our project name.c ( .c extension is must) >>save.

7. Paste the following two cmd files in our project folder.

a.F2812_EzDSP_RAM_lnk.cmd

c.DSP281x_GlobalVariableDefs.c

8. Project >> Add files to project.

a. In file of type : All files

b. Ctrl + Select the following files

☞projectname.c

☞DSP281x_GlobalVariableDefs.c

☞F2812_EzDSP_RAM_lnk.cmd

9.Project >> Build Option.

a.In compiler tab, select Preprocessor

>>  Search path(-i): C:\CCStudio_v3.3\C2000\cgtools\lib

>>   Incl libraries (-l): rts2800_ml.lib.

>>   Stack Size (-stack): 0x400 >> ok.

10.Project >> Build (or) Rebuild all.

11.Connections for TMS320F2812 KIT:

a.Connect 5v adapter to TMS320F2812 KIT.

b.Connect usb cable to TMS320F2812 KIT from pc.

c.Power on the TMS320F2812 KIT.

12.Debug >> connect.

13.File >> Load Program >> Browse and select the projectname.out file >> open

14.Debug >> Go main.

15.View >> memory

a.Enter an Address: 0x3F9100 >> Enter.

b.Type the input.

>>   For example:

```1.0x3F9100 – 0x0001

2.0x3F9101 – 0x0001

3.0x3F9102 – 0x0001

4.0x3F9103 – 0x0001
```

16.View >> memory

a.Enter an Address: 0x3F9200 >> Enter.

>>   For example:

```1.0x3F9200 – 0x0001

2.0x3F9201 – 0x0001

3.0x3F9202 – 0x0001

4.0x3F9203 – 0x0001
```

a.Enter an Address: 0x3F9300 >> Enter.

18.Debug >> Run.

19.Debug >> Halt.

20.See the output at following location,

>>   For example:

```1.0x3F9300 – 0x0004

2.0x3F9301 – 0x0004

3.0x3F9302 – 0x0004

4.0x3F9303 – 0x0004
```

## Program for Circular Convolution using TMS320F2812 DSP

``````void main()
{
int *in1,*in2,*out,*temp,i,sum=0,j;
in1 = (int *)0x003F9100;
in2 = (int *)0x003F9200;
out = (int *)0x003F9300;
temp = (int *)0x003F9400;
for(i=0;i<4;i++)
{
if(i == 1)
temp[i+2] = in1[i];
else if(i == 3)
temp[i-2] = in1[i];
else
temp[i] = in1[i];
}
for(i=0;i<4;i++)
{
sum = 0;
for(j=0;j<4;j++)
{
sum+=(in2[j] * temp[j]);
}
out[i] = sum;
rot(temp);
}
while(1);
}

rot(int *x)
{
int t;
t = x[0];
x[0] = x[3];
x[3] = x[2];
x[2] = x[1];
x[1] = t;
}
﻿``````

## Result

Thus, the Circular Convolution of two given discrete sequence has performed and the result is stored at memory location (0x3F9300).

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