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IDFT 8 POINT USING DIF

Aim

To perform the 8 point IDFT using DIF process from a given discrete sequence in TMS320F2812 KIT.


Requirements


 
Theory

The algorithm for ifft(X) is the same as the algorithm for fft(X), except for a sign change and a scale factor of n = length(X). As for fft, the execution time for ifft depends on the length of the transform. It is fastest for powers of two. It is almost as fast for lengths that have only small prime factors. It is typically several times slower for lengths that are prime or which have large prime factors.


FFT algorithms can be used to compute an inverse DFT without any change in algorithm. The inverse DFT of an N-point sequence X(k) , k = 0,1, 2, . . . . ., N-1 is defined as




idft-8-dit-formula


 

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


  • Setup Code Composer Studio v3.3
  • Code Composer Studio

1. Open Setup Code Composer Studio v3.3.


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


  • In family, select C28xx.
  • In platform, select xds100 usb emulator.
  • In Endianness, select little.
  • 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.


  • Project name : type the project name.
  • Location : Browse, select the project location .
  • Project Type : Executable(.out)
  • Target : TMS320C28XX. Finish.

5. File → New → Source file.


  • Type the program in untitled window.

6. File → Save.


  • 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.


  • F2812_EzDSP_RAM_lnk.cmd
  • DSP281x_Headers_nonBIOS.cmd
  • DSP281x_GlobalVariableDefs.c

8. Project → Add files to project.


  • In file of type : All files
  • Ctrl + Select the following files
        -  projectname.c
        -  DSP281x_GlobalVariableDefs.c
        -  F2812_EzDSP_RAM_lnk.cmd
        -  DSP281x_Headers_nonBIOS.cmd open.

9. Project → Build Option.


In compiler tab, select Preprocessor


  • Include search path(-i) : C:\tidcs\c28\DSP281x\v120\DSP281x_headers\include

In linker tab, select libraries


  • Search path(-i) : C:\CCStudio_v3.3\C2000\cgtools\lib
  • Incl libraries(-l) : rts2800_ml.lib.

In linker tab, select Basic


  • Stack Size(-stack): 0x400 ok.

10. Project → Build (or) Rebuild all.


11. Connections for TMS320F2812 KIT



12. Debug → connect.


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


14. Debug → Go main.


15. View → Watch window → watch1.


  • Type the following array variable.
        -  Xr( sequence output)

16. Debug → Run.


17. Debug → Halt


18. See the output at following location, View &rarr memory


Enter An Address : 0x3F9200 → Enter.


Type the input


For example


  • 0x3F9200 – 0x0008
  • 0x3F9201 – 0x0007
  • 0x3F9202 – 0x0008
  • 0x3F9203 – 0x0007
  • 0x3F9204 – 0x0000
  • 0x3F9205 – 0x0000
  • 0x3F9206 – 0x0000
  • 0x3F9207 – 0x0000

19. Or see the ouput at watch window.




idft-8-point-dit-output-watch-window


Note: watch window will show exact decimal values, processor memory location will show a hexadecimal values.


Program

 

#include "DSP281x_Device.h"

#include <math.h>

void InitSystem();

float tr[8],ti[8],s1r[8],s1i[8],s2r[8],s2i[8],Xr[8],Xi[8],Yr[8],Yi[8],tempr[8],tempi[8];

const float xr[8] = {4,      1,  0,     1,  0,      1,  0,      1 };  // real part input

const float xi[8] = {0,  2.414,  0, 0.414,  0, -0.414,  0, -2.414 };     // imaginary part input

const float W0r = 1,

                        W0i = 0,

                        W1r = 0.707,

                        W1i = -0.707,

                        W2r = 0,

                        W2i = -1,                       

                        W3r = -0.707,

                        W3i = -0.707;

void main()

{

        int *Seq_out;

        int i=0;

Seq_out = (int *)0x003F9200;

        InitSystem();

 

        // stage one process

        s1r[0] = (xr[0] + xr[4]);

        s1i[0] = (xi[0] + xi[4]);

        s1r[1] = (xr[1] + xr[5]);

        s1i[1] = (xi[1] + xi[5]);

        s1r[2] = (xr[2] + xr[6]);

        s1i[2] = (xi[2] + xi[6]);

        s1r[3] = (xr[3] + xr[7]);

        s1i[3] = (xi[3] + xi[7]);

        s1r[4] = (xr[0] - xr[4]);

        s1i[4] = (xi[0] - xi[4]);

                tempr[0] = (xr[1] - xr[5]);

                tempi[0] = (xi[1] - xi[5]);

        s1r[5] = ((tempr[0] * W1r) - (tempi[0] * W1i));

        s1i[5] = ((tempr[0] * W1i) + (tempi[0] * W1r));

                tempr[1] = (xr[2] - xr[6]);

                tempi[1] = (xi[2] - xi[6]);

        s1r[6] = ((tempr[1] * W2r) - (tempi[1] * W2i));

        s1i[6] = ((tempr[1] * W2i) + (tempi[1] * W2r));

                tempr[2] = (xr[3] - xr[7]);

                tempi[2] = (xi[3] - xi[7]);

        s1r[7] = ((tempr[2] * W3r) - (tempi[2] * W3i));

        s1i[7] = ((tempr[2] * W3i) + (tempi[2] * W3r));

 

// stage two process

        s2r[0] = (s1r[0] + s1r[2]);                                                                                                                                                                                                             

        s2i[0] = (s1i[0] + s1i[2]);

 

        s2r[1] = (s1r[1] + s1r[3]);

        s2i[1] = (s1i[1] + s1i[3]);

        s2r[2] = (s1r[0] - s1r[2]);

        s2i[2] = (s1i[0] - s1i[2]);

                tempr[3] = (s1r[1] - s1r[3]);

                tempi[3] = (s1i[1] - s1i[3]);

        s2r[3] = ((tempr[3] * W2r) - (tempi[3] * W2i));

        s2i[3] = ((tempr[3] * W2i) + (tempi[3] * W2r));

        s2r[4] = (s1r[4] + s1r[6]);

        s2i[4] = (s1i[4] + s1i[6]);

        s2r[5] = (s1r[5] + s1r[7]);

        s2i[5] = (s1i[5] + s1i[7]);

        s2r[6] = (s1r[4] - s1r[6]);

        s2i[6] = (s1i[4] - s1i[6]);

                tempr[4] = s1r[5] - s1r[7];

                tempi[4] = s1i[5] - s1i[7];

        s2r[7] = ((tempr[4] * W2r) - (tempi[4] * W2i));

        s2i[7] = ((tempr[4] * W2i) + (tempi[4] * W2r));

 

//  output

        Xr[0] = (s2r[0] + s2r[1]);                                                                                                                                                                                                             

        Xi[0] = (s2i[0] + s2i[1]);

        Xr[1] = (s2r[0] - s2r[1]);                                                                                                                                                                                                             

        Xi[1] = (s2i[0] - s2i[1]);

        Xr[2] = (s2r[2] + s2r[3]);                                                                                                                                                                                                             

        Xi[2] = (s2i[2] + s2i[3]);

        Xr[3] = (s2r[2] - s2r[3]);                                                                                                                                                                                                             

        Xi[3] = (s2i[2] - s2i[3]);

        Xr[4] = (s2r[4] + s2r[5]);                                                                                                                                                                                                             

        Xi[4] = (s2i[4] + s2i[5]);

        Xr[5] = (s2r[4] - s2r[5]);                                                                                                                                                                                                             

        Xi[5] = (s2i[4] - s2i[5]);

        Xr[6] = (s2r[6] + s2r[7]);                                                                                                                                                                                                             

        Xi[6] = (s2i[6] + s2i[7]);

        Xr[7] = (s2r[6] - s2r[7]);                                                                                                                                                                                                             

        Xi[7] = (s2i[6] - s2i[7]);

 

// bit reversal

tr[0] = Xr[0];

        ti[0] = Xi[0];

        tr[1] = Xr[4];

        ti[1] = Xi[4];

        tr[2] = Xr[2];

        ti[2] = Xi[2];

        tr[3] = Xr[6];

        ti[3] = Xi[6];

        tr[4] = Xr[1];

        ti[4] = Xi[1];

        tr[5] = Xr[5];

        ti[5] = Xi[5];

        tr[6] = Xr[3];

        ti[6] = Xi[3];

        tr[7] = Xr[7];

        ti[7] = Xi[7];

 

// sending output array to memory location        

        for(i=0;i<8;i++)

        {      

                *Seq_out ++= tr[i];

        }

        for(;;);

}

void InitSystem()

{

                EALLOW;

                SysCtrlRegs.WDCR= 0x0068;            // Setup the watchdog

                                                                        // 0x0068  to disable the Watchdog , Prescaler = 1

                                                                        // 0x00AF  to NOT disable the Watchdog, Prescaler = 64

                SysCtrlRegs.SCSR = 0;                  // Watchdog generates a RESET      

                SysCtrlRegs.PLLCR.bit.DIV = 10;        // Setup the Clock PLL to multiply by 5

                SysCtrlRegs.HISPCP.all = 0x1; // Setup Highspeed Clock Prescaler to divide by 2

                SysCtrlRegs.LOSPCP.all = 0x2; // Setup Lowspeed CLock Prescaler to divide by 4

                // Peripheral clock enables set for the selected peripherals.  

                SysCtrlRegs.PCLKCR.bit.EVAENCLK=0;

                SysCtrlRegs.PCLKCR.bit.EVBENCLK=0;

                SysCtrlRegs.PCLKCR.bit.SCIAENCLK=0;

                SysCtrlRegs.PCLKCR.bit.SCIBENCLK=0;

                SysCtrlRegs.PCLKCR.bit.MCBSPENCLK=0;

                SysCtrlRegs.PCLKCR.bit.SPIENCLK=0;

                SysCtrlRegs.PCLKCR.bit.ECANENCLK=0;

                SysCtrlRegs.PCLKCR.bit.ADCENCLK=0;

                EDIS;

}

      


Result

Thus, the 8 point IDFT of given sequence has performed and the result is stored at memory location(0x3F9200).