快速傅立叶变换FFT算法实验

1、. 快速傅立叶变换(FFT)算法实验实验目的：1. 加深对DFT 算法原理和基本性质的理解；2. 熟悉FFT 的算法原理和FFT 子程序的算法流程和应用；3. 学习用FFT 对连续信号和时域信号进行频谱分析的方法。程序流程图:傅立叶变换是一种将信号从时域到频域的变换形式，是声学、语音、电信和信号处理等领域中的一种重要分析工具。离散傅立叶变换（DFT）是连续傅立叶变换在离散系统中的表现形式，由于DFT 的计算量很大，因此在很长时间内其应用受到很大的限制。快速傅立叶变换（FFT）是离散傅立叶变换的一种高效运算方法。由于我们在计算DFT 时一次复数乘法需用四次实数乘法和二次实数加法；一次复数加法则需

2、二次实数加法。运算一个X（k）需要4N 次复数乘法及2N+2（N-1）=2（2N-1）次实数加法。所以整个DFT运算总共需要4N2 次实数乘法和N*2(2N-1)=2N(2N-1)次实数加法。如此一来，计算时乘法次数和加法次数都是和N2 成正比的，当N 很大时，运算量是可观的，因而需要改进对DFT 的算法减少运算速度。我们可以将DFT 运算中有些项合并。我们先设序列长度为N=2L，L 为整数。将N=2L 的序列x(n)(n=0,1,，N-1)，按N的奇偶分成两组，也就是说我们将一个N 点的DFT 分解成两个N/2 点的DFT，他们又重新组合成一个如下式所表达的N 点DFT：一般来说，输入被假定

3、为连续的。当输入为纯粹的实数的时候，我们就可以利用左右对称的特性更好的计算DFT。这样的RFFT 优化算法是包装算法：首先2N 点实数的连续输入称为“进包”。其次N 点的FFT 被连续运行。最后作为结果产生的N 点的合成输出是“打开”成为最初的与DFT 相符合的2N 点输入。使用这一思想，我们可以划分FFT 的大小，它有一半花费在包装输入O（N）的操作和打开输出上。AD原理图源程序*include<math.h>*include"DSP2833x_Device.h"/ DSP2833x Headerfile Include File*include"D

4、SP2833x_Examples.h"/ DSP2833x Examples Include Fi*include"comm.h"*include"i_cmplx.h"*include"ext_inf.h"/*/*if (CPU_FRQ_150MHZ) / Default - 150 MHz SYSCLKOUT*define ADC_MODCLK 0x3 / HSPCLK = SYSCLKOUT/2*ADC_MODCLK2 = 150/(2*3) = 25.0 MHz*endif*if (CPU_FRQ_100MHZ)*de

5、fine ADC_MODCLK 0x2 / HSPCLK = SYSCLKOUT/2*ADC_MODCLK2 = 100/(2*2) = 25.0 MHz*endif*define ADC_CKPS 0x1 / ADC module clock = HSPCLK/2*ADC_CKPS = 25.0MHz/(1*2) = 12.5MHz*define ADC_SHCLK 0xf / S/H width in ADC module periods = 16 ADC clocks*define AVG 1000 / Average sample limit*define ZOFFSET 0x00 /

6、 Average Zero offset*define BUF_SIZE 160 / Sample buffer size/*/unsignedint SampleLong;*define SAMPLELONG 3/unsignedint Ad_data1536=0;unsignedint Ad_data11536=0;unsignedint convcount = 0;volatileunsignedint adconvover =0;/int m=0;double n;double p,q;COMPLEX DDataBuffer512=0;Uint32 mod512;/unsignedin

7、t i;/*/ Prototype statements for functions found within this erruptvoidadc_isr(void);/*/voidmain(void)*if SAMPLELONG=1SampleLong =256;*endif*if SAMPLELONG=2SampleLong =512;*endif*if SAMPLELONG=3SampleLong =1024;*endif/ Step 1. Initialize System Control:/ PLL, WatchDog, enable Peripheral Cloc

8、ks/ This example function is found in the DSP2833x_SysCtrl.c file. InitSysCtrl();/ Step 2. Initialize GPIO:/ This example function is found in the DSP2833x_Gpio.c file and/ illustrates how to set the GPIO to it's default state. InitGpio(); / Skipped for this example/ Step 3. Clear all interrupts

9、 and initialize PIE vector table:/ Disable CPU interrupts DINT;/ Initialize the PIE control registers to their default state./ The default state is all PIE interrupts disabled and flags/ are cleared./ This function is found in the DSP2833x_PieCtrl.c file. InitPieCtrl();/ Disable CPU interrupts and c

10、lear all CPU interrupt flags: IER = 0x0000; IFR = 0x0000;/ Initialize the PIE vector table with pointers to the shell Interrupt/ Service Routines (ISR)./ This will populate the entire table, even if the interrupt/ is not used in this example. This is useful for debug purposes./ The shell ISR routine

11、s are found in DSP2833x_DefaultIsr.c./ This function is found in DSP2833x_PieVect.c. InitPieVectTable();/ Interrupts that are used in this example are re-mapped to/ ISR functions found within this file. EALLOW; / This is needed to write to EALLOW protected register PieVectTable.ADCINT = &adc_isr

12、; EDIS; / This is needed to disable write to EALLOW protected registers/ Step 4. Initialize all the Device Peripherals:/ This function is found in DSP2833x_InitPeripherals.c/ InitPeripherals(); / Not required for this example InitAdc(); / For this example, init the ADC/ Step 5. User specific code, e

13、nable interrupts:/ Enable ADCINT in PIE PieCtrlRegs.PIEIER1.bit.INTx6 = 1; IER |= M_INT1; / Enable CPU Interrupt 1 EINT; / Enable Global interrupt INTM ERTM; / Enable Global realtime interrupt DBGM AdcRegs.ADCTRL1.bit.ACQ_PS = ADC_SHCLK; AdcRegs.ADCTRL3.bit.ADCCLKPS = ADC_CKPS; AdcRegs.ADCTRL1.bit.S

14、EQ_CASC = 1; / 0 Non-Cascaded Mode; 1 Cascaded Mode AdcRegs.ADCTRL2.bit.INT_ENA_SEQ1 = 0x1; AdcRegs.ADCTRL2.bit.RST_SEQ1 = 0x1; AdcRegs.ADCCHSELSEQ1.bit.CONV00 = 0x6; AdcRegs.ADCMAXCONV.bit.MAX_CONV1 = 15; AdcRegs.ADCTRL2.bit.SOC_SEQ1 = 0x1 ; for(;)if (adconvover=1)for(i=0;i<(SampleLong/2);i+)DDa

15、taBufferi.real=Ad_data2*i; /short int DDataBufferi.imag=Ad_data2*i+1; /short intswitch(SampleLong)case 256:/*256 point*/ fft256(DDataBuffer,256); m=0;for(i=0;i<128;i+) p=DDataBufferi.real; q=DDataBufferi.imag; n=(long)p*(long)p+(long)q*(long)q; modm=sqrt(n); m+; break;case 512: /*512 point*/ fft5

16、12(DDataBuffer,512); m=0;for(i=0;i<256;i+) p=DDataBufferi.real; q=DDataBufferi.imag; n=(long)p*(long)p+(long)q*(long)q; modm=sqrt(n); m+; break;case 1024: /*1024 point*/ fft1024(DDataBuffer,1024); m=0;for(i=0;i<512;i+) p=DDataBufferi.real; q=DDataBufferi.imag; n=(long)p*(long)p+(long)q*(long)q; modm=sqrt(n); m+; break; adconvover=0; convcount =0; interruptvoidadc_isr(void)/ If 40 conversions have been logged, start overif(convcount = SampleLong) adconvover = 1; else Ad_dataconvcount = AdcRegs.ADCRESULT0 >>4; convcou