这次的任务是要用单片机做FFT(快速离散傅利叶变换),我觉得单片机越来越无敌了...

于是,连续几天被埋在时间与空间的斗争中.因为单片机的硬件资源和条件所限,不能像PC上的MatLab那样方便地进行FFT,我们单片机 (SPCE061A)的时钟频率最快约为50MHz,其RAM为2K字,ROM为32K字.从前学数据结构和算法的时候,千方百计想着用时间换空间还是用 空间换时间,现在才发现,那时是站着说话不腰疼,因为无论拿什么换什么,都是行得通的,损失的效率对于PC应用来说(就我现在的水平),是可以忽略不计 的,毕竟不是ACM(此理论的唯一一次失手就是在某次ACM比赛上).

整体来说,单片机最大的弱点还是在于速度太慢,根本不可能进行实时FFT,而手动启动来进行运算的速度恐怕也慢得让人难以接受.为了加速,我几天苦苦挣扎 于算法的优化上.若不是因为数据精度还有一定的要求(汗~),不能采用8Bit数据,我肯定会将两个数据压缩到一个字(16位)中去以节省空间.坚决榨干 单片机的每一滴油!我将所有的冗余计算全部转化为变量表示独立计算然后重复利用,而常量,哪怕是局部的,我也将它写成常数表(虽然还不知道如何在C中将常 数表写入ROM区,再汗一个~).现在唯一的希望就在,单片机对浮点数运算的支持能力上...从前碰到浮点数我都会转化为整数,舍不得拿单片机来算浮点 数,而这次计算量实在太大了一点儿... 到目前为止,只在GCC上编译通过,并且结果是正确的(与MabLab对照),接下来还是任重而道远啊~

贴出主要部分代码:

/************************************************************ //FFT(快速离散傅利叶变换) //本例为8级256点数据

//HUST STI OE0402 POPAPPLE //popapple@gmail.com //2007-8-9 18:10:20

************************************************************/

#include \

#define LEVEL 8 //级数 #define LENGTH 256 //点数

//用结构体来表示复数

typedef struct _JComplex {

float real; float image;

}JComplex,*pJComplex;

typedef unsigned int uint;

//WN为复常数码表,为提高计算速度 //其值为exp(-j*2*pi/LENGTH)^n //n为[0..LENGTH/2-1] JComplex WN[LENGTH/2]= {

{ 1.0000,-0.0000},{ 0.9997,-0.0245},{ 0.9988,-0.0491},{ 0.9973,-0.0736},{ 0.9952,-0.0980},

{ 0.9925,-0.1224},{ 0.9892,-0.1467},{ 0.9853,-0.1710},{ 0.9808,-0.1951},{ 0.9757,-0.2191},

{ 0.9700,-0.2430},{ 0.9638,-0.2667},{ 0.9569,-0.2903},{ 0.9495,-0.3137},{ 0.9415,-0.3369},

{ 0.9330,-0.3599},{ 0.9239,-0.3827},{ 0.9142,-0.4052},{ 0.9040,-0.4276},{ 0.8932,-0.4496},

{ 0.8819,-0.4714},{ 0.8701,-0.4929},{ 0.8577,-0.5141},{ 0.8449,-0.5350},{ 0.8315,-0.5556},

{ 0.8176,-0.5758},{ 0.8032,-0.5957},{ 0.7883,-0.6152},{ 0.7730,-0.6344},{ 0.7572,-0.6532},

{ 0.7410,-0.6716},{ 0.7242,-0.6895},{ 0.7071,-0.7071},{ 0.6895,-0.7242},{ 0.6716,-0.7410},

{ 0.6532,-0.7572},{ 0.6344,-0.7730},{ 0.6152,-0.7883},{ 0.5957,-0.8032},{ 0.5758,-0.8176},

{ 0.5556,-0.8315},{ 0.5350,-0.8449},{ 0.5141,-0.8577},{ 0.4929,-0.8701},{ 0.4714,-0.8819},

{ 0.4496,-0.8932},{ 0.4276,-0.9040},{ 0.4052,-0.9142},{ 0.3827,-0.9239},{ 0.3599,-0.9330},

{ 0.3369,-0.9415},{ 0.3137,-0.9495},{ 0.2903,-0.9569},{ 0.2667,-0.9638},{ 0.2430,-0.9700},

{ 0.2191,-0.9757},{ 0.1951,-0.9808},{ 0.1710,-0.9853},{ 0.1467,-0.9892},{ 0.1224,-0.9925},

{ 0.0980,-0.9952},{ 0.0736,-0.9973},{ 0.0491,-0.9988},{ 0.0245,-0.9997},{ 0.0000,-1.0000},

{-0.0245,-0.9997},{-0.0491,-0.9988},{-0.0736,-0.9973},{-0.0980,-0.9952},{-0.1224,-0.9925},

{-0.1467,-0.9892},{-0.1710,-0.9853},{-0.1951,-0.9808},{-0.2191,-0.9757},{-0.2430,-0.9700},

{-0.2667,-0.9638},{-0.2903,-0.9569},{-0.3137,-0.9495},{-0.3369,-0.9415},{-0.3599,-0.9330},

{-0.3827,-0.9239},{-0.4052,-0.9142},{-0.4276,-0.9040},{-0.4496,-0.8932},{-0.4714,-0.8819},

{-0.4929,-0.8701},{-0.5141,-0.8577},{-0.5350,-0.8449},{-0.5556,-0.8315},{-0.5758,-0.8176},

{-0.5957,-0.8032},{-0.6152,-0.7883},{-0.6344,-0.7730},{-0.6532,-0.7572},{-0.6716,-0.7410},

{-0.6895,-0.7242},{-0.7071,-0.7071},{-0.7242,-0.6895},{-0.7410,-0.6716},{-0.7572,-0.6532},

{-0.7730,-0.6344},{-0.7883,-0.6152},{-0.8032,-0.5957},{-0.8176,-0.5758},{-0.8315,-0.5556},

{-0.8449,-0.5350},{-0.8577,-0.5141},{-0.8701,-0.4929},{-0.8819,-0.4714},{-0.8932,-0.4496},

{-0.9040,-0.4276},{-0.9142,-0.4052},{-0.9239,-0.3827},{-0.9330,-0.3599},{-0.9415,-0.3369},

{-0.9495,-0.3137},{-0.9569,-0.2903},{-0.9638,-0.2667},{-0.9700,-0.2430},{-0.9757,-0.2191},

{-0.9808,-0.1951},{-0.9853,-0.1710},{-0.9892,-0.1467},{-0.9925,-0.1224},{-0.9952,-0.0980},

{-0.9973,-0.0736},{-0.9988,-0.0491},{-0.9997,-0.0245} };

//复数乘法,进出参数均为结构体指针

void JC_Mul(pJComplex pjc_1,pJComplex pjc_2,pJComplex pjc_r)

{

pjc_r->real = (pjc_1->real)*(pjc_2->real) - (pjc_1->image)*(pjc_2->image); pjc_r->image = (pjc_1->real)*(pjc_2->image) + (pjc_1->image)*(pjc_2->real);