请帮助解释傅里叶变换的代码
在网上找了一个音频播放同时显示波形的代码，主要是为了学习傅里叶变换。
我第一次接触，理解不了。
请懂得的朋友帮助解释。
谢谢。
class CFastFourierTransform
{
private:
float* xre;//实部
float* xim;//虚部
float* mag;
float* fftSin;//正弦
float* fftCos;//余弦
int* fftBr;
int ss;
int ss2;
int nu;
int nu1;
int BitRev(int j, int nu);
void PrepareFFTTables();
public:
CFastFourierTransform(int pSampleSize);
~CFastFourierTransform(void);
float* Calculate(float* pSample, size_t pSampleSize);
};
//构造函数
CFastFourierTransform::CFastFourierTransform(int pSampleSize)
{
xre = NULL;
xim = NULL;
mag = NULL;
fftSin = NULL;
fftCos = NULL;
fftBr = NULL;
ss = pSampleSize;//样本大小
ss2 = ss >> 1;//相当除以2
nu = (int) (log((float)ss) / log((float)2));
nu1 = nu - 1;
xre = new float[ss]; // real part
xim = new float[ss]; // image part
mag = new float[ss2];
PrepareFFTTables();
}
//析构函数容易懂，没有贴
//下面3个函数，完全没理解
void CFastFourierTransform::PrepareFFTTables()
{
int n2 = ss2;
int nu1 = nu - 1;
fftSin = new float[nu * n2];
fftCos = new float[nu * n2];
int k = 0;
int x = 0;
for (int l = 1; l <= nu; l++) {
while (k < ss) {
for (int i = 1; i <= n2; i++) {
float p = (float)BitRev(k >> nu1, nu);
float arg = (PI_2 * p) / (float) ss;
fftSin[x] = (float) sin(arg);
fftCos[x] = (float) cos(arg);
k++;
x++;
}
k += n2;
}
k = 0;
nu1--;
n2 >>= 1;
}
fftBr = new int[ss];
for (k = 0; k < ss; k++)
fftBr[k] = BitRev(k, nu);
}
int CFastFourierTransform::BitRev(int j, int nu) {
int j1 = j;
int k = 0;//返回值
for (int i = 1; i <= nu; i++) {
int j2 = j1 >> 1;
k = ((k << 1) + j1) - (j2 << 1);
j1 = j2;
}
return k;
}
float* CFastFourierTransform::Calculate(float* pSample, size_t pSampleSize) {
int n2 = ss2;
int nu1 = nu - 1;
int wAps = pSampleSize / ss;
size_t a = 0;
for (size_t b = 0; a < pSampleSize; b++) {
xre[b] = pSample[a];
xim[b] = 0.0F;
a += wAps;
}
int x = 0;
for (int l = 1; l <= nu; l++) {
for (int k = 0; k < ss; k += n2) {
for (int i = 1; i <= n2; i++) {
float c = fftCos[x];
float s = fftSin[x];
int kn2 = k + n2;
float tr = xre[kn2] * c + xim[kn2] * s;
float ti = xim[kn2] * c - xre[kn2] * s;
xre[kn2] = xre[k] - tr;
xim[kn2] = xim[k] - ti;
xre[k] += tr;
xim[k] += ti;
k++;
x++;
}
}
nu1--;
n2 >>= 1;
}
for (int k = 0; k < ss; k++) {
int r = fftBr[k];
if (r > k) {
float tr = xre[k];
float ti = xim[k];
xre[k] = xre[r];
xim[k] = xim[r];
xre[r] = tr;
xim[r] = ti;
}
}
mag[0] = (float) sqrt(xre[0] * xre[0] + xim[0] * xim[0]) / (float) ss;
for (int i = 1; i < ss2; i++)
mag[i] = (2.0F * (float) sqrt(xre[i] * xre[i] + xim[i] * xim[i])) / (float) ss;
return mag;
}
//下面是调用代码，可以不解释
void CSpectrumAnalyser::Process(float pFrameRateRatioHint)
{
if(IsIconic(m_Player->m_hWnd) == TRUE)
return;
for (int a = 0; a < m_SampleSize; a++) {
m_Left[a] = (m_Left[a] + m_Right[a]) / 2.0f;
}
float c = 0;
float pFrrh = pFrameRateRatioHint;
float* wFFT = m_FFT->Calculate(m_Left, m_SampleSize);//调用傅里叶变换
float wSadfrr = m_saDecay * pFrrh;
float wBw = ((float) m_width / (float) m_saBands);
RECT rect;
rect.left = 0;
rect.top = 0;
rect.right = rect.left + m_winwidth;
rect.bottom = rect.top + m_winheight;
FillRect(m_hdcMem, &rect, m_hbrush);
for (int a = 0, bd = 0; bd < m_saBands; a += (INT)m_saMultiplier, bd++) {
float wFs = 0;
for (int b = 0; b < (INT)m_saMultiplier; b++) {
wFs += wFFT[a + b];
}
wFs = (wFs * (float) log(bd + 2.0F));
if(wFs > 0.005F && wFs < 0.009F)
wFs *= 9.0F * PI;
else if(wFs > 0.01F && wFs < 0.1F)
wFs *= 3.0F * PI;
else if(wFs > 0.1F && wFs < 0.5F)
wFs *= PI; //enlarge PI times, if do not, the bar display abnormally, why??
if (wFs > 1.0F) {
wFs = 0.9F;
}
if (wFs >= (m_oldFFT[a] - wSadfrr)) {
m_oldFFT[a] = wFs;
} else {
m_oldFFT[a] -= wSadfrr;
if (m_oldFFT[a] < 0) {
m_oldFFT[a] = 0;
}
wFs = m_oldFFT[a];
}
drawSpectrumAnalyserBar(&rect, (int) c, m_height, (int) wBw - 1, (int) (wFs * m_height), bd);
c += wBw;
}
BitBlt(m_hdcScreen, 2, 41, m_winwidth, m_winheight, m_hdcMem, 0, 0, SRCCOPY);
}
