FSK解码原理及实现方法

1.解码数学原理
条件:
    FSK的频率为：1200/2200-->1/0;
    wc = 1700,即(1200+2200)/2,设delta = +500/-500;
    T是采样周期
    则:
        1200 可表示为cos((wc-delta)*t);
        2200 可表示为cos((wc+delta)*t);
设第n次采样值为cos((wc+/-delta)*(t-T)),第n+1采样值为cos((wc+/-delta)*t).
有：
value(n)*value(n+1) =
cos((wc+/-delta)*t)*cos((wc+/-delta)*(t-T)) 
= [cos((wc+/-delta)*t+(wc+/-delta)*(t-T))+cos((wc+/-delta)*t-(wc+/-delta)*(t-
T))]/2
= [cos(2*(wc+/-delta)*t-(wc+/-delta)*T) + cos((wc+/-delta)*T)]/2    
        (1)
        (H)                (L)
将(1)式通过一个低通滤波器,则(1)式的(H)项即2位频率被滤掉，只剩下(L)项:
(1)--->Lowpass filter--->cos((wc+/-delta)*T)
再看:
    cos((wc+/-delta)*T) = cos(wc*T+/-delta*T)    (2)
    IF:    wc*T = PI/2   
    则 cos(wc*T+/-delta*T) = cos(PI/2+/-delta*T)
                       = -/+sin(delta*T)    (3)
(3)式则是FSK的值，
2.滤波器.
    对于来电显示，下面这段程序可以达到解码的要求
    定义:
    #define    FSKBUF 4
    byte    g_cADCResult;//A/D的采样值
    int    currentx,currenty,lastx,last_sample;
    int    g_iFSKBuf[FSKBUF];
    int    g_iFSKAvg;
    int    g_iFSKBuf1[FSKBUF];
    int    g_iFSKAvg1;
    int    g_iFSKBuf2[FSKBUF];
    int    g_iFSKAvg2;
    byte    g_cFSKBufPoint;
    //在滤波之前将变量初化为0
    程序实现:(每次采样要做以下工作，注意采样频率和CID的波特率不是倍数关系
    currentx = g_cADCResult;
    currenty = last_sample;
    last_sample = currentx;
    //last sample in currenty,now sample in currenx;
    currenty  *= currentx;//cos(t)*cos(t-T) = -/+sin(delta*T);
    //------avg--lowpass filter;
    g_iFSKAvg -= g_iFSKBuf[g_cFSKBufPoint];
    g_iFSKBuf[g_cFSKBufPoint] = currenty;
    g_iFSKAvg += currenty;
    currenty = g_iFSKAvg;
    //---------end filter;
    g_iFSKAvg1 -= g_iFSKBuf1[g_cFSKBufPoint];
    g_iFSKBuf1[g_cFSKBufPoint] = currenty;
    g_iFSKAvg1 += currenty;
    currenty = g_iFSKAvg1;
    //second filter over
    g_iFSKAvg2 -= g_iFSKBuf2[g_cFSKBufPoint];
    g_iFSKBuf2[g_cFSKBufPoint] = currenty;
    g_iFSKAvg2 += currenty;
    currenty = g_iFSKAvg2;
    //third filter over
    g_cFSKBufPoint++;
    g_cFSKBufPoint %= FSKBUF;
    if(currenty>0)
    {
        //接收到bit 1
    }
    else
    {
        //接收到bit 0
    }