FSK解碼原理及實(shí)現(xiàn)方法

1.解碼數(shù)學(xué)原理
條件:
??? FSK的頻率為：1200/2200-->1/0;
??? wc = 1700,即(1200+2200)/2,設(shè)delta = +500/-500;
??? T是采樣周期
??? 則:
??????? 1200 可表示為cos((wc-delta)*t);
??????? 2200 可表示為cos((wc+delta)*t);
設(shè)第n次采樣值為cos((wc+/-delta)*(t-T)),第n+1采樣值為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)
將(1)式通過一個低通濾波器,則(1)式的(H)項(xiàng)即2位頻率被濾掉，只剩下(L)項(xiàng):
(1)--->Lowpass filter--->cos((wc+/-delta)*T)
再看:
??? cos((wc+/-delta)*T) = cos(wc*T+/-delta*T)??? (2)
??? IF:??? wc*T = PI/2???
??? 則 cos(wc*T+/-delta*T) = cos(PI/2+/-delta*T)
?????????????????????? = -/+sin(delta*T)??? (3)
(3)式則是FSK的值，
2.濾波器.
??? 對于來電顯示，下面這段程序可以達(dá)到解碼的要求
??? 定義:
??? #define??? FSKBUF 4
??? byte??? g_cADCResult;//A/D的采樣值
??? 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;
??? //在濾波之前將變量初化為0
??? 程序?qū)崿F(xiàn):(每次采樣要做以下工作，注意采樣頻率和CID的波特率不是倍數(shù)關(guān)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
??? }