WAV系列之一：G711編解碼原理及代碼實現

參考自：https://blog.csdn.net/u012323667/article/details/79214336
　　　　https://blog.csdn.net/szfhy/article/details/52448906

G711也稱爲PCM（脈衝編碼調製），是國際電信聯盟制定出來的一套語音壓縮標準，主要用於電話。G711編碼的聲音清晰度好，語音自然度高，但壓縮效率低，數據量大常在32Kbps以上(推薦使用64Kbps)。它主要用脈衝編碼調製對音頻採樣，採樣率爲8KHz。它利用一個64Kbps未壓縮通道傳輸語音訊號。其壓縮率爲1：2，即把16位數據壓縮成8位。G.711是主流的波形聲音編解碼器。

G.711 標準下主要有兩種壓縮算法。一種是µ-law algorithm （又稱often u-law, ulaw, mu-law），主要運用於北美和日本；另一種是a-law algorithm，主要運用於歐洲和世界其他地區。其中，後者是特別設計用來方便計算機處理的。這兩種算法都使用一個採樣率爲8kHz的輸入來創建64Kbps的數字輸出。

1、a-law

a-law也叫g711a，輸入的是13位（其實是S16的高13位），使用在歐洲和其他地區，這種格式是經過特別設計的，便於數字設備進行快速運算。在WAV文件中的識別標誌是 WAVE_FORMAT_ALAW。

目前最主要的用途是將13bit的數據轉化成爲8bit的數據，13bit的最高位是符號位，轉化成爲的8bit並不是線性的，而是每幾位都有其意義。

• 第7位： 代表符號位，1表示正數，0表示負數，這點和一般的計算機系統正好相反
• 第4-6位： 這實際上是一個表示一種冪級數的位
• 第0-3位： 是具體的量化數值

運算過程如下：

（1） 取符號位並取反得到s，

（2） 獲取強度位eee，獲取方法如圖所示

（3） 獲取高位樣本位wxyz

（4） 組合爲seeewxyz，將seeewxyz逢偶數位取反，編碼完畢

示例：

輸入pcm數據爲3210，二進制對應爲（0000 1100 1000 1010）

二進制變換下排列組合方式（0 0001 1001 0001010）

（1） 獲取符號位最高位爲0，取反，s=1

（2） 獲取強度位0001，查表，編碼制應該是eee=100

（3） 獲取高位樣本wxyz=1001

（4） 組合爲11001001，逢偶數位取反爲10011100

編碼完畢。

編碼代碼如下：

#define MAX  (32635)   
void encode(unsigned char *dst, short *src, size_t len)
{ 
   for(int i = 0; i < len ; i++)
    {

 //      *dst++ =  *src++;
        short pcm  = *src++;
        int sign = (pcm & 0x8000) >> 8;
        if(sign != 0)
            pcm = -pcm;
        if(pcm > MAX)   pcm = MAX;
        int exponent = 7;
        int expMask;
        for(expMask = 0x4000; (pcm & expMask) == 0 && exponent >0; exponent--,expMask >>= 1){}
        int mantissa = (pcm >> ((exponent == 0) ? 4 : (exponent + 3))) & 0x0f;
        unsigned char alaw = (unsigned char)(sign | exponent << 4 | mantissa);
        *dst++ = (unsigned char)(alaw ^0xD5);   
    }     
} 

譯碼代碼如下：

void decode(short *dst, unsigned char *src, size_t len)
{
    for(size_t i=0; i < len  ; i++)
    {
        unsigned char alaw = *src++;
        alaw ^= 0xD5;
        int sign = alaw & 0x80;
        int exponent = (alaw & 0x70) >> 4;
        int data = alaw & 0x0f;
        data <<= 4;
        data += 8;   //丟失的a 寫1
        if(exponent != 0)  //將wxyz前面的1補上
            data += 0x100;
        if(exponent > 1)
            data <<= (exponent - 1);

        *dst++ = (short)(sign == 0 ? data : -data);

    }
} 

從編解碼的過程中，不難看出這種編碼方式的思路：
首先，我們確定目的，原始的碼流是13bit，除去符號位，12bit；我們需要將其轉化成爲8bit，除去符號位，還有7bit。

基本是思想就是：記錄符號位，記錄下最有效數據位（也就是除去符號位第一個1）後的4位，記錄下這4位移動到最低位所需的次數（放在0-3位中），解碼的時候根據這些信息還原，也就是最高的5位會是準確的，後面緊跟一個1是用來補償捨棄的數據，這就是誤差的來源。

但是在實際的操作中，是會直接將最後4位捨棄，然後在開始保留數據操作，也就是要是有效數據小於4位，最後全捨棄了，就會補償爲8。若大於4位小於8位，最後準確的數據可能就不會有5位了。

2、µ-law

µ-law也叫g711µ，使用在北美和日本，輸入的是14位，編碼算法就是查表，沒啥複雜算法，就是基礎值+平均偏移值，具體示例如下：

pcm=2345

（1）取得範圍值

+4062 to +2015 in 16 intervals of 128

（2）得到基礎值0x90，

（3）間隔數128，

（4）區間基本值4062，

（5）當前值2345和區間基本值差異4062-2345=1717，

（6）偏移值=1717/間隔數=1717/128，取整得到13，

（7）輸出爲0x90+13=0x9D

爲了簡化編碼過程，原始的線性幅度增加了33，使得編碼範圍從(0 - 8158)變爲(33 - 8191)。結果如下表所示：

Biased Linear Input Code	Compressed Code
00000001wxyza	000wxyz
0000001wxyzab	001wxyz
000001wxyzabc	010wxyz
00001wxyzabcd	011wxyz
0001wxyzabcde	100wxyz
001wxyzabcdef	101wxyz
01wxyzabcdefg	110wxyz
1wxyzabcdefgh	111wxyz

每個偏置線性輸入碼都有一個前導1來標識段號。段號的值等於7減去前導0的個數。量化間隔的個數是直接可用的四個位wxyz。後面的位(a - h)被忽略。

由上可見，這種編碼方式和a-Law是極爲類似的，是將14bit的數據編碼成爲8bit的數據（最高位都是符號位），8bit的每位數據的意義和a-Law編碼是一致的。但是和a-Law不同的是，這是對14bit的數據進行壓縮，並且壓縮完後的數據不僅僅是偶數位取反，而是每一位都需要做取反操作。

並且，注意到表中，這裏的最高位都是從1開始，和a-Law相比，這裏加了一位，但是seg還是3bit，所以對照兩表的第一個數是有明顯差異的，於是每個數加33是很有必要的，然後在解碼的時候減去，相當於移位就直接減少了一種情況。

注意：在g711.c代碼中，BIAS的值是0x84，該值是由33<<2得來的。

g711.c代碼如下：

/*
 * This source code is a product of Sun Microsystems, Inc. and is provided
 * for unrestricted use.  Users may copy or modify this source code without
 * charge.
 *
 * SUN SOURCE CODE IS PROVIDED AS IS WITH NO WARRANTIES OF ANY KIND INCLUDING
 * THE WARRANTIES OF DESIGN, MERCHANTIBILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE, OR ARISING FROM A COURSE OF DEALING, USAGE OR TRADE PRACTICE.
 *
 * Sun source code is provided with no support and without any obligation on
 * the part of Sun Microsystems, Inc. to assist in its use, correction,
 * modification or enhancement.
 *
 * SUN MICROSYSTEMS, INC. SHALL HAVE NO LIABILITY WITH RESPECT TO THE
 * INFRINGEMENT OF COPYRIGHTS, TRADE SECRETS OR ANY PATENTS BY THIS SOFTWARE
 * OR ANY PART THEREOF.
 *
 * In no event will Sun Microsystems, Inc. be liable for any lost revenue
 * or profits or other special, indirect and consequential damages, even if
 * Sun has been advised of the possibility of such damages.
 *
 * Sun Microsystems, Inc.
 * 2550 Garcia Avenue
 * Mountain View, California  94043
 */

/*
 * g711.c
 *
 * u-law, A-law and linear PCM conversions.
 */
#define	SIGN_BIT	(0x80)		/* Sign bit for a A-law byte. */
#define	QUANT_MASK	(0xf)		/* Quantization field mask. */
#define	NSEGS		(8)		/* Number of A-law segments. */
#define	SEG_SHIFT	(4)		/* Left shift for segment number. */
#define	SEG_MASK	(0x70)		/* Segment field mask. */

static short seg_end[8] = {0xFF, 0x1FF, 0x3FF, 0x7FF,
			    0xFFF, 0x1FFF, 0x3FFF, 0x7FFF};

/* copy from CCITT G.711 specifications */
unsigned char _u2a[128] = {			/* u- to A-law conversions */
	1,	1,	2,	2,	3,	3,	4,	4,
	5,	5,	6,	6,	7,	7,	8,	8,
	9,	10,	11,	12,	13,	14,	15,	16,
	17,	18,	19,	20,	21,	22,	23,	24,
	25,	27,	29,	31,	33,	34,	35,	36,
	37,	38,	39,	40,	41,	42,	43,	44,
	46,	48,	49,	50,	51,	52,	53,	54,
	55,	56,	57,	58,	59,	60,	61,	62,
	64,	65,	66,	67,	68,	69,	70,	71,
	72,	73,	74,	75,	76,	77,	78,	79,
	81,	82,	83,	84,	85,	86,	87,	88,
	89,	90,	91,	92,	93,	94,	95,	96,
	97,	98,	99,	100,	101,	102,	103,	104,
	105,	106,	107,	108,	109,	110,	111,	112,
	113,	114,	115,	116,	117,	118,	119,	120,
	121,	122,	123,	124,	125,	126,	127,	128};

unsigned char _a2u[128] = {			/* A- to u-law conversions */
	1,	3,	5,	7,	9,	11,	13,	15,
	16,	17,	18,	19,	20,	21,	22,	23,
	24,	25,	26,	27,	28,	29,	30,	31,
	32,	32,	33,	33,	34,	34,	35,	35,
	36,	37,	38,	39,	40,	41,	42,	43,
	44,	45,	46,	47,	48,	48,	49,	49,
	50,	51,	52,	53,	54,	55,	56,	57,
	58,	59,	60,	61,	62,	63,	64,	64,
	65,	66,	67,	68,	69,	70,	71,	72,
	73,	74,	75,	76,	77,	78,	79,	79,
	80,	81,	82,	83,	84,	85,	86,	87,
	88,	89,	90,	91,	92,	93,	94,	95,
	96,	97,	98,	99,	100,	101,	102,	103,
	104,	105,	106,	107,	108,	109,	110,	111,
	112,	113,	114,	115,	116,	117,	118,	119,
	120,	121,	122,	123,	124,	125,	126,	127};

static int
search(
	int		val,
	short		*table,
	int		size)
{
	int		i;

	for (i = 0; i < size; i++) {
		if (val <= *table++)
			return (i);
	}
	return (size);
}

/*
 * linear2alaw() - Convert a 16-bit linear PCM value to 8-bit A-law
 *
 * linear2alaw() accepts an 16-bit integer and encodes it as A-law data.
 *
 *		Linear Input Code	Compressed Code
 *	------------------------	---------------
 *	0000000wxyza			000wxyz
 *	0000001wxyza			001wxyz
 *	000001wxyzab			010wxyz
 *	00001wxyzabc			011wxyz
 *	0001wxyzabcd			100wxyz
 *	001wxyzabcde			101wxyz
 *	01wxyzabcdef			110wxyz
 *	1wxyzabcdefg			111wxyz
 *
 * For further information see John C. Bellamy's Digital Telephony, 1982,
 * John Wiley & Sons, pps 98-111 and 472-476.
 */
unsigned char
linear2alaw(
	int		pcm_val)	/* 2's complement (16-bit range) */
{
	int		mask;
	int		seg;
	unsigned char	aval;

	if (pcm_val >= 0) {
		mask = 0xD5;		/* sign (7th) bit = 1 */
	} else {
		mask = 0x55;		/* sign bit = 0 */
		pcm_val = -pcm_val - 8;
	}

	/* Convert the scaled magnitude to segment number. */
	seg = search(pcm_val, seg_end, 8);

	/* Combine the sign, segment, and quantization bits. */

	if (seg >= 8)		/* out of range, return maximum value. */
		return (0x7F ^ mask);
	else {
		aval = seg << SEG_SHIFT;
		if (seg < 2)
			aval |= (pcm_val >> 4) & QUANT_MASK;
		else
			aval |= (pcm_val >> (seg + 3)) & QUANT_MASK;
		return (aval ^ mask);
	}
}

/*
 * alaw2linear() - Convert an A-law value to 16-bit linear PCM
 *
 */
int
alaw2linear(
	unsigned char	a_val)
{
	int		t;
	int		seg;

	a_val ^= 0x55;

	t = (a_val & QUANT_MASK) << 4;
	seg = ((unsigned)a_val & SEG_MASK) >> SEG_SHIFT;
	switch (seg) {
	case 0:
		t += 8;
		break;
	case 1:
		t += 0x108;
		break;
	default:
		t += 0x108;
		t <<= seg - 1;
	}
	return ((a_val & SIGN_BIT) ? t : -t);
}

#define	BIAS		(0x84)		/* Bias for linear code. */

/*
 * linear2ulaw() - Convert a linear PCM value to u-law
 *
 * In order to simplify the encoding process, the original linear magnitude
 * is biased by adding 33 which shifts the encoding range from (0 - 8158) to
 * (33 - 8191). The result can be seen in the following encoding table:
 *
 *	Biased Linear Input Code	Compressed Code
 *	------------------------	---------------
 *	00000001wxyza			000wxyz
 *	0000001wxyzab			001wxyz
 *	000001wxyzabc			010wxyz
 *	00001wxyzabcd			011wxyz
 *	0001wxyzabcde			100wxyz
 *	001wxyzabcdef			101wxyz
 *	01wxyzabcdefg			110wxyz
 *	1wxyzabcdefgh			111wxyz
 *
 * Each biased linear code has a leading 1 which identifies the segment
 * number. The value of the segment number is equal to 7 minus the number
 * of leading 0's. The quantization interval is directly available as the
 * four bits wxyz.  * The trailing bits (a - h) are ignored.
 *
 * Ordinarily the complement of the resulting code word is used for
 * transmission, and so the code word is complemented before it is returned.
 *
 * For further information see John C. Bellamy's Digital Telephony, 1982,
 * John Wiley & Sons, pps 98-111 and 472-476.
 */
unsigned char
linear2ulaw(
	int		pcm_val)	/* 2's complement (16-bit range) */
{
	int		mask;
	int		seg;
	unsigned char	uval;

	/* Get the sign and the magnitude of the value. */
	if (pcm_val < 0) {
		pcm_val = BIAS - pcm_val;
		mask = 0x7F;
	} else {
		pcm_val += BIAS;
		mask = 0xFF;
	}

	/* Convert the scaled magnitude to segment number. */
	seg = search(pcm_val, seg_end, 8);

	/*
	 * Combine the sign, segment, quantization bits;
	 * and complement the code word.
	 */
	if (seg >= 8)		/* out of range, return maximum value. */
		return (0x7F ^ mask);
	else {
		uval = (seg << 4) | ((pcm_val >> (seg + 3)) & 0xF);
		return (uval ^ mask);
	}

}

/*
 * ulaw2linear() - Convert a u-law value to 16-bit linear PCM
 *
 * First, a biased linear code is derived from the code word. An unbiased
 * output can then be obtained by subtracting 33 from the biased code.
 *
 * Note that this function expects to be passed the complement of the
 * original code word. This is in keeping with ISDN conventions.
 */
int
ulaw2linear(
	unsigned char	u_val)
{
	int		t;

	/* Complement to obtain normal u-law value. */
	u_val = ~u_val;

	/*
	 * Extract and bias the quantization bits. Then
	 * shift up by the segment number and subtract out the bias.
	 */
	t = ((u_val & QUANT_MASK) << 3) + BIAS;
	t <<= ((unsigned)u_val & SEG_MASK) >> SEG_SHIFT;

	return ((u_val & SIGN_BIT) ? (BIAS - t) : (t - BIAS));
}

/* A-law to u-law conversion */
unsigned char
alaw2ulaw(
	unsigned char	aval)
{
	aval &= 0xff;
	return ((aval & 0x80) ? (0xFF ^ _a2u[aval ^ 0xD5]) :
	    (0x7F ^ _a2u[aval ^ 0x55]));
}

/* u-law to A-law conversion */
unsigned char
ulaw2alaw(
	unsigned char	uval)
{
	uval &= 0xff;
	return ((uval & 0x80) ? (0xD5 ^ (_u2a[0xFF ^ uval] - 1)) :
	    (0x55 ^ (_u2a[0x7F ^ uval] - 1)));
}