Goeff Probert
Compute signal power with fixed-point calculators
Embedded Systems Programming
October, 2003
Listing 1: Fixed-point signal level calculator
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#define MAX_TERM
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27
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#define SCALE
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131072
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// 2^17
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// LOG10_2NM1[n] = 131072 * 100 * 10 * log10((2^n)/(2^n-1)) n >= 1
int32_t const LOG10_2NM1[MAX_TERM] =
{
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0,
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39456604,
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16375970,
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7601120,
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3673781,
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1807258,
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896457,
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446464,
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222794,
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111288,
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55617,
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27802,
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13899,
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6949,
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3474,
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1737,
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869,
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434,
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217,
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109,
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54,
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27,
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14,
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7,
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3,
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2,
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1
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};
// LOG10_2N[n] = -131072 * 100 * 10 * log10(2^n) 0 <= n < 32
int32_t const LOG10_2N[] =
{
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0, |
-39456604,
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-78913207,
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-118369811,
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-157826414,
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-197283018,
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-236739622,
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-276196225,
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-315652829,
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-355109432,
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-394566036,
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-434022640,
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-473479243,
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-512935847,
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-552392450,
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-591849054,
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-631305657,
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-670762261,
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-710218865,
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-749675468,
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-789132072,
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-828588675,
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-868045279,
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-907501883,
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-946958486,
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-986415090,
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-1025871693,
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-1065328297,
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-1104784901,
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-1144241504,
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-1183698108,
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-1223154711
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};
int32_t
intLog10(uint32_t x)
{
uint32_t z;
int32_t y;
int k;
/*
* log10(0) = -infiniti
*/
if (x == 0) return (-2147483648); // largest negative int32_t value
/*
* Left shift the argument until 1 <= x < 2.
*/
for (k = 0; k < 32; k++)
{
if (x & 0x80000000) break;
x <<= 1;
}
/*
* y is a function of the number of shifts just made.
*/
y = LOG10_2N[k];
/*
* Begin Knuth's log algorithm.
*/
z = x >> 1;
for (k = 1; k < MAX_TERM; )
{
if (x == 0x80000000) break;
if ((x - z) < 0x80000000)
{
z >>= 1;
k++;
}
else
{
x -= z;
z = x >> k;
y += LOG10_2NM1[k];
}
}
return (y);
} /* intLog10() */
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#define M0_ALAW -159540501
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// log10(((1120**2 + 2624**2)/2) << 5)
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#define M0_ULAW -81494089
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// log10(((2207**2 + 5215**2)/2) << 5)
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int32_t
dBm0(uint32_t avesq, int32_t m0)
{
return ((intLog10(avesq << 5) - m0) / SCALE);
} /* dBm0() */