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Zero poles at half nyquist

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This commit is contained in:
Robin. P. Clark 2019-09-10 09:12:01 +01:00
parent e82ae9f183
commit 5d5a2cb72f
3 changed files with 196 additions and 7 deletions
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1
Makefile
View File

@ -3,4 +3,5 @@
two_pole:
gcc -o tp two_pole_7_8.c -lm
./tp > tp.dat
vi tp.dat
gnuplot < tp.gpt

4
tp.gpt
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@ -1,7 +1,9 @@
#plot "tp.dat" using 1:3 title "input", "tp.dat" using 1:5 title "two pole", "tp.dat" using 1:6 title "34LAG", "tp.dat" using 1:7 title "78LAG"
plot "tp.dat" using 1:3 title "input" with linespoints, "tp.dat" using 1:5 title "two pole" with linespoints, "tp.dat" using 1:7 title "78LAG" with linespoints, "tp.dat" using 1:9 title "78LAG TWICE" with linespoints
#plot "tp.dat" using 1:3 title "input" with linespoints, "tp.dat" using 1:5 title "two pole" with linespoints, "tp.dat" using 1:7 title "78LAG" with linespoints, "tp.dat" using 1:9 title "78LAG TWICE" with linespoints, "tp.dat" using 1:11 title "two pole 15 16"
plot "tp.dat" using 1:3 title "input" with linespoints, "tp.dat" using 1:5 title "two pole" with linespoints, "tp.dat" using 1:11 title "two pole 15 16" with linespoints, "tp.dat" using 1:13 title "zero only" with linespoints
plot "tp.dat" using 1:3 title "input" with linespoints, "tp.dat" using 1:5 title "two pole" with linespoints, "tp.dat" using 1:15 title "zero only^2" with linespoints, "tp.dat" using 1:17 title "zero only^3" with linespoints,"tp.dat" using 1:19 title "zero only^4" with linespoints
!sleep 10
!sleep 10

198
two_pole_7_8.c
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@ -23,7 +23,7 @@
int16_t /* squared version of LAG_7_8 */
two_pole_7_8 ( int16_t input ) {
static int32_t y1=0,y2=0;
static int32_t y1=0,y2=0, x1,x2;
int32_t * res;
int32_t y0;
@ -45,7 +45,7 @@ two_pole_7_8 ( int16_t input ) {
y0 = x0 +
y0 = x0 +
// (14.0 / 8.0) * (double) y1
// this is 7/4
y1 + y1 - (y1>>2)
@ -67,6 +67,8 @@ two_pole_7_8 ( int16_t input ) {
y2 = y1;
y1 = y0;
x2 = x1;
x1 = x0;
//res = (short int *)&y0;
//res++;
@ -77,13 +79,185 @@ two_pole_7_8 ( int16_t input ) {
return y0>>(BIN_FRACS+3); // divide back down for scaling and then divide by 8 filter gain // *res;
}
int16_t /* squared version of LAG_7_8 */
two_pole_7_8_zg ( int16_t input ) { // with zero guard
static int32_t y1=0,y2=0, x1,x2;
int32_t * res;
int32_t y0;
int32_t x0 = input;
// x0 times 0.125
// the minus 3 divides by 8 : DOUBLE POLE
x0 <<= (BIN_FRACS-3) ; // now all calculations are done times BIN_FRACS^2
// this works stabley but not well WHY?
//y0 = x0 + y1-(y1>>3) - ((y2>>1) + (y2>>2) + (y2>>6));
// should be
//y0 = x0 + y1+y1-(y1>>2) - (y2>>1 + y2>>2 + y2>>6);
//
//
// OK this works well
// y0 = x0 + (14.0 / 8.0) * (double) y1 - (49.0/64.0) * (double) y2;
y0 = (x0>>1) + (x0>>2) + (x0>>6) + (x2>>1) + // 49/64 * x0 + 1/2 * x2
// (14.0 / 8.0) * (double) y1
// this is 7/4
y1 + y1 - (y1>>2)
//
//
// - (49.0/64.0) * (double) y2;
//
- ( (y2>>1) + // half
(y2>>2) + // quarter
(y2>>6) ); // 64th
//
// y0 = x0/64 + (y1 * 7) / 4 + (y2*49)/64;
// see what happens when y2>>6 is left out. I theory d.c goes unstable
// and yes it does! 25AUG2019
// y0 = x0 + y1-(y1>>3) - (y2>>1 + y2>>2 /* + y2>>6*/);
y2 = y1;
y1 = y0;
x2 = x1;
x1 = x0;
//res = (short int *)&y0;
//res++;
//printf("y0=%X res should be %X res=%x\n",y0, y0>>16, res);
//
// the plus 3 divides by 8
return y0>>(BIN_FRACS+3); // divide back down for scaling and then divide by 8 filter gain // *res;
}
#define BIN_FRACS_15_16 9
// this is a 64 bit machine (the pi)
//
int16_t /* squared version of LAG_7_8 */
two_pole_15_16 ( int16_t input ) {
static int32_t y1=0,y2=0, x1, x2;
int32_t * res;
int32_t y0;
int32_t x0 = input;
// x0 times 0.125
// the minus 3 divides by 8 : DOUBLE POLE
x0 <<= (BIN_FRACS_15_16) ; // now all calculations are done times BIN_FRACS^2
y0 = x0 +
// (30.0 / 16.0) * (double) y1
// this is 7/8
y1 + y1 - (y1>>3)
//
//
// - (49.0/64.0) * (double) y2;
//
- ( (y2>>1) + // half
(y2>>2) + // quarter
(y2>>3) + // eighth
(y2>>8) // 256th
);
y2 = y1;
y1 = y0;
// gain of the filter is 256 ((1/16)^2) if x0 is allowed in withiout pre-dividing
//
y0 >>= 8;
return y0>>(BIN_FRACS_15_16); // divide back down for scaling and then divide by 8 filter gain // *res;
}
#define RAND_RANGE 500
#define DC_TERM 1500
int zero_only_2 ( int input )
{
static int x0,x1,x2,x3,x4;
int res;
// (z^2+1)^2
// z^4 z^2 1
res = input + 2*x2 + x4;
x4 = x3;
x3 = x2;
x2 = x1;
x1 = input;
return res/4;
}
int zero_only_3 ( int input )
{
static int x0,x1,x2,x3,x4;
static int x5,x6,x7,x8,x9;
int res;
// (z^2+1)^3
// z^6 z^4 2z^3 z^2 2*z 1
res = input + x2 +2*x3 + x4 +2*x2 + x6;
x8 = x7;
x7 = x6;
x6 = x5;
x5 = x4;
x4 = x3;
x3 = x2;
x2 = x1;
x1 = input;
return res/8;
}
int zero_only_4 ( int input )
{
static int x0,x1,x2,x3,x4;
static int x5,x6,x7,x8,x9;
int res;
// z^8 2z^6 2z^5 2z^4 4z^3 2z^2 2z^1 + 1
res = input + 2*x2 +2*x3 + x4 + 4*x5 + 2*x6 + 2*x7 + x8;
x8 = x7;
x7 = x6;
x6 = x5;
x5 = x4;
x4 = x3;
x3 = x2;
x2 = x1;
x1 = input;
return res/16;
}
int main () {
int i;
int16_t val,res, res34, res78, res78_2, rr;
int i, zo2,zo3,zo4;
int16_t val,res, res34, res78, res78_2, rr, res_1516;
for (i=0;i<1000;i++) {
@ -99,12 +273,22 @@ int main () {
res = two_pole_7_8 ( val );
res_1516 = two_pole_15_16 ( val );
zo2 = zero_only_2 (val);
zo3 = zero_only_3 (val);
zo4 = zero_only_4 (val);
res34 = (((res34<<2) - res34)>>2) + (val>>2);
res78 = (((res78<<3) - res78)>>3) + (val>>3);
res78_2 = (((res78_2<<3) - res78_2)>>3) + (res78>>3); // feed res78 into another should be the same as two pole
printf ("%d val %d res %d res34 %d res78 %d res78_2 %d\n",i, val,res, res34, res78, res78_2);
// 1 3 5 7 9 11 13 15 17 19
printf ("%d val %d res %d res34 %d res78 %d res78_2 %d res_1516 %d zo2 %d zo3 %d zo4 %d EOL\n",
i, val,res, res34, res78, res78_2, res_1516, zo2, zo3, zo4);
}
@ -112,3 +296,5 @@ int main () {
}