1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
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
|
//
// msequence_example.c
//
// This example demonstrates the auto-correlation properties of a
// maximal-length sequence (m-sequence). An m-sequence of a
// certain length is used to generate two binary sequences
// (buffers) which are then cross-correlated. The resulting
// correlation produces -1 for all values except at index zero,
// where the sequences align.
// SEE ALSO: bsequence_example.c
//
#include <stdlib.h>
#include <stdio.h>
#include <complex.h>
#include <math.h>
#include "liquid.h"
#define OUTPUT_FILENAME "msequence_example.m"
int main(int argc, char*argv[])
{
// options
unsigned int m=5; // shift register length, n=2^m - 1
// create and initialize m-sequence
msequence ms = msequence_create_default(m);
msequence_print(ms);
unsigned int n = msequence_get_length(ms);
signed int rxx[n]; // auto-correlation
// create and initialize first binary sequence on m-sequence
bsequence bs1 = bsequence_create(n);
bsequence_init_msequence(bs1, ms);
// create and initialize second binary sequence on same m-sequence
bsequence bs2 = bsequence_create(n);
bsequence_init_msequence(bs2, ms);
// when sequences are aligned, autocorrelation is equal to length
rxx[0] = 2*bsequence_correlate(bs1, bs2) - n;
// when sequences are misaligned, autocorrelation is equal to -1
unsigned int i;
for (i=0; i<n; i++) {
// compute auto-correlation
rxx[i] = 2*bsequence_correlate(bs1, bs2)-n;
// circular shift the second sequence
bsequence_circshift(bs2);
}
// p/n sequence
signed int x[n];
for (i=0; i<n; i++)
x[i] = bsequence_index(bs1, i);
// clean up memory
bsequence_destroy(bs1);
bsequence_destroy(bs2);
msequence_destroy(ms);
// print results
for (i=0; i<n; i++)
printf("rxx[%3u] = %3d\n", i, rxx[i]);
//
// export results
//
FILE * fid = fopen(OUTPUT_FILENAME,"w");
if (!fid) {
fprintf(stderr,"error: %s, cannot open output file '%s' for writing\n", argv[0], OUTPUT_FILENAME);
exit(1);
}
fprintf(fid,"%% %s : auto-generated file\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n\n");
fprintf(fid,"n = %u;\n", n);
fprintf(fid,"p = zeros(1,n);\n");
for (i=0; i<n; i++) {
fprintf(fid,"x(%6u) = %3d;\n", i+1, x[i]);
fprintf(fid,"rxx(%6u) = %12.8f;\n", i+1, rxx[i] / (float)n);
}
// plot results
fprintf(fid,"figure;\n");
fprintf(fid,"t = 0:(n-1);\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," stairs(t,x);\n");
fprintf(fid," axis([-1 n -0.2 1.2]);\n");
fprintf(fid," ylabel('x');\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(t,rxx,t,rxx);\n");
fprintf(fid," axis([-1 n -0.5 1.2]);\n");
fprintf(fid," xlabel('delay (samples)');\n");
fprintf(fid," ylabel('auto-correlation');\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
return 0;
}
|
