Question

Could you please help me with this assignment?

The purpose of this assignment is to simulate the transmission and reception of a text message
(i.e., character string) over a noisy communications channel. Suppose we wish to transmit the
string “Hello.” We can translate this string into a bit stream as shown below:
String: H e l l o . \0 (note: the last character \0 is the null terminator character)
ASCII: 72 101 108 108 111 46 0
Binary: 01001000 01100101 01101100 01101100 01101111 00101110
00000000
Notice how this string can be expressed as 8 x 7 = 56 bits. Suppose we transmit each of these
bits as voltages on an electrical signal (for simplicity, +1.0 V for binary 1 and 0.0 V for binary 0).
We can simulate noise by encoding these bits in a double array of length 56 and then adding
noise samples to the 1.0 and 0.0 values that will initially be loaded into the array. With a small
amount of noise (low SNR), the values in this array for the first character “H” may be:
0.0143, 0.9985, -0.00124, 0.1076, 1.00325, 0.00173, 0.0563, 0.00474
With low noise, it is clear that the voltages “near” 0 represent binary 0 and the voltages “near” 1
represent binary 1. As a general rule, a receiver will take any voltages less than 0.5 and treat
them as binary 0 and any voltages greater than or equal to 0.5 and treat them as binary 1.

Problem:

Problem 2 Write a function double add noise (double signal double SNR, int size) that accepts a signal of binary voltages (as a double array), a signal-to-noise ratio, and the size of the input array. The output should be a new array containing noisy signal samples Recall that the average power (per sample) of a discrete signal (array in this case) xInl is given as: N-1 signal N Also, recall that signal-to-noise ratio is defined as: signal SNR 510 G2 here o (sigma) is the noise standard deviation (per sample)

Answer 1

#include<stdio.h>
#include<math.h>
#include<stdlib.h>

double guassian_noise(double mu, double sigma)
{
static double U, V;
static int sample = 0;
double X; // this will be the outputted random guassian number

if(sample == 0)
{
U = ((double) rand())/RAND_MAX;
V = ((double) rand())/RAND_MAX;
X = sqrt(-2*log(U))*cos(2*M_PI*V);
}
else
{
X = sqrt(-2*log(U))*sin(2*M_PI*V);
}

sample = (sample+1)%2;
return sigma*X + mu;
}

double compute_sigma(double *signal, double snr, int size)
{
double p = 0;

int i;

for(i = 0; i < size; i++)
{
p += signal[i]*signal[i];
}

p = p/size;

snr = snr*(0.1);
double sigma = sqrt((p/pow(10, snr)));
return sigma;
}

double* add_noise(double *signal, double snr, int size)
{
int i = 0;
double sigma = compute_sigma(signal, snr, size);
for(i = 0; i < size; i++)
{
double noise = guassian_noise(0, sigma);
signal[i] += noise;
}
return signal;
}

int main()
{
double signal[] = {1,1,1,1,1,1,1,1,1,0};
add_noise(signal, 2, 10);

int i = 0;

for(i = 0; i < 10; i++)
{
printf("%f\n", signal[i]);
}

return 0;
}

/*

In driver program please set appropriate value of snr and array

*/