sinad

Create two signals. Both signals have a fundamental frequency of $$\pi /4$$ rad/sample with amplitude 1 and the first harmonic of frequency $$\pi /2$$ rad/sample with amplitude 0.025. One of the signals additionally has additive white Gaussian noise with variance $$0.05^2$$.

Create the two signals. Set the random number generator to the default settings for reproducible results. Determine the SINAD for the signal without additive noise and compare the result to the theoretical SINAD.

n = 0:159;
x = cos(pi/4*n)+0.025*sin(pi/2*n);
rng default

y = cos(pi/4*n)+0.025*sin(pi/2*n)+0.05*randn(size(n));
r = sinad(x)

r = 
32.0412

powfund = 1;
powharm = 0.025^2;
thSINAD = 10*log10(powfund/powharm)

thSINAD = 
32.0412

Determine the SINAD for the sinusoidal signal with additive noise. Show how including the theoretical variance of the additive noise approximates the SINAD.

r = sinad(y)

r = 
22.8085

varnoise = 0.05^2;
thSINAD = 10*log10(powfund/(powharm+varnoise))

thSINAD = 
25.0515

Create a signal with a fundamental frequency of 1 kHz and unit amplitude, sampled at 480 kHz. The signal additionally consists of the first harmonic with amplitude 0.02 and additive white Gaussian noise with variance $$0.01^2$$.

Determine the SINAD and compare the result with the theoretical SINAD.

fs = 48e4;
t = 0:1/fs:1-1/fs;
rng default

x = cos(2*pi*1000*t)+0.02*sin(2*pi*2000*t)+0.01*randn(size(t));
r = sinad(x,fs)

r = 
32.2058

powfund = 1;
powharm = 0.02^2;
varnoise = 0.01^2;
thSINAD = 10*log10(powfund/(powharm+varnoise*(1/fs)))

thSINAD = 
33.9794

Create a signal with a fundamental frequency of 1 kHz and unit amplitude, sampled at 480 kHz. The signal additionally consists of the first harmonic with amplitude 0.02 and additive white Gaussian noise with standard deviation 0.01. Set the random number generator to the default settings for reproducible results.

Obtain the periodogram of the signal and use the periodogram as the input to sinad.

fs = 48e4;
t = 0:1/fs:1-1/fs;

rng default
x = cos(2*pi*1000*t)+0.02*sin(2*pi*2000*t)+0.01*randn(size(t));

[pxx,f] = periodogram(x,rectwin(length(x)),length(x),fs);
r = sinad(pxx,f,'psd')

r = 
32.2109

Generate a sinusoid of frequency 2.5 kHz sampled at 50 kHz. Add Gaussian white noise with standard deviation 0.00005 to the signal. Pass the result through a weakly nonlinear amplifier. Plot the SINAD.

fs = 5e4;
f0 = 2.5e3;
N = 1024;
t = (0:N-1)/fs;

ct = cos(2*pi*f0*t);
cd = ct + 0.00005*randn(size(ct));

amp = [1e-5 5e-6 -1e-3 6e-5 1 25e-3];
sgn = polyval(amp,cd);

sinad(sgn,fs);

The plot shows the spectrum used to compute the ratio and the region treated as noise. The DC level and the fundamental are excluded from the noise computation. The fundamental is labeled.