sinad

r = sinad(x) returns the signal to noise and distortion ratio (SINAD) in dBc of the real-valued sinusoidal signal x. The SINAD is determined using a modified periodogram of the same length as the input signal. The modified periodogram uses a Kaiser window with β = 38.

r = sinad(x,fs) specifies the sample rate fs of the input signal x. If you do not specify fs, then the sample rate defaults to 1.

r = sinad(pxx,f,'psd') specifies the input pxx as a one-sided power spectral density (PSD) estimate. f is a vector of frequencies corresponding to the PSD estimates in pxx.

r = sinad(sxx,f,rbw,'power') specifies the input as a one-sided power spectrum. rbw is the resolution bandwidth over which each power estimate is integrated.

[r,totdistpow] = sinad(___) returns the total noise and harmonic distortion power (in dB) of the signal.

sinad(___) with no output arguments plots the spectrum of the signal in the current figure window and labels its fundamental component. It uses different colors to draw the fundamental component, the DC value, and the noise. The SINAD appears above the plot.

Examples

SINAD for Signal with One Harmonic or One Harmonic Plus Noise

Create two signals. Both signals have a fundamental frequency of $π / 4$ rad/sample with amplitude 1 and the first harmonic of frequency $π / 2$ rad/sample with amplitude 0.025. One of the signals additionally has additive white Gaussian noise with variance $0.0 5^{2}$ .

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

SINAD for Signal with Sample Rate

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 $0.0 1^{2}$ .

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

SINAD from Periodogram

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

SINAD of Amplified Signal

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);

Figure contains an axes object. The axes object with title SINAD: 72.10 dB contains 7 objects of type line, text. These objects represent Fundamental, Noise and Distortion, DC (excluded).

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.

Input Arguments

`x` — Real-valued sinusoidal input signal
vector

Real-valued sinusoidal input signal, specified as a row or column vector.

Example: cos(pi/4*(0:159))+cos(pi/2*(0:159))

Data Types: single | double

`fs` — Sample rate
positive scalar

Sample rate, specified as a positive scalar. The sample rate is the number of samples per unit time. If the unit of time is seconds, then the sample rate has units of Hz.

`pxx` — One-sided PSD estimate
vector

One-sided PSD estimate, specified as a real-valued, nonnegative column vector.

The power spectral density must be expressed in linear units, not decibels. Use db2pow to convert decibel values to power values.

Example: [pxx,f] = periodogram(cos(pi./[4;2]*(0:159))'+randn(160,2)) specifies the periodogram PSD estimate of a noisy two-channel sinusoid sampled at 2π Hz and the frequencies at which it is computed.

Data Types: single | double

`f` — Cyclical frequencies
vector

Cyclical frequencies corresponding to the one-sided PSD estimate, pxx, specified as a row or column vector. The first element of f must be 0.

Data Types: double | single

`sxx` — Power spectrum
nonnegative real-valued row or column vector

Power spectrum, specified as a real-valued nonnegative row or column vector.

The power spectrum must be expressed in linear units, not decibels. Use db2pow to convert decibel values to power values.

Example: [sxx,w] = periodogram(cos(pi./[4;2]*(0:159))'+randn(160,2),'power') specifies the periodogram power spectrum estimate of a two-channel sinusoid embedded in white Gaussian noise and the normalized frequencies at which it is computed.

`rbw` — Resolution bandwidth
positive scalar

Resolution bandwidth, specified as a positive scalar. The resolution bandwidth is the product of the frequency resolution of the discrete Fourier transform and the equivalent noise bandwidth of the window.

Output Arguments

`r` — Signal to noise and distortion ratio in dBc
real-valued scalar

Signal to noise and distortion ratio in dBc, returned as a real-valued scalar.

`totdistpow` — Total noise and harmonic distortion power of the signal
real-valued scalar

Total noise and harmonic distortion power of the signal, returned as a real-valued scalar expressed in dB.

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