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# sinad() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

exampler = 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. exampler = sinad(x,fs) specifies the sampling frequency fs of the input signal x. If you do not specify fs, the sampling frequency defaults to 1. exampler = 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 of the signal. examplesinad(___) 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.

r = sinad(x) exampler = sinad(x,fs) exampler = sinad(pxx,f,'psd') exampler = sinad(sxx,f,rbw,'power')[r,totdistpow] = sinad(___)sinad(___) example

SINAD for Signal with One Harmonic or One Harmonic Plus NoiseOpen This Example Create two signals. Both signals have a fundamental frequency of rad/sample with amplitude 1 and the first harmonic of frequency rad/sample with amplitude 0.025. One of the signals additionally has additive white Gaussian noise with variance . 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) powfund = 1; powharm = 0.025^2; thSINAD = 10*log10(powfund/powharm) r = 32.0412 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) varnoise = 0.05^2; thSINAD = 10*log10(powfund/(powharm+varnoise)) r = 22.8085 thSINAD = 25.0515 SINAD for Signal with Sample RateOpen This Example 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 . 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) powfund = 1; powharm = 0.02^2; varnoise = 0.01^2; thSINAD = 10*log10(powfund/(powharm+varnoise*(1/fs))) r = 32.2058 thSINAD = 33.9794 SINAD from PeriodogramOpen This Example 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 SINAD of Amplified SignalOpen This Example Generate a sinusoid of frequency 2.5 kHz sampled at 50 kHz. Reset the random number generator. Add Gaussian white noise with standard deviation 0.00005 to the signal. Pass the result through a weakly nonlinear amplifier. Plot the SINAD. rng default 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.Related ExamplesAnalyzing Harmonic Distortion