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Distortion Measurements

Generate 2048 samples of a sinusoid of frequency 2.5 kHz sampled at 50 kHz. Add white Gaussian noise such that the signal-to-noise ratio (SNR) is 80 dB.

Fs = 5e4; 
f0 = 2.5e3;
N = 2048;
t = (0:N-1)/Fs;
SNR = 80;

x = cos(2*pi*f0*t);
x = x+randn(size(x))*std(x)/db2mag(SNR);

Pass the result through a weakly nonlinear amplifier represented by a polynomial. The amplifier introduces spurious tones at the frequencies of the harmonics.

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

Plot the signal spectrum and annotate the SNR, verifying that it has the expected value. The snr function computes the power ratio of the fundamental to the noise floor and ignores the DC component and the harmonics.

snr(x,Fs);

Figure contains an axes object. The axes object with title SNR: 79.86 dB contains 17 objects of type line, text. These objects represent Fundamental, Noise, DC and Harmonics (excluded).

Plot the signal spectrum and annotate the total harmonic distortion (THD). The thd function computes the power ratio of the harmonics to the fundamental and ignores the DC component and the noise floor.

thd(x,Fs);

Figure contains an axes object. The axes object with title THD: -72.08 dB contains 16 objects of type line, text. These objects represent Fundamental, Harmonics, DC and Noise (excluded).

Plot the signal spectrum and annotate the signal to noise and distortion ratio (SINAD). The sinad function computes the power ratio of the fundamental to the harmonics and the noise floor. It ignores only the DC component.

sinad(x,Fs);

Figure contains an axes object. The axes object with title SINAD: 71.43 dB contains 7 objects of type line, text. These objects represent Fundamental, Noise and Distortion, DC (excluded).

Verify that the SNR, THD, and SINAD obey the equation

10-SNR/10+10THD/10=10-SINAD/10.

lhs = 10^(-snr(x,Fs)/10)+10^(thd(x,Fs)/10)
lhs = 7.2203e-08
rhs = 10^(-sinad(x,Fs)/10)
rhs = 7.1997e-08

Plot the signal spectrum and annotate the spurious-free dynamic range (SFDR). The SFDR is the power ratio of the fundamental to the strongest spurious component ("spur"). In this case, the spur corresponds to the third harmonic.

sfdr(x,Fs);

Figure contains an axes object. The axes object with title SFDR: 72.16 dB contains 9 objects of type patch, line, text. These objects represent SFDR, Fundamental, Spurs, DC (excluded).

See Also

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