Measure Total Harmonic Distortion

This example shows how to measure the total harmonic distortion (THD) of a sinusoidal signal. The example uses the following scenario: A manufacturer of audio speakers claims the model A speaker produces less than 0.09% harmonic distortion at 1 kHz with a 1 volt input. The harmonic distortion is measured with respect to the fundamental (THD-F).

Assume you record the following data obtained by driving the speaker with a 1 kHz tone at 1 volt. The data is sampled at 44.1 kHz for analysis.

Fs = 44.1e3; t = 0:1/Fs:1; x = cos(2*pi*1000*t)+8e-4*sin(2*pi*2000*t)+2e-5*cos(2*pi*3000*t-pi/4)+...8 e-6 *罪(2 *π* 4000 * t);

获得DB中输入信号的总谐波失真。指定六个谐波用于计算THD。这包括1 kHz的基本频率。输入44.1 kHz的采样频率。确定谐波的频率及其功率估计。

nharm = 6; [thd_db,harmpow,harmfreq] = thd(x,Fs,nharm);

The functionthdoutputs the total harmonic distortion in dB. Convert the measurement from dB to a percentage to compare the value against the manufacturer's claims.

percent_thd = 100*(10^(thd_db/20))

percent_thd = 0.0800

The value you obtain indicates that the manufacturer's claims about the THD for speaker model A are correct.

You can obtain further insight by examining the power (dB) of the individual harmonics.

T = table(harmfreq,harmpow,'VariableNames',{'Frequency','Power'})

T=6×2 tableFrequency Power _________ _______ 1000 -3.0103 2000 -64.949 3000 -96.99 4000 -104.95 4997.9 -306.1 5998.9 -310.62

The total harmonic distortion is approximately $$-62$$dB. If you examine the power of the individual harmonics, you see that the major contribution comes from the harmonic at 2 kHz. The power at 2 kHz is approximately 62 dB below the power of the fundamental. The remaining harmonics do not contribute significantly to the total harmonic distortion. Additionally, the synthesized signal contains only four harmonics, including the fundamental. This is confirmed by the table, which shows a large power reduction after 4 kHz. Therefore, repeating the calculation with only four harmonics does not change the total harmonic distortion significantly.

Plot the signal spectrum, display the total harmonic distortion on the figure title, and annotate the harmonics.

thd(x,Fs,nharm);

See Also

thd

相关话题

• Analyzing Harmonic Distortion