thd() - Signal Processing
exampler = thd(x) returns
the total harmonic distortion (THD) in dBc of the real-valued sinusoidal
signal x. The total harmonic distortion is determined
from the fundamental frequency and the first five harmonics using
a modified periodogram of the same length as the input signal. The
modified periodogram uses a Kaiser window with β =
38.
exampler = thd(x,fs,n) specifies
the sampling rate fs and the number of harmonics
(including the fundamental) to use in the THD calculation.
r = thd(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.
exampler = thd(pxx,f,n,'psd') specifies
the number of harmonics (including the fundamental) to use in the
THD calculation.
exampler = thd(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 = thd(sxx,f,rbw,n,'power') specifies
the number of harmonics (including the fundamental) to use in the
THD calculation.
example[r,harmpow,harmfreq]
= thd(___) returns the powers and frequencies
of the harmonics (including the fundamental).
examplethd(___) with no output arguments
plots the spectrum of the signal and annotates the harmonics in the
current figure window. It uses different colors to draw the fundamental
component, the harmonics, and the DC level and noise. The THD appears
above the plot. The fundamental and harmonics are labeled. The DC
term is excluded from the measurement and is not labeled.
Syntax
<![CDATA[r = thd(x) exampler = thd(x,fs,n) exampler = thd(pxx,f,'psd')r = thd(pxx,f,n,'psd') exampler = thd(sxx,f,rbw,'power') exampler = thd(sxx,f,rbw,n,'power')[r,harmpow,harmfreq]
= thd(___) examplethd(___) example]]>
Example
<![CDATA[Determine THD for a Signal with Two HarmonicsOpen This Example
This example shows explicitly how to calculate the total harmonic distortion in dBc for a signal consisting of the fundamental and two harmonics. The explicit calculation is checked against the result returned by thd.
Create a signal sampled at 1 kHz. The signal consists of a 100 Hz fundamental with amplitude 2 and two harmonics at 200 and 300 Hz with amplitudes 0.01 and 0.005. Obtain the total harmonic distortion explicitly and using thd.t = 0:0.001:1-0.001;
x = 2*cos(2*pi*100*t)+0.01*cos(2*pi*200*t)+0.005*cos(2*pi*300*t);
tharmdist = 10*log10((0.01^2+0.005^2)/2^2)
r = thd(x)
tharmdist =
-45.0515
r =
-45.0515
Specify Number of HarmonicsOpen This Example
Create a signal sampled at 1 kHz. The signal consists of a 100 Hz fundamental with amplitude 2 and three harmonics at 200, 300, and 400 Hz with amplitudes 0.01, 0.005, and 0.0025.
Set the number of harmonics to 3. This includes the fundamental. Accordingly, the power at 100, 200, and 300 Hz is used in the THD calculation.t = 0:0.001:1-0.001;
x = 2*cos(2*pi*100*t)+0.01*cos(2*pi*200*t)+ ...
0.005*cos(2*pi*300*t)+0.0025*sin(2*pi*400*t);
r = thd(x,1000,3)
r =
-45.0515
Specifying the number of harmonics equal to 3 ignores the power at 400 Hz in the THD calculation.Specify Number of Harmonics (PSD Input)Open This Example
Create a signal sampled at 1 kHz. The signal consists of a 100 Hz fundamental with amplitude 2 and three harmonics at 200, 300, and 400 Hz with amplitudes 0.01, 0.005, and 0.0025.
Obtain the periodogram PSD estimate of the signal and use the PSD estimate as the input to thd. Set the number of harmonics to 3. This includes the fundamental. Accordingly, the power at 100, 200, and 300 Hz is used in the THD calculation.t = 0:0.001:1-0.001;
fs = 1000;
x = 2*cos(2*pi*100*t)+0.01*cos(2*pi*200*t)+ ...
0.005*cos(2*pi*300*t)+0.0025*sin(2*pi*400*t);
[pxx,f] = periodogram(x,rectwin(length(x)),length(x),fs);
r = thd(pxx,f,3,'psd')
r =
-45.0515
THD from Power SpectrumOpen This Example
Determine the THD by inputting the power spectrum obtained with a Hamming window and the resolution bandwidth of the window.
Create a signal sampled at 10 kHz. The signal consists of a 100 Hz fundamental with amplitude 2 and three odd-numbered harmonics at 300, 500, and 700 Hz with amplitudes 0.01, 0.005, and 0.0025. Specify the number of harmonics to 7. Determine the THD.fs = 10000;
t = 0:1/fs:1-1/fs;
x = 2*cos(2*pi*100*t)+0.01*cos(2*pi*300*t)+ ...
0.005*cos(2*pi*500*t)+0.0025*sin(2*pi*700*t);
[sxx,f] = periodogram(x,hamming(length(x)),length(x),fs,'power');
rbw = enbw(hamming(length(x)),fs);
r = thd(sxx,f,rbw,7,'power')
r =
-44.8396
Harmonic Powers and Corresponding FrequenciesOpen This ExampleCreate a signal sampled at 10 kHz. The signal consists of a 100 Hz fundamental with amplitude 2 and three odd-numbered harmonics at 300, 500, and 700 Hz with amplitudes 0.01, 0.005, and 0.0025. Specify the number of harmonics to 7. Determine the THD, the power at the harmonics, and the corresponding frequencies.fs = 10000;
t = 0:1/fs:1-1/fs;
x = 2*cos(2*pi*100*t)+0.01*cos(2*pi*300*t)+ ...
0.005*cos(2*pi*500*t)+0.0025*sin(2*pi*700*t);
[r,harmpow,harmfreq] = thd(x,10000,7);
[harmfreq harmpow]
ans =
100.0000 3.0103
201.0000 -321.0983
300.0000 -43.0103
399.0000 -281.9259
500.0000 -49.0309
599.0000 -282.1066
700.0000 -55.0515
The powers at the even-numbered harmonics are on the order of
dB, which corresponds to an amplitude of
.THD of an 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 THD.
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);
thd(sgn,fs);
The plot shows the spectrum used to compute the ratio and the region treated as noise. The DC level is excluded from the computation. The fundamental and harmonics are labeled.Related ExamplesAnalyzing Harmonic Distortion]]>
Output / Return Value
Limitations
Alternatives / See Also
Reference