The Boeing Company
Question
Asked 2nd Nov, 2016
What do harmonics signify in the FFT spectrum of a signal?
While carrying out FFT spectrum of a signal, harmonics of a frequency appear at higher frequencies than fundamental frequency. My question is if fundamental frequency is the highest one in the signal, what would harmonics of that fundamental frequency signify in the signal?
For example, I have a signal in length scale having 1mm length which comprise of 100 same frequency components of constant magnitude. Then the spectrum will show a sharp peak at 100 hz. Additionally it will show harmonics at 200, 300, 400hz.... What do these harmonics signify in that signal (as these components don't exist in the signal) ?
Most recent answer
When the Fourier Transform (or FFT) shows the presence of harmonics, it simply means that SOMETHING in the circuit creates this extra energy. The presence of harmonics may be completely to be expected, and may require additional means to deal with them. We should not assume that the existence of harmonics is always bad.
Here's a simple example. If one samples a signal, taking very short samples as a first step to create a digital stream of the signal, then you must expect to see a string of harmonics, spread apart as a function of the sampling rate. So, when decoding the digital signal, you will require a low-pass filter, to remove those harmonics.
A similar effect occurs when demodulating single sideband. You use a local oscillator, at the receiver, to create harmonics of the SSB signal spectrum, and then you adjust the oscillator frequency until you combine an upper sideband and lower sideband of that SSB signal, to re-create the original double sideband AM baseband spectrum.
In short, the existence of harmonics is not necessarily bad news. "Some of my best friends are harmonics."
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Popular answers (1)
blueice BVBA, Zaventem, Belgium
Dear Anuj,
Fourier transform (fast or otherwise) is a decomposition of a signal in sine and cosine components.
If you have a signal that is repetitive with a wavelength of say 10 mS, and besides the fourier transform component at 100 Hz, you find components at 200 Hz and 300 Hz (and so on), this means your signal is not a sine.
The physical meaning of the decomposition is, that if you add sines and cosines with the respective frequency of the FFT bins, and the respective amplitude of the FFT bins, you get back your original signal. Fourier transform is no more or no less than a decomposition of the signal in sines and cosines.
Eg, if I have any signal, and its fourier transform only has peaks around 100 Hz, 200 Hz, 300 Hz, with complex values a100, a200, a300, I can decompose the signal as:
let w1 = 2*PI*100
x(t) = a1*(cos(w1t)+jsin(w1t)) +
a2*(cos(2w1t)+jsin(2w1t)) +
a3*(cos(3w1t)+jsin(3w1t))
Cheers,
Henri
10 Recommendations
All Answers (6)
blueice BVBA, Zaventem, Belgium
Dear Anuj,
Fourier transform (fast or otherwise) is a decomposition of a signal in sine and cosine components.
If you have a signal that is repetitive with a wavelength of say 10 mS, and besides the fourier transform component at 100 Hz, you find components at 200 Hz and 300 Hz (and so on), this means your signal is not a sine.
The physical meaning of the decomposition is, that if you add sines and cosines with the respective frequency of the FFT bins, and the respective amplitude of the FFT bins, you get back your original signal. Fourier transform is no more or no less than a decomposition of the signal in sines and cosines.
Eg, if I have any signal, and its fourier transform only has peaks around 100 Hz, 200 Hz, 300 Hz, with complex values a100, a200, a300, I can decompose the signal as:
let w1 = 2*PI*100
x(t) = a1*(cos(w1t)+jsin(w1t)) +
a2*(cos(2w1t)+jsin(2w1t)) +
a3*(cos(3w1t)+jsin(3w1t))
Cheers,
Henri
10 Recommendations
Saad Dahlab University
Hello
I suggest you use the RFT Ramanujan Fourier Transform
Cordially
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If you input a pure sine wave into, say, an amplifier and get harmonics, this means that there is a non-linearity. For example, if an amplifier has a non-linearity that is quadratic, you'd get a 2nd harmonic:
(sin wt)2 = 1/2 - 1/2cos 2wt
Different non-linearities will generate different harmonics, even sub-harmonics, which are below the fundamental.
6 Recommendations
Saad Dahlab University
Harmonics represents all secondary frequencies
We can use another transforms another that fourier
Cordially
The Boeing Company
When the Fourier Transform (or FFT) shows the presence of harmonics, it simply means that SOMETHING in the circuit creates this extra energy. The presence of harmonics may be completely to be expected, and may require additional means to deal with them. We should not assume that the existence of harmonics is always bad.
Here's a simple example. If one samples a signal, taking very short samples as a first step to create a digital stream of the signal, then you must expect to see a string of harmonics, spread apart as a function of the sampling rate. So, when decoding the digital signal, you will require a low-pass filter, to remove those harmonics.
A similar effect occurs when demodulating single sideband. You use a local oscillator, at the receiver, to create harmonics of the SSB signal spectrum, and then you adjust the oscillator frequency until you combine an upper sideband and lower sideband of that SSB signal, to re-create the original double sideband AM baseband spectrum.
In short, the existence of harmonics is not necessarily bad news. "Some of my best friends are harmonics."
2 Recommendations
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