Calculating Harmonics from FFT of sin(x) Function

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bugatti79
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Hi Folks,

The Fourier Cosine Transform of [tex]cos(x)[/tex] for [tex]0<x<a[/tex] and 0 everywhere else is given as

[tex]F(\omega)=\displaystyle\frac{1}{\sqrt{2 \pi}}[\frac{\sin a (1-\omega)}{1-\omega}+\frac{\sin a (1+\omega)}{1+\omega}][/tex]

I can plot this and we get a continuous amlitude spectrum of [tex]F(\omega)[/tex] against [tex](\omega)[/tex]

but how do I extract/obtain the harmonic of this function which we know has just one harmonic. How do i extract this mathematically and/or from the graph say?

Thanks
 
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bugatti79 said:
Hi Folks,

The Fourier Cosine Transform of [tex]cos(x)[/tex] for [tex]0<x<a[/tex] and 0 everywhere else is given as

[tex]F(\omega)=\displaystyle\frac{1}{\sqrt{2 \pi}}[\frac{\sin a (1-\omega)}{1-\omega}+\frac{\sin a (1+\omega)}{1+\omega}][/tex]

I can plot this and we get a continuous amlitude spectrum of [tex]F(\omega)[/tex] against [tex](\omega)[/tex]

but how do I extract/obtain the harmonic of this function which we know has just one harmonic. How do i extract this mathematically and/or from the graph say?

Thanks

The function would have only one harmonic if it were defined as $\cos x$ for $- \infty< x < + \infty$ ... but it is not so ...

Kind regards

$\chi$ $\sigma$
 
chisigma said:
The function would have only one harmonic if it were defined as $\cos x$ for $- \infty< x < + \infty$ ... but it is not so ...

Kind regards

$\chi$ $\sigma$

Is there not one harmonic over 1 period?

In either case, is it possible to determine how many harmonics there are? The reason I ask is because i want to find the harmonics of a more complicated function like an amplitude modulation signal when i do the fft

$$A_c[1+A_1\cos(\omega_1 t+\phi_1)]\cos(\omega_c+\phi_c)$$

thanks
 
bugatti79 said:
Is there not one harmonic over 1 period?

In either case, is it possible to determine how many harmonics there are? The reason I ask is because i want to find the harmonics of a more complicated function like an amplitude modulation signal when i do the fft

$$A_c[1+A_1\cos(\omega_1 t+\phi_1)]\cos(\omega_c+\phi_c)$$

thanks

... there is a little detail... the function is non periodic... and that means that its spectrum doesn't contain 'harmonics' but is a continuos function...

Kind regards

$\chi$ $\sigma$