fourier transform of sin(A * cos(2*pi*f*t))?

[talking]

What is Fourier transform of sin(A * cos(2*pi*f*t)), where A and f are constant?

 

[zorro]

Look for spectra of Frequency Modulated (FM) signals in any text about (analog) communications theory.
It's a discrete spectrum (a sum of Dirac deltas), whose coefficients are Bessel functions of the first kind.
Regards

Z

 

[7h3 l33+ P$yCh0]

I disagree with above post by zorro.

If the frequency of sinusoid is constant as mentioned by OP, the fourier transform is just an impulse at frequency '\[{f }_{ 0}\]'
Answer would be

(\[{ A}^{ 2}\]/4) (\[\delta\](f \[\pm\] \[{f }_{0 }\]))

 

[zorro]

If the frequency of sinusoid is constant as mentioned by OP, ...

NO! The function is sin(A * cos(2*pi*f*t)) .

It's not A*cos(2*pi*f₀*t) , whose FT is A/2 * [\[\delta\](f+f₀)+\[\delta\](f-f₀)]

Z

 

[7h3 l33+ P$yCh0]

Oops... missed that. In that case you were right. it's a FM wave with infinte harmonics