Mar 27, 2014 #1 T talking Member level 2 Joined Jan 27, 2010 Messages 44 Helped 0 Reputation 0 Reaction score 0 Trophy points 1,286 Activity points 1,654 What is Fourier transform of sin(A * cos(2*pi*f*t)), where A and f are constant?
Mar 27, 2014 #2 Z zorro Advanced Member level 4 Joined Sep 6, 2001 Messages 1,130 Helped 357 Reputation 712 Reaction score 298 Trophy points 1,363 Location Argentina Activity points 8,913 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
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
Apr 3, 2014 #3 7 7h3 l33+ P$yCh0 Junior Member level 1 Joined Jul 4, 2013 Messages 17 Helped 1 Reputation 2 Reaction score 1 Trophy points 3 Location Somewhere on Space time fabric Activity points 58 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 \[\pm\] \[{f }_{0 }\]))
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 \[\pm\] \[{f }_{0 }\]))
Apr 3, 2014 #4 Z zorro Advanced Member level 4 Joined Sep 6, 2001 Messages 1,130 Helped 357 Reputation 712 Reaction score 298 Trophy points 1,363 Location Argentina Activity points 8,913 7h3 l33+ P$yCh0 said: If the frequency of sinusoid is constant as mentioned by OP, ... Click to expand... 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 Last edited: Apr 3, 2014
7h3 l33+ P$yCh0 said: If the frequency of sinusoid is constant as mentioned by OP, ... Click to expand... 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
Apr 3, 2014 #5 7 7h3 l33+ P$yCh0 Junior Member level 1 Joined Jul 4, 2013 Messages 17 Helped 1 Reputation 2 Reaction score 1 Trophy points 3 Location Somewhere on Space time fabric Activity points 58 Oops... missed that. In that case you were right. it's a FM wave with infinte harmonics