Graphing Fourier Spectra of AM Signals with Sin^3 Carrier

[scubaman]

Homework Statement

I am trying to figure out how to graph the signal spectra of an AM signal where the message m(t) is multiplied by the carrier, which is sin^3 (wt) instead of cos (wt). I can do the FT but I do not know how to graph this since there are imaginary numbers as coefficients

Also, I do not know how to do the Fourier transform of say sin(3x). You get to this point:

kj/8 ∫m(t) e^-j6pi(f-f0)t dt what do I do with the 6pi?

Homework Equations

Euler's identity for sin(x), sin^3(x) = (3/4)sin(x) - (1/4)sin(3x)

y(t), the output, = km(t)sin^3(ωt)

The Attempt at a Solution

Using these two equations I have found the FT of the signal to be as follows:

Y(f) = -[((3kj)/8)F(f-f0) + ((3kj)/8)F(f+f0)] + F{ the sin(3x) function, which IDK how to do!}

Just don't know how to graph that or get the second portion of the answer. Thanks

 

[rude man]

I don't see how you can graph anything if you're not given what m(t) is. Such as m(t) = m0 sin(w0t)?