Register to reply

Fourier Transform of sin(wt+phi)

by zanderace
Tags: fourier, sinwt, transform
Share this thread:
zanderace
#1
Oct1-12, 11:08 PM
P: 1
1. The problem statement, all variables and given/known data

I've been stuck on this for a while:

Find the Fourier transform of f(t)=sin([itex]\omega0[/itex]t+[itex]\phi[/itex])



2. Relevant equations

I know that I have to use F(ω)=[itex]\int[/itex]f(x)e^-iωt dt (between - and + infinity) to solve this

3. The attempt at a solution

So far I have: F(ω)=[itex]\int[/itex]Sin(ω0t+[itex]\phi[/itex])e^-i[itex]\omega[/itex]tdt
=[itex]\int[/itex](e^i[itex]\omega[/itex]0t+[itex]\phi[/itex] - e^-it[itex]\omega[/itex]0+[itex]\phi[/itex])/2i * e^-i[itex]\omega[/itex]t dt

(Both evaluated between - and +infinity, and ω0 means ω subscript 0)

But I'm really not sure where to go with this next. Any help or pointers would be really appreciated! Also sorry for my equation writing but I'm completely new to LATEX. Thank you.
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
Dick
#2
Oct1-12, 11:23 PM
Sci Advisor
HW Helper
Thanks
P: 25,228
The answer is going to involve a sum of Dirac delta functions. You might want to look up how the integral of a complex exponential is related to the Dirac delta.


Register to reply

Related Discussions
Laplace transform and fourier transform Calculus & Beyond Homework 2
Purpose of fourier series and fourier transform Advanced Physics Homework 4
What is the point of Fourier Series if you can do the Fourier Transform? General Math 9
Fourier Series / Fourier Transform Question Electrical Engineering 6
The difference between Fourier Series, Fourier Transform and Laplace Transform General Physics 1