# Fourier Transform H(t).cos(w0t)

1. Feb 6, 2012

### tsumi

1. The problem statement, all variables and given/known data

Fourier Transform f(t)=H(t).cos(ω0t) ,using the transform of H(t)

H(t)=Heaviside function (also known as signal function if I ain't wrong)

2. Relevant equations

(1) FT[f(t)] = ∫ f(t).e^-(iωt) dt

(2) FT[H(t)] = pi.δ(ω) + 1/iω

(3) δ(ω) = Delta Dirac Function

(4) FT[cos(ω0t)] = pi (δ(ω-ω0) + δ(ω+ω0))

3. The attempt at a solution

I used equation (1) to get it, integrating by parts. The first part of parts integration yealds 0, then the new integral has the derivative of H(t), which is not bad since we can use the derivative propertie of the transform, but integrating cos(ω0t).e^-(iωt) yealds something quite far from the expected result. Am I on the right way? Any suggestions?

Thank you for any help

2. Feb 6, 2012

### vela

Staff Emeritus