- #1

JustPeter

- 2

- 0

I'm having trouble with the following:

A ﬁnite-time signal is the result of a ﬁlter G(t) applied to a signal. The ﬁlter is simply “on” (1) for t ∈ [0,T] and oﬀ (“0”) otherwise. If x(t) is the signal, and x(ω),its Fourier transform, compute the Fourier transform of the ﬁltered signal. Next, take a simple sine for x(t), x(t) = sin(ω0t), and compute the Fourier transform for the ﬁnite-time signal. Write the result, it must involve the ﬁlter, and integrations should stretch [−∞,∞]

I don't really know what to do exactly, with the first problem.

I can try calculating the Fourier transform of the filter:

G(ω)= ∫

_{0}

^{T}e

^{-iωt}dt = -1/(iω)⋅(e

^{-iωT}-1)

The Fourier transform of the signal is: x(ω)

The convolution theorum says that the convolution of two functions is the product of the Fourier-transformed functions. Which makes: G(ω)x(ω).

But I have the idea that this isn't right. Could one of you guys assist me?

Peter