Fourier Transform Simple Problem

Discussion in 'Homework Help' started by lksnc, Nov 19, 2012.

  1. lksnc

    Thread Starter New Member

    Nov 19, 2012
    I have a simple question.

    x(t) = derivative of [sin(t)/(pi*t) convolution sin(2t)/(pi*t)] dt.

    I need the Fourier Transform of x(t).

    Let's call the second part h(t). So, h(t) = sin(2t)/pi*t. Using tables, the Fourier Transform of h(t) would be
    1, if |ω| < 2
    0, if |ω| > 2

    Calling the other part g(t) = sin(t)/pi*t, the Fourier Transform would be
    1, if |ω| < 1
    0, if |ω| > 1

    So, I know I have to use the convolution property, which states that:
    g(t) convolution h(t) = G(jω) times H(jω).... just the multiplication of the Fourier Transforms.

    Can somebody help me with this part? This multiplication would result in what?

    If I get that, then I just need to apply the derivative formula for the Fourier Transform to get to my answer. In other words, X(jω) = jω * G(jω) * H(jω), right?

    Help please!