Thread: Fourier transformation

Hi

I am trying to calculate the Fourier transformation of the function

f(x)=exp(-x)*(the characteristic function running from 0 to 1, both included)

what I have got so far is this

|f_hat(gamma)|=|int_from -infinty to infinity (f(x)*exp(-2*pi*i*x*gamma)dx)|

= int_o to 1(exp(-x)*exp(-2*pi*i*x*gamma)dx)

and then what? Have I made a mistake somewhere along the way or is it simply a case of having got stuck?

thanks in advance

Originally Posted by Ase

Hi

I am trying to calculate the Fourier transformation of the function

f(x)=exp(-x)*(the characteristic function running from 0 to 1, both included)

what I have got so far is this

|f_hat(gamma)|=|int_from -infinty to infinity (f(x)*exp(-2*pi*i*x*gamma)dx)|

= int_o to 1(exp(-x)*exp(-2*pi*i*x*gamma)dx)

and then what? Have I made a mistake somewhere along the way or is it simply a case of having got stuck?

thanks in advance

Then what ....? Use a well known index law to write the integrand in the form e^{kx} and then integrate.

Hi mrfantastic

I am well aware of the index law. The "then what" referred to what happens to the gamma. I can only integrate over x but what happens to gamma?

Originally Posted by Ase

Hi mrfantastic

I am well aware of the index law. The "then what" referred to what happens to the gamma. I can only integrate over x but what happens to gamma?

The integral is respect to x so gamma is treated as a constant as far as the integration is concerned. So the result of the integration is a function of gamma, which ought to be no surprise.

Ok. Thanks a lot. I was just under the impression that the end result should be a number (not a function).