An interestinc characterisitic of fourier transform is...

an interestinc characterisitic of fourier transform is linearity and this can be used to compute the fourier transform of complicated functions by decomposing into sum of simple functions. using linearity property determine the fourier transform of the raised cosine pusle given as g(t)=1/2rect(2t)

The functions f(t) and F(w) are related as follows: f(t) = F(w) (Eq.1) The general form of the Fourier Transform is: F(w) = ∫ f(t)e^(-jwt) dt (Eq.2) Since both functions are convertible, the inverse Fourier transform of F(w) will produce f(t) through the following expression: f(t) = ∫ F(w)e^(jwt) dw (Eq.3) In this laboratory session, the Fourier Transform for a rectangular pulse will be given by the following expression: F(w) = T sinc(wT/2) f(t) = (1/T) rect(t/T) (Eq.4) The continuous frequency spectrum shown in Figure 2 (right) is a graphical representation of the Fourier Transform. The duration T can also be considered as a periodic pulse of infinite period. The amplitude spectrum is called the amplitude spectrum, while its phase is called the phase spectrum. F(w) = T sinc(wT/2) f(t) = (1/T) rect(t/T) Figure 2: A rectangular pulse and its Fourier transform.

Adi S.