[PDF] fourier transform of rectangular pulse train

How to solve Fourier transforms?

Fourier transform is purely imaginary. For a general real function, the Fourier transform will have both real and imaginary parts. We can write f˜(k)=f˜c(k)+if˜ s(k) (18) where f˜ s(k) is the Fourier sine transform and f˜c(k) the Fourier cosine transform. One hardly ever uses Fourier sine and cosine transforms.

Why does the Fourier transform use a complex number?

Why is the Fourier transform complex? The complex Fourier transform involves two real transforms, a Fourier sine transform and a Fourier cosine transform which carry separate infomation about a real function f (x) defined on the doubly infinite interval (-infty, +infty). The complex algebra provides an elegant and compact representation.

Is Fourier transform applicable to periodic functions?

The main drawback of Fourier series is, it is only applicable to periodic signals. There are some naturally produced signals such as nonperiodic or aperiodic, which we cannot represent using Fourier series.

What is a Fourier transformation?

The Fourier transform, named after Joseph Fourier, is an integral transform that decomposes a signal into its constituent components and frequencies. The Fourier transform (FT) is capable of decomposing a complicated waveform into a sequence of simpler elemental waves (more specifically, a weighted sum of sines and cosines).