### Fourier Transform

**Chapter 1 Introduction
**We already know that almost every

**periodic**function

**f(t)**can be decomposed into

**cosines**and

**snusoids**with different amplitudes

**An**and

**Bn**and with

**nω0**pulsations. What about the “normal” functions

**f(t)**, meaning

**non-periodic**? It’s similar, only their decomposition into

**harmonics**is more difficult to imagine. Their amplitudes

**An**and

**Bn**are infinitely

**small**. Successive harmonics are infinitely close to each other. Otherwise, their successive pulsations

**nω0**and

**(n+1)ω0**are “almost” the same. And the

**“first harmonic”**for

**ω0=0**is an

**infinitesimal**constant component! For now, the above text may not be entirely clear. I’m sure you will after reading the whole article. But you’ll probably notice the analogy between

**Series**and

**Fourier Transform**.

**Fig. 1-1**

Analogies

**1.**The

**F(jω) Fourier Transform**is equivalent to the formula for the

**nth**complex amplitude

**cn**of the Fourier Series.

Both, i.e.

**F(jω)**and

**cn**were created on the basis of the time function

**f(t)**.

**2.**The

**Inverse Fourier Transform**is equivalent to the

**Fourier Series**formula. Both rebuild the function

**f(t)**from harmonics.