### Fourier Transform

**Chapterł 1 Introduction.**We already know that almost

**every**periodic function

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

**cosine**and

**sine**with different amplitudes

**An**and

**Bn**and with pulsations

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

**f(t)**, i.e.

**aperiodic**functions? It is similar, only their decomposition into harmonics is more difficult to imagine. Their amplitudes

**An**and

**Bn**are

**infinitesimally**small. Successive harmonics are located infinitely close to each other. Otherwise, their subsequent 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. You definitely will after reading the entire article. But I think you’ll notice the

**analogy**between the

**Series**and the

**Fourier Transform**.

**Analogies**

Fig. 1-1

Fig. 1-1

**1. The Fourie**r transform

**F(jω)**is equivalent to the formula for the nth complex amplitude cn of the

**Fourier Series**. Both, i.e.

**F(jω)**and

**cn**were created based on the time function

**f(t)**.

**2. The Inverse Fourier**Transform is equivalent to the

**Fourier Series**formula.

**Both**of them again build the function

**f(t)**based on

**harmonics**.