# 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**.

**Fig. 1-1**Analogies

**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**.