## What are Fourier epicycles?

Epicycles as Fourier (trigonometric) series. From the mathematical view- point, a circular rotation around the origin of the coordinate system can be described in simple trigonometric terms: x(t) = r · cos(ω · t + ϕ), y(t) = r · sin(ω · t + ϕ), i.e., equivalently, as x(t) = x0 · cos(ω · t) − y0 · sin(ω · t);

## Can we draw anything with Fourier series?

Using our Fourier transform we can calculate the sine and cosine coefficients that give us the speed and size of connected circles that would imitate our drawing. You can again make you own drawing in the square, to see how the circles imitate it using Fourier analysis.

**How do you find the complex Fourier series?**

Complex Form of Fourier Series

- If necessary to expand a function of period we can use the following expressions:
- We calculate the coefficients and for.
- If then If then.
- We can transform the series and write it in the real form. Rename: Then.
- Graph of the function and its Fourier approximation for and are shown in Figure.

### What is the difference between discrete Fourier transform DFT and Fast Fourier Transform FFT?

Discrete Fourier Transform (DFT) is the discrete version of the Fourier Transform (FT) that transforms a signal (or discrete sequence) from the time domain representation to its representation in the frequency domain. Whereas, Fast Fourier Transform (FFT) is any efficient algorithm for calculating the DFT.

### Why Fourier series is used?

Fourier series is just a means to represent a periodic signal as an infinite sum of sine wave components. A periodic signal is just a signal that repeats its pattern at some period. The primary reason that we use Fourier series is that we can better analyze a signal in another domain rather in the original domain.

**What is the purpose of Fourier series?**

The Fourier Series allows us to model any arbitrary periodic signal with a combination of sines and cosines.

#### What is the main purpose of Fourier analysis?

Fourier analysis allows one to evaluate the amplitudes, phases, and frequencies of data using the Fourier transform. More powerful analysis can be done on the Fourier transformed data using the remaining (i.e., time-independent) variation from other variables.

#### Why do we need complex Fourier series?

Originally Answered: When the Fourier transform Why use a complex number? If you just use sine or cosine, it will turn out you can only analyze odd or even function signal respectively. If you just use sine or cosine, it will turn out you can only analyze odd or even function signal respectively.

**What is meant by complex Fourier series?**

The complex Fourier series is presented first with pe- riod 2π, then with general period. The connection with the real-valued Fourier series is explained and formulae are given for converting be- tween the two types of representation.