# Fourier series

A Fourier series is a mathematical series that uses sinusoidal functions to approximate periodic functions. It is named after French mathematician and physicist Joseph Fourier, who introduced the concept in the early 19th century.

Fourier series are used in many engineering applications, such as signal processing, to approximate periodic signals with a finite number of terms. The sinusoidal functions in a Fourier series are often called harmonics, and the approximated periodic function is sometimes called the Fourier series expansion of the original periodic function.

A Fourier series is composed of a sum of sinusoidal functions with different frequencies. The Fourier coefficients of the series are complex numbers that represent the amplitudes of the sinusoidal functions. The frequencies of the sinusoidal functions are integer multiples of a common fundamental frequency.

The first term in a Fourier series is called the zeroeth harmonic, and it represents the DC component, or the average value, of the periodic function. The next term is the first harmonic, which represents the fundamental frequency. The second harmonic is the second multiple of the fundamental frequency, and so on.

The Fourier series of a periodic function is periodic with the same period as the function. The amplitude of each harmonic in the series is determined by the equation:

A_n = frac{1}{T} int_{-T/2}^{T/2} f(t

What is the formula for Fourier series? The Fourier series is a series of complex numbers that are used to represent a periodic function. The function can be represented as a sum of sinusoidal functions. The Fourier series is named after Joseph Fourier, who showed that any periodic function can be represented as a sum of sinusoidal functions.

##### What is Fourier series and its applications?

A Fourier series is a mathematical representation of a function as the sum of a series of sinusoidal functions. It is named after French mathematician Joseph Fourier, who introduced the concept in 1807.

Fourier series are used in signal processing and communications to represent signals as the sum of sinusoidal functions. They are also used in engineering and physics to represent periodic functions.

Fourier series have many applications in electronics. They can be used to design filters, to model signals, and to analyze circuits.

#### What are two types of Fourier series?

There are two types of Fourier series: discrete and continuous.

Discrete Fourier series are used to represent signals that are sampled at regular intervals. Continuous Fourier series are used to represent signals that are continuous in time.

##### Why Fourier series is used?

Fourier series is used in many branches of engineering, but it is especially useful in electronics. This is because Fourier series can be used to represent periodic signals, which are common in electronic devices. For example, a sine wave can be represented as a Fourier series. This means that Fourier series can be used to analyze and design electronic circuits. Where is Fourier used? Fourier analysis is used in many electronic devices, including cell phones, televisions, and radios. It is also used in signal processing and data compression.