Basic question about trigonometric series and transforms thereof

1. How does the trigonometric Fourier series represent?
2. What are the applications of FFT?
3. What is the need of FFT algorithm?

How does the trigonometric Fourier series represent?

The trigonometric Fourier series is a periodic function of period T0 = 2π/ω0. If the function g(t) is periodic with period T0, then a Fourier series representing g(t) over an interval T0 will also represent g(t) for all t.

What are the applications of FFT?

FFT Applications

These techniques can be used for a variety of signals such as audio and speech, radar, communication, and other sensor data signals. FFT is also sometimes used as an intermediate step for more complex signal processing techniques. In image processing, FFT is used for filtering and image compression.

What is the need of FFT algorithm?

The FFT algorithm is one of the heavily used in many DSP applications. It is used whenever the signal needs to be processed in the spectral, or frequency domain. It is so efficient to implement, that sometimes even FIR filtering functions are performed using an FFT.