# Question: What does the Fourier transform tell us?

Contents

The Fourier transform gives us insight into what sine wave frequencies make up a signal. You can apply knowledge of the frequency domain from the Fourier transform in very useful ways, such as: Audio processing, detecting specific tones or frequencies and even altering them to produce a new signal.

## What do Fourier transforms show?

A Fourier transform shows what frequencies are in a signal. The Fourier transform plots the amplitudes and phases of these cosines and sines against their respective frequencies. Fourier transforms are important, because many signals make more sense when their frequencies are separated.

## What is the significance of Fourier transform in system analysis?

The Fourier transform is used to analyze problems involving continuous-time signals or mixtures of continuous- and discrete-time signals. The discrete-time Fourier transform is used to analyze problems involving discrete-time signals or systems.

## What is the formula of Fourier transformation?

The function F(ω) is called the Fourier transform of the function f(t). Symbolically we can write F(ω) = F{f(t)}.