A Fourier transform is a mathematical operation used to decompose a complex wave into its component frequencies. It converts a time-domain signal into a frequency-domain signal, showing how much of each frequency is present in the original signal.
The purpose of a Fourier transform is to analyze and understand the frequency components of a signal. It is often used in signal processing, image processing, and data analysis to identify patterns and extract information from complex signals.
Fourier transform has a wide range of applications in various fields such as engineering, physics, mathematics, and computer science. Some common applications include signal filtering, image reconstruction, data compression, and solving differential equations.
Fourier transform is used for continuous signals, while Fourier series is used for periodic signals. Fourier transform gives a continuous spectrum of frequencies, while Fourier series gives a discrete set of frequencies. Additionally, Fourier transform can handle signals with infinite duration, while Fourier series is limited to signals with finite duration.
The inverse Fourier transform is the reverse operation of the Fourier transform. It converts a frequency-domain signal back to the time-domain, reconstructing the original signal. This allows us to analyze a signal in both the time and frequency domains.