Fourier Transform is a mathematical technique used to decompose a complex function into simpler functions. It transforms a function from the time or spatial domain to the frequency domain, revealing the frequency components of the original function.
The steps for performing Fourier Transform are:
Fourier Transform has various applications in fields such as engineering, physics, signal processing, and image processing. Some common applications include analyzing signals in communication systems, filtering out noise from signals, and compressing digital images.
Fourier Transform is used for continuous functions with infinite domain, while Fourier Series is used for periodic functions with a finite domain. Fourier Transform gives the frequency components of a function in the frequency domain, while Fourier Series gives the frequency components as a sum of sine and cosine functions in the time domain.
Fourier Transform is not suitable for functions with discontinuities or sharp changes, as it assumes the function is continuous. It also requires the function to be integrable, which means it must have a finite area under the curve. Additionally, the Fourier Transform may not exist for some functions, such as those that grow too quickly or have infinite frequency components.