Fourier transformation is a mathematical operation that decomposes a function into its underlying frequencies, allowing us to analyze the function in the frequency domain instead of the time or spatial domain.
Fourier transformation is important because it allows us to understand the underlying frequencies present in a signal or function. This is useful in many fields such as engineering, physics, and data analysis.
Fourier transformation works by breaking down a function into an infinite sum of sine and cosine waves with different frequencies and amplitudes. This allows us to see the individual frequencies that make up the function.
Some simple examples of Fourier transformation include analyzing the frequency components of a musical note, decomposing a rectangular pulse signal, and understanding the frequency content of a digital image.
The difference between Fourier transformation and Fourier series is that Fourier transformation is used for continuous functions while Fourier series is used for periodic functions. Fourier series decomposes a periodic function into a sum of sine and cosine waves, while Fourier transformation can be used for any type of function.