Fourier transform

1. What are Fourier transforms used for?
2. What is the Fourier transform formula?
3. What is an example of a Fourier transform?
4. How do you explain Fourier transform?

What are Fourier transforms used for?

The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent.

What is the Fourier transform formula?

The function F(ω) is called the Fourier transform of the function f(t). Symbolically we can write F(ω) = Ff(t). f(t) = F−1F(ω). ... However, (5) is really a mathematical transformation for obtaining one function from another and (4) is then the inverse transformation for recovering the initial function.

What is an example of a Fourier transform?

The Fourier transform is commonly used to convert a signal in the time spectrum to a frequency spectrum. Examples of time spectra are sound waves, electricity, mechanical vibrations etc. The figure below shows 0,25 seconds of Kendrick's tune. As can clearly be seen it looks like a wave with different frequencies.

How do you explain Fourier transform?

The Fourier transform is a mathematical function that decomposes a waveform, which is a function of time, into the frequencies that make it up. The result produced by the Fourier transform is a complex valued function of frequency.