What is the Fourier transform?
Q: What is the Fourier transform?
A: The Fourier transform is a mathematical function that can be used to find the base frequencies that a wave is made of. It takes a complex wave and finds the frequencies that make it up, allowing it to identify the notes that make up a chord.
Q: What are some uses of the Fourier transform?
A: The Fourier transform has many uses in cryptography, oceanography, machine learning, radiology, quantum physics as well as sound design and visualization.
Q: How is the Fourier transform calculated?
A: The Fourier transform of a function f(x) is given by F(α) = ∫−∞+∞f(x)e−2πiαxdx where α is a frequency. This returns a value representing how prevalent frequency α is in the original signal. The inverse Fourier transform is given by f(x) = ∫−∞+∞F(α)e+2πixαdα.
Q: What does an output of a Fourier Transform look like?
A: An output of a Fourier Transform can be called either a frequency spectrum or distribution because it displays a distribution of possible frequencies of the input.
Q: How do computers calculate Fast Fourier Transforms?
A: Computers use an algorithm called Fast Fourier Transform (FFT) to quickly calculate any but the simplest signals' transforms.
Q: What does looking at signals with respect to time not show us?
A: Looking at signals with respect to time does not make it obvious what notes are present in them; many signals make more sense when their frequencies are separated and analyzed individually instead.
