Howtosignalprocessing
- What is DFT useful for?
- Why do we need DFT in image processing?
- What happens if we apply DFT twice to a signal?
- Why we use DFT instead of DTFT?
What is DFT useful for?
Chemists use DFT to calculate the approximate electronic structures of molecules or materials and thus predict their properties. The exact electronic structure of any system can be found by solving the Schrödinger equation, which mathematically describes a system's quantum mechanical wave function.
Why do we need DFT in image processing?
In image processing, the samples can be the values of pixels along a row or column of a raster image. The DFT is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers.
What happens if we apply DFT twice to a signal?
Applying the DFT twice results in a scaled, time reversed version of the original series. The transform of a constant function is a DC value only.
Why we use DFT instead of DTFT?
DFT (Discrete Fourier Transform) is a practical version of the DTFT, that is computed for a finite-length discrete signal. The DFT becomes equal to the DTFT as the length of the sample becomes infinite and the DTFT converges to the continuous Fourier transform in the limit of the sampling frequency going to infinity.
