DFT meaning in Maths ?

Answer:

What is Discrete Fourier Transform mean?

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle.

The DFT is the most important discrete transform, used to perform Fourier analysis in many practical applications. In digital signal processing, the function is any quantity or signal that varies over time, such as the pressure of a sound wave, a radio signal, or daily temperature readings, sampled over a finite time interval (often defined by a window function). 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.

Since it deals with a finite amount of data, it can be implemented in computers by numerical algorithms or even dedicated hardware. These implementations usually employ efficient fast Fourier transform (FFT) algorithms; so much so that the terms "FFT" and "DFT" are often used interchangeably. Prior to its current usage, the "FFT" initialism may have also been used for the ambiguous term "finite Fourier transform".

reference

Full Form	Category
Direct Funds Transfer	Business
Downey Financial Capital Trust I	Business
Detroit Film Theatre	Community
Detroit Federation of Teachers	Community
Designed For Test	Computing
Distributed Function Terminal	Computing
Diagnostic Function Test	Computing
Dynamic Fault Tree	Computing
Derma Fusion Technology	Computing
Dermal Fusion Technology	Computing
Digital Film Technology	Computing
Demand Flow Technology	Computing
DraftCoin	Cryptocurrency
DeFiat	Cryptocurrency
DigiFinexToken	Cryptocurrency
dFuture	Cryptocurrency
Dry Film Thickness	Electronics
Deep Flow Technique	Electronics
Design for Testability	Electronics
Dongfeng Trucks	General
Design For Test	General
Diesel Forklift Truck	General
Dunkirk And Fredonia Telephone	General
Doom Family Thugs	General
Damn Fast Transit	General
Dirty Five Thirty	General
Defibrillator Function Test	General
Depth First Tree	General
Dolleh Figure Thingeh	General
Density functional	General
Dat Functional Type	General
Department of Foreign Trade	General
Dolleh Figure Thingehz	General
Designer for Tomorrow	General
Daily Funded Trade	General
Direct Fourier Transform	General
Dual Fuel Tactical	General
Data Foundation and Terminology	General
Discrete Function Transform	General
Deployed For Training	General
Department For Transport	General
Diesel Fuel Tax	General
Diesel Fuel Treatment	General
Data Fuel Tracer	General
Discrete Fourier Transform	Maths
Dementia of Frontal Type	Medical
Density Function Theory	Medical
Design Fluency Test	Medical
Diastolic Filling Time	Medical
Distance From Target	Medical
Diabetes Friendly Thursdays	Medical
Deployment for Training	Military and Defence
Drive Fitness Test	Sports
Down for Two	Sports
Dupont Fabros Technology	Technology
Dual Frame Technology	Technology