2.3. 1 Discrete Fourier Transform DFT ODFT: a Fourier representation of a finite length sequence which itself is a sequence rather than a continuous function and it corresponds to samples equally spaced in frequency of the Fourier transform of the 羽q!-))是=∑x-k=01w-1 (2205) n=0 DFr:x)=12x(k÷=1x()n=01…N-1(2060 e x(n△t) wherekfo), X(n) and X(k) are periods for and respectively, and At and fo are generalized to be unity
❑DFT: a Fourier representation of a finitelength sequence which itself is a sequence rather than a continuous function, and it corresponds to samples equally spaced in frequency of the Fourier transform of the signal. where , x(n) and X(k) are periods for and respectively, and Δt and f0 are generalized to be unity. 2.3.1 Discrete Fourier Transform (DFT) : ( ) ( ) ( ) 0,1, , 1 1 2 1 = = = − − = − = − DFT X k x n e x n W k N n k N N n o N n o n k N j (2.205) ( ) ( ) ( ) 0,1, , 1 1 1 : 1 2 1 = = = − − = − = − X k W n N N X k e N IDFT x n N K o N K o nk N nk N j (2.206) N j N W e 2 − = x ˆ(nt) ( ) ˆ 0 X kf
2.3. 1 Discrete Fourier Transform DFT UThe true meaning of the DFT. It is possible to sample and truncate any continuous time signals and make dft of it to get a discrete spectrum, whose envelope is the estimate of the true spectrum of the original continuous signal UDF T process sampling in time domain truncating in time domain sampling in frequency domain
❑The true meaning of the DFT: – It is possible to sample and truncate any continuous time signals and make DFT of it to get a discrete spectrum, whose envelope is the estimate of the true spectrum of the original continuous signal. ❑DFT process: – sampling in time domain; – truncating in time domain; – sampling in frequency domain. 2.3.1 Discrete Fourier Transform (DFT)
2. 3. 1 Discrete Fourier Transform DFT) X (f) SI(t ÷ 0 T s1()=∑6(-n) S(0)-元.∑引/- Fig. 2.64 Graphical representation of the DFT(a
2.3.1 Discrete Fourier Transform (DFT) Fig. 2.64 Graphical representation of the DFT (a)