the discrete time fourier transform

... Trong miền tần số: phương pháp Fourier Transform. - Trong miền thời gian và tần số: STFT( Short Time Fourier Transform) . 2.4.1. Phương pháp Fourier: 2.4.1.1. Biến đổi Fourier: Cho một hàm f(t) ... được một biến đổi Fourier cục bộ, chúng ta có thể định nghĩa một biến đổi Fourier cửa sổ. Tín hiệu đầu vào được nhân với một hàm cửa sổ W (t - τ) và sau đó lấy biến đổi Fourier của nó. Kết ... đổi Fourier của nó được định nghĩa: () () () tfedtetfF titj , ωω ω == ∫ ∞ ∞− − (2.14) Biến đổi Fourier ngược là: () () ∫ ∞ ∞− = ωω π ω deFtf tj 2 1 (2.15) Giả sử rằng biến đổi Fourier...

Ngày tải lên: 01/04/2013, 16:14

Ngày tải lên: 08/04/2014, 12:26

Ngày tải lên: 21/06/2014, 07:20

Ngày tải lên: 30/10/2014, 20:11

... on the shape of the waveform being decomposed. Chapter 8- The Discrete Fourier Transform 145 Type of Transform Example Signal Fourier Transform Fourier Series Discrete Time Fourier Transform Discrete ... This class of Fourier Transform is sometimes called the Discrete Fourier Series, but is most often called the Discrete Fourier Transform. You might be thinking that the names given to these four ... ] 141 CHAPTER 8 The Discrete Fourier Transform Fourier analysis is a family of mathematical techniques, all based on decomposing signals into sinusoids. The discrete Fourier transform (DFT) is the family...

Ngày tải lên: 13/09/2012, 09:49

... INTRODUCTION TO THE DFT Page 5 Having completely understood the DFT and its inverse mathemati- cally, we go on to proving various Fourier Theorems, such as the “shift theorem,” the “convolution theorem,” ... values in the “obvious way” as integers from 0 to 2 N−1 −1, and then the negative DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O. Smith, CCRMA, Stanford, Winter 2002. The latest ... Warshofsky, and the Editors of Time- Life Books, Sound and Hearing, Life Science Library, Time- Life Books, Alexandria, VA, 1965, p. 173. DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),”...

Ngày tải lên: 31/03/2014, 15:21

... ≤  E x E y . Summary We have now covered all the most important transforms: continuous time: Laplace, Fourier, Fourier Series, discrete time: Z, DTFT, DTFS, DFT/FFT The first six are for pencil and paper ... from the samples using the Dirichlet interpolation formula - see text. Review FT family tree. 5.1.2 The discrete Fourier transform (DFT) For the rest of this chapter, our primary focus will be time- limited ... ω 0 = 2π N k 0 , then the sinc is sampled only at the peak and the nulls, which gives the Dirac impulse form above. Otherwise the sinc is sampled at many nonzero values, which gives the messy form...

Ngày tải lên: 08/06/2014, 20:19

Ngày tải lên: 21/06/2014, 16:20

Ngày tải lên: 22/06/2014, 23:20

... derive the execution time for the FFT. The time required for the bit reversal is negligible. In each of the stagesLog 2 N there are butterfly computations. This means the execution time for theN/2 program ... for the price of single FFT. One of the signals is placed in the real part of the time domain, and the other signal is placed in the imaginary part. After calculating the complex DFT (via the ... discovered the FFT at the right time, the beginning of the computer revolution. The FFT is based on the complex DFT, a more sophisticated version of the real DFT discussed in the last four chapters. These...

Ngày tải lên: 13/09/2012, 09:50

... we restrict the mathematics to be real numbers, problems arise. In other words, these problems are not solved by the complex Fourier transform, they are introduced by the real Fourier transform. In the ... Fourier Transforms A time domain signal can be either continuous or discrete, and it can be either periodic or aperiodic. This defines four types of Fourier transforms: the Discrete Fourier Transform ... the Discrete Fourier Transform (discrete, periodic), the Discrete Time Fourier Transform (discrete, aperiodic), the Fourier Series (continuous, periodic), and the Fourier Transform (continuous, aperiodic)....

Ngày tải lên: 13/09/2012, 10:20

... 0,  NÀ1 n0 W kn N  N. Therefore we obtain XkcNdk; k  0, 1, , N À 1: 7.1.3 Circular Convolution The Fourier transform, the Laplace transform, and the z -transform of the linear con- volution of two time functions ... 7:1:9 The computational frequency resolution of the DFT is equal to the frequency increment f s =N, and is sometimes referred to as the bin spacing of the DFT outputs. The spacing DISCRETE FOURIER ... to evaluating the discrete- time Fourier transform X! at the N equally spaced frequencies ! k  2pk=N, k  0, 1, , N À 1. If the sequence x(n) has a finite duration of length N, the DFT of a...

Ngày tải lên: 28/10/2013, 05:15

... (1.19b) whereω  =ωTisthenormalizedDTfrequencyaxisexpressedinradians.NotethatS(e jωT )= S(e jω  )consistsofaninfinitenumberofreplicasoftheCTspectrumS(jω),positionedatintervals of(2π/T)ontheωaxis(oratintervalsof2πontheω  axis),asillustratedinFig.1.8.Notethatif S(jω)isbandlimitedwithabandwidthω c ,andifTischosensufficientlysmallsothatω s >2ω c , thentheDTspectrumisacopyofS(jω)(scaledby1/T)inthebaseband.Thelimitingcaseof ω s =2ω c iscalledtheNyquistsamplingfrequency.WheneveraCTsignalissampledatorabove theNyquistrate,noaliasingdistortionoccurs(i.e.,thebasebandspectrumdoesnotoverlapwiththe higher-orderreplicas)andtheCTsignalcanbeexactlyrecoveredfromitssamplesbyextractingthe basebandspectrumofS(e jω  )withanideallow-passfilterthatrecoverstheoriginalCTspectrumby removingallspectralreplicasoutsidethebasebandandscalingthebasebandbyafactorofT. 1.5 TheDiscreteFourierTransform ToobtainthediscreteFouriertransform(DFT)thecontinuousfrequencydomainoftheDTFT issampledatNpointsuniformlyspacedaroundtheunitcircleinthez-plane,i.e.,atthepoints c  1999byCRCPressLLC response ... TheDiscreteTimeFourierTransform ThediscretetimeFouriertransform(DTFT)canbeobtainedbyusingtheDTsamplingmodeland consideringtherelationshipobtainedin(1.12)tobethedefinitionoftheDTFT.LettingT=1so thatthesamplingperiodisremovedfromtheequationsandthefrequencyvariableisreplacedwith c  1999byCRCPressLLC Jenkins, ... ThefamilytreeofCTFouriertransform isshowninFig.1.10,wherethemostgeneral,andconsequentlythemostpowerful,Fouriertransform is the classical complex Fourier transform (or equivalently, the bilateral Laplace transform) ....

Ngày tải lên: 27/01/2014, 03:20

... bias but at the same time increases the variance. On the other hand, the use of the Rectangular window makes a FTE biased even for high SNR. In Fig. 21 the behavior of the estimator as the number ... than the TFBMPM. Nevertheless, the rmse obtained with the TFBMPM is less than the one computed using the Standard window as seen in Fig. 19. This is because the Standard window reduces the bias ... f O 1 compared to the CRB for the best case estimation. The peaks show the threshold of the TFBMPM. (N D t) 01 is 0.125 Hz and the maximum D f studied In Figs. 17 and 18 the windows are shown in both time...

Ngày tải lên: 26/03/2014, 00:29

... Conclusions Previously, discrete- time modelling of the source waveforms used in subtractive sound synthesis has focused on reducing aliasing occurring in the waveform synthesis. The target of these oscillators ... its simplicity. The parameters g, b,anda,thegainfactor, the filter zero, and the filter pole, respectively, of H eq (z) were estimated from the recorded data using the approach described above. The estimated ... comparison. Furthermore, the difference between the textbook wave- form and the analogue oscillator output depends on the fundamental frequency. This can be seen in Figure 2 where the waveform and the spectrum...

Ngày tải lên: 21/06/2014, 05:20

Ngày tải lên: 21/06/2014, 17:20

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 21/06/2014, 22:20

Ngày tải lên: 23/06/2014, 01:20