discrete fourier transform applications ppt

Ngày tải lên: 22/06/2014, 23:20

... decomposed. Chapter 8- The Discrete Fourier Transform 145 Type of Transform Example Signal Fourier Transform Fourier Series Discrete Time Fourier Transform Discrete Fourier Transform signals that ... term: transform, is extensively used in Digital Signal Processing, such as: Fourier transform, Laplace transform, Z transform, Hilbert transform, Discrete Cosine transform, etc. Just what is a transform? To ... ] 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...

Ngày tải lên: 13/09/2012, 09:49

... waw w j++ t e a- 22 2 wa a + )2/( 22 s t e - 2/ 22 2 ws ps - e t etu a- )( wa j + 1 t tetu a- )( 2 )( 1 wa j + Ø Trigonometric Fourier Series () å ¥ = ++= 1 000 )sin()cos()( n nn ntbntaatf ww where ò òò = == T n T T n dtnttf T b dtnttf T adttf T a 0 0 0 0 0 0 )sin()( 2 ... Series () å ¥ = ++= 1 000 )sin()cos()( n nn ntbntaatf ww where ò òò = == T n T T n dtnttf T b dtnttf T adttf T a 0 0 0 0 0 0 )sin()( 2 and, )cos()( 2 , )( 1 w w Ø Complex Exponential Fourier Series ò å - ¥ -¥= == T ntj n n ntj n dtetf T FeFtf 0 0 )( 1 where, )( w w Signals &...

Ngày tải lên: 13/12/2013, 12:15

... Destructive Interference . . . . . 74 5.2 Exponentials . . 76 DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O. Smith, CCRMA, Stanford, Winter 2002. The latest draft and linked ... again. Fortunately for us, all audio signals can be defined so DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O. Smith, CCRMA, Stanford, Winter 2002. The latest draft and linked ... even (−1) n/2 n! θ n sin(θ)= ∞  n≥0 n odd (−1) (n−1)/2 n! θ n DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O. Smith, CCRMA, Stanford, Winter 2002. The latest draft and linked...

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 ... 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 signals ... with no effect since x[n] = 0 for n = L, . . . , N −1. The above expression is called the discrete Fourier transform or (DFT). The DFT is always defined, since it is a finite sum! Since x[n] is time-limited,...

Ngày tải lên: 08/06/2014, 20:19

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Ngày tải lên: 21/06/2014, 22:20

... frequencies f k  kf s N , k  0, 1, , N À 1: 7:3:1 322 FAST FOURIER TRANSFORM AND ITS APPLICATIONS DFT and z -transform Consider a sequence x(n) having the z -transform X(z) with an ROC that includes the unit ... Circular Convolution The Fourier transform, the Laplace transform, and the z -transform of the linear con- volution of two time functions are simply the products of the transforms of the individual ... 0.; 338 FAST FOURIER TRANSFORM AND ITS APPLICATIONS Compared with LM required by direct FIR filtering, the computational saving is significant when both L and M are large. For many applications, ...

Ngày tải lên: 28/10/2013, 05:15

... showed that a discrete Fourier transform of length N can be rewritten as the sum of two discrete Fourier transforms, each of length N/2. One of the two is formed from the 12.1 Fourier Transform of Discretely ... generate the required powers of W . So, the discrete Fourier transform appears to be an O(N 2 ) process. These appearances are deceiving! The discrete Fourier transform can, in fact, be computed in ... Fourier Transform (Englewood Cliffs, NJ: Prentice-Hall). Elliott, D.F., and Rao, K.R. 1982, Fast Transforms: Algorithms, Analyses, Applications (New York: Academic Press). 12.2 Fast Fourier Transform...

Ngày tải lên: 21/01/2014, 18:20

... REFERENCES AND FURTHER READING: Nussbaumer, H.J. 1982, Fast Fourier Transform and Convolution Algorithms (New York: Springer- Verlag). 12.5 Fourier Transforms of Real Data in Two and Three Dimensions Two-dimensional ... data[], unsigned long nn[], int ndim, int isign) Replaces data by its ndim-dimensional discrete Fourier transform, if isign is input as 1. nn[1 ndim] is an integer array containing the lengths ... rows. If isign is input as −1, data is replaced by its inverse transform times the product of the lengths of all dimensions. 12.5 Fourier Transforms of Real Data in Two and Three Dimensions 525 Sample...

Ngày tải lên: 21/01/2014, 18:20

... citation purposes) 13. David-Vaudey E, Burghardt A, Keshari K, Brouchet A, Ries M, Majum- dar S: Fourier Transform Infrared Imaging of focal lesions in human osteoarthritic cartilage. Eur Cell Mater ... IW, Lewis EN, Spencer RG: Imaging of collagen and proteoglycan in cartilage sections using Fourier transform infrared spectral imaging. Arth Rheum 2001, 44:846-855. 17. Wetzl DL, Post GR, Lodder ... Y, Ramakrishnan N, Bidthanapally A: The Depth-dependent Anisotropy of Articular Cartilage by Fourier- Transform Infrared Imaging (FTIRI). Osteo Cart 2007, 15:780-788. 24. Ramakrishnan N, Xia Y,...

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Ngày tải lên: 22/07/2014, 02:21

... frequency domain multiplexing. The Discrete Time Fourier Transform The Discrete Time Fourier Transform (DTFT) is the member of the Fourier transform family that operates on aperiodic, discrete signals. The ... four members of the Fourier transform family (Fourier transform, Fourier Series, DFT, and DTFT). Figure 10-1 provides an example of how homogeneity is a property of the Fourier transform. Figure ... properties of the Fourier Transform, how a mathematical change in one domain results in a mathematical change in the other domain. Linearity of the Fourier Transform The Fourier Transform is linear,...

Ngày tải lên: 13/09/2012, 09:49

... called Fourier transform pairs. Several common pairs are presented in this chapter. Delta Function Pairs For discrete signals, the delta function is a simple waveform, and has an equally simple Fourier ... one domain is discrete, the other domain must be periodic, and vice versa. This holds for all four members of the Fourier transform family. Since the DFT views both domains as discrete, it must ... function. Forsin(x)/x continuous signals, the rectangular pulse and the sinc function are Fourier transform pairs. For discrete signals this is only an approximation, with the error being due to aliasing....

Ngày tải lên: 13/09/2012, 09:49