discrete time fourier transform properties ppt

... 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 ... called 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 ... practical uses in DSP. 185 CHAPTER 10 Fourier Transform Properties The time and frequency domains are alternative ways of representing signals. The Fourier transform is the mathematical relationship...

Ngày tải lên: 13/09/2012, 09:49

... 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) ... kết thúc của sự kiện thì Fourier không phát hiện được. 2.4.2. Phương pháp STFT: Để đạt được một biến đổi Fourier cục bộ, chúng ta có thể định nghĩa một biến đổi Fourier cửa sổ. Tín hiệu đầu ... 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

... 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

... matrices S t (j)=  P t−j,t/t C t T −δ 0,j H t R t  C t −1 ( j = 0, 1, ···, L − 1 ) , (82) 65 New Smoothers for Discrete- time Linear Stochastic Systems with Unknown Disturbances Discrete Time Systems 52 Chang, K. C.; Tian, Z. & Saha, R. ... filter reaches its steady state. In this case, the EC P is given by (13). Now, 74 Discrete Time Systems Discrete Time Systems 50 This completes the proof of Theorem 2. Proof of Theorem 3 a., ... matrix. 55 New Smoothers for Discrete- time Linear Stochastic Systems with Unknown Disturbances This chapter investigates the behavior of the Kalman filter for discrete- time linear systems whose output...

Ngày tải lên: 20/06/2014, 01:20

... as P k+1|k =  P 11,k+1|k P 12,k+1|k P T 12,k +1|k P 22,k+1|k  , (50) 101 Kalman Filtering for Discrete Time Uncertain Systems Kalman Filtering for Discrete Time Uncertain Systems 15 above its error variance prediction, i.e., ... concentration of a given medicine in his patient. Kalman Filtering for Discrete Time Uncertain Systems 6 12 Discrete Time Systems Using (74), we can simplify the expressions for Φ ∗ k , K ∗ k and ... E  e (j) i,k  2 , (81) E  e (j) i,k  ≈ 1 N N ∑ j=1 e (j) i,k , (82) 104 Discrete Time Systems Kalman Filtering for Discrete Time Uncertain Systems 13 Step 0 (Initial conditions):  x 0|−1 = x 0 and...

Ngày tải lên: 20/06/2014, 01:20

... the discrete time Riccati equation (7), then it also is a stabilizing solution to the discrete time Riccati inequality (6). According to the concept of stabilizing solution of discrete time ... will consider two discrete time mixed LQR/ H ∞ control problems. One is the discrete time state feedback mixed LQR/ H ∞ control problem, another is the non-fragile discrete time state feedback ... Feedback Control of Discrete- time LTI Systems: Scaling LMI Approaches Discrete Time Systems 140 Fig. 1. Responses of the system for nonlinear descriptor system in discrete time 7. References...

Ngày tải lên: 20/06/2014, 01:20

Ngày tải lên: 20/06/2014, 01:20

Ngày tải lên: 20/06/2014, 01:20

Ngày tải lên: 20/06/2014, 01:20

Ngày tải lên: 20/06/2014, 01:20

Ngày tải lên: 20/06/2014, 01:20

Ngày tải lên: 20/06/2014, 01:20

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 ... repeat themselves in a periodic fashion. This type of Fourier transform is called the Discrete Time Fourier Transform. Periodic -Discrete These are discrete signals that repeat themselves in a periodic...

Ngày tải lên: 13/09/2012, 09:49

... 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 ... enhance its utility for analyzing finite-length signals. Many DFT properties are similar to those of the Fourier transform and the z -transform. However, there are some differences. For example, the ... 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...

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 ... equation (12.1.6) is called the discrete Fourier transform of the N points h k . Let us denote it by H n , H n ≡ N−1  k=0 h k e 2πikn/N (12.1.7) The discrete Fourier transform maps N complex numbers...

Ngày tải lên: 21/01/2014, 18:20

... 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 ... 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 ... two-dimensional grid 0 ≤ k 1 ≤ N 1 − 1, 0 ≤ k 2 ≤ N 2 − 1, we can define its two-dimensional discrete Fourier transform as a complex function H(n 1 ,n 2 ), defined over the same grid, H(n 1 ,n 2 )≡ N 2 −1  k 2 =0 N 1 −1  k 1 =0 exp(2πik 2 n 2 /N 2 )exp(2πik 1 n 1 /N 1 )...

Ngày tải lên: 21/01/2014, 18:20

Ngày tải lên: 06/03/2014, 17:20

... assets. Their initial prices at time t = 0 areknown, theirfuture pricesat timet = 1 aredescribed asrandom variables onsome probability space. Trading takes place at time t = 0. Already in this simple ... one-period model, these assets are priced at the initial time t = 0 and at the final time t = 1. We assume that the i th asset is available at time 0 for a price π i ≥ 0. The collection π = (π 0 ,π 1 , ... investor at time t = 0 will also depend on the information available at time 0. Thus, we assume that ξ = (ξ 0 ,ξ 1 , ,ξ d ) is an F 0 -measurable random vector. The asset prices observed at time t...

Ngày tải lên: 08/03/2014, 23:20

... 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),” by ... 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