rectangular rule on numerical integration

... Backward Difference Rule on Numerical Differentiation 284 6.3.2 Forward Difference Rule on Numerical Differentiation 286 6.3.3 Left-Side (Rectangular) Rule on Numerical Integration 287 6.3.4 ... Integration 287 6.3.4 Right-Side (Rectangular) Rule on Numerical Integration 288 6.3.5 Bilinear Transformation (BLT) – Trapezoidal Rule on Numerical Integration ... ] * gb [n ] Fig 1.14 Approximation of a continuous–time convolution by a discrete–time convolution The above example implies that the continuous-time convolution x(t) ∗ g(t) can be approximated...

Ngày tải lên: 29/08/2015, 10:44

... zero locations can be represented in either polar or rectangular form Polar notation has the advantage of being more consistent with the natural organization of the z-plane In comparison, rectangular ... location on the circle is given by: F and T, the corresponding location on the ellipse, Fr and Tr , is given by: Fr ' F sinh(v) / k EQUATION 33-9 Circular to elliptical transform These equations ... location on a circle to a corresponding location on an ellipse The variables, NP and PR, are the number of poles in the filter, and the percent ripple in the passband, respectively The location on...

Ngày tải lên: 13/09/2012, 10:20

... is the response due to input only, and the zero input response is due to the initial states (initial conditions) only We repeat it in order to avoid the common confusion that occurs among students! ... computing the response due to input function only Students are advised to know the exact definition and meaning of the zero input response and zero state response, without any confusion between these ... difference equations and finding the response of discrete-time systems when the input function and initial conditions are given Instead of deriving all the properties one after another, as is done in many...

Ngày tải lên: 29/09/2013, 21:20

Ngày tải lên: 24/12/2013, 12:16

... Function and Manipulation of Block Diagram Open-Loop Time Response • Solution (cont.) The time response in this case: Pulse Transfer Function and Manipulation of Block Diagram Open-Loop Time Response ... partial fraction • Inversion formula method: using inversion integral 𝑦 𝑛𝑇 = 2𝜋𝑗 𝑌 𝑧 𝑧 −1 𝑑𝑧 𝑟 Pulse Transfer Function and Manipulation of Block Diagram Definition • Pulse Transfer Function is • A ... Content • The Sampling Process • The z-Transform • Pulse Transfer Function and Manipulation of Block Diagram • Exercises Prior to Lecture • Conventional Control System Sampled data control...

Ngày tải lên: 23/07/2015, 15:24

... 4.3.3 System function of LTI • Solution • The unit sample response 50 4.4 Inverse Z- transform • By contour integration • By power series expansion • By partial fraction expansion 51 ... 4.3.3 System function of LTI • System function • From a linear constant coefficient equation • We have, 47 4.3.3 System function of LTI • Or equivalently 48 4.3.3 System function of LTI • Example ... transform = closed-form expressions + ROC 11 4.1 Z - transform • Example • Solution – The first power series converges if |z| > |a| – The second power series converges if |z| < |b| 12 • Case...

Ngày tải lên: 08/04/2016, 22:05

... dài từ đầu vào transistor tới điểm mắc dây chêm song song hở mạch 0,138ƛ Để triệt tiêu phần điện kháng – j0,3 cần mắc thêm dây chêm hở mạch song song có giá trị j0,3 Chiều dài dây chêm 0,18ƛ  ... đầu vào phía nguồn Sử dụng phương pháp dây chêm song song hở mạch, ta có: Γin = Γs* = 0,153∟131.4o Từ Γin ta xác định Zin , đường tròn có Γ = const, ta xác định điểm dẫn nạp Yt = Yin cách lấy ... suất Wilkinson : Cửa R0 l/4 Vin1 Cửa R R0 Ra R0 Cửa Vin2 Hình : Sơ đồ mạch ghép chia công suất Wilkinson với nguồn cửa Chiều dài nhánh thiết kế l/4, mạch ghép – chia công suất Wilkinson hoạt động...

Ngày tải lên: 26/12/2015, 10:19

Ngày tải lên: 03/08/2012, 23:27

... expected 21st Annual Spears Foundation Conference on Health Conference Purpose The 21st Annual Spears Foundation Conference on Health provides professional education and networking for doctors, dentists, ... fundraiser (a) donor (b) donate (c) donated (d) donation 113 The retail industry spends $28 billion on IT and related systems annually (a) nearly (b) yearly (c) monthly (d) continually 114 My ... Foundation Conference on Health is to foster the awareness and early prevention of improper childhood nutrition within the field of healthcare The conference aims to: ■ broaden the discussion on nutrition...

Ngày tải lên: 15/08/2012, 11:01

... Matlab để tìm biến đổi z v biến đổi z ngợc Trong Matlab, hộp công cụ hệ thống điều khiển hỗ trợ việc thiết kế hệ thống điều khiển thời gian rời rạc Trong phần n y đề cập đến số lệnh thông dụng ... biến đổi z ngợc H m thời gian y ( t ) đợc xác định nh sau: y ( t ) = y ( nT ) ( t nT ) n=0 Trong chơng n y giới hạn tìm hiểu phơng pháp v thông qua ví dụ Phơng pháp 1: Chuỗi lũy thừa Phơng ... Chú ý từ phơng trình (1.23), thông tin đầu y ( z ) thời điểm lấy mẫu 1.3.1 Các hệ thống vòng hở Trong phần n y khảo sát số ví dụ thao tác sơ đồ khối hệ vòng hở Ví dụ 1.7: Hình 1.10 trình b y hệ...

Ngày tải lên: 20/08/2012, 10:27

... th CPU s d ng + Specification/Family/Ext.Family/Model/ExtModel/Stepping/Revision: Nh ng ch s nh n d ng CPU, thư ng b n ch quan tâm t i tên c a CPU t ng Specification , n u mu n bi t rõ hơn, b ... n m tab About r i nh n vào Validation C a s hình bên s xu t hi n - B n nh n vào Save Validation file r i ch n m t v trí thích h p - Nh n vào liên k t Validation Web page màu xanh da tr i Step2 ... - M c BIOS: + Brand: Nhà s n xu t BIOS + Version: S phiên b n BIOS + Date: Ngày phát hành b n BIOS ang s d ng - M c Graphic Interface: + Version: Ki u giao ti p (thông d ng AGP ho c PCI Express)...

Ngày tải lên: 23/08/2012, 09:45

... TIME FUNCTION PLC Process Applications Second-Order Step Response (A1/s) for ζ = (Critically Damped) Second-Order Step Response (A1/s) for ζ < (Underdamped) A (τ1s + 1)(τ2s + 1) Second-Order Transfer ... Function (Hp(s)) for ζ > (Overdamped) ωn A (τs + 1)2 s + 2ζωns + Second-Order Transfer Function (Hp(s)) for ζ = (Critically Damped) Second-Order Transfer Function (Hp(s)) for ζ < (Underdamped) Second-Order ... = 0.632 t = 0.865 Hp(s) = Out In t t 2π or fn ωn td+1 PROCESS RESPONSE Process Responses and Transfer Functions Table 14-2 continued −t ⎛ τe τ − τ e AA2 ⎜1 + 1 ⎜ τ2 − τ1 ⎝ ⎞ ⎟ ⎟ ⎠ (0 < ψ < π...

Ngày tải lên: 24/08/2012, 21:55

... following equations convert the frequency domain from rectangular to polar notation, and vice versa: EQUATION 8-6 Rectangular- to-polar conversion The rectangular representation of the frequency ... referred to earlier Although the conversion is only a simple normalization, it is a common bug in computer programs Look out for it! In equation form, the conversion between the two is given by: ... should you use rectangular notation and when should you use polar? Rectangular notation is usually the best choice for calculations, such as in equations and computer programs In comparison, graphs...

Ngày tải lên: 13/09/2012, 09:49

... correlation can be performed as a convolution This is done by flipping one of the signals left-for-right In mathematical form, a[ n ] t b[n ] is convolution, while a[ n ] t b[& n ] is correlation In ... considering how signals overflow between periods Two examples of this have already been presented, circular convolution and analog-to-digital conversion In circular convolution, multiplication ... compression & expansion of signals, and amplitude modulation Compression and Expansion, Multirate methods As shown in Fig 10-12, a compression of the signal in one domain results in an expansion in...

Ngày tải lên: 13/09/2012, 09:49

... distortion occurred in an analog signal, you would remove the offending harmonics with an antialias filter before digitization Harmonic aliasing is only a problem when nonlinear operations are ... of a rectangular pulse A rectangular pulse in one domain corresponds to a sinc function in the other domain Alternatively, the DTFT can be used to express the frequency spectrum as a fraction of ... represent the longer signal The key here is that "selecting N samples from a longer signal" is the same as multiplying the longer signal by a rectangular pulse The ones in the rectangular pulse...

Ngày tải lên: 13/09/2012, 09:49

... CORRELATION 5010 'Upon entry, N% contains the number of points in the DFT, and 5020 'XR[ ] and XI[ ] contain the real and imaginary parts of the time domain 5030 'Upon return, REX[ ] and IMX[ ] contain ... must be combined to form the two components of the product (such as in Eq 9-1) The following discussion on "How the FFT works" uses this jargon of complex notation That is, the singular terms: signal, ... interlaced decomposition done in the time domain In other words, the frequency domain operation must correspond to the time domain procedure of combining two point signals by interlacing Consider two time...

Ngày tải lên: 13/09/2012, 09:50

... the contributions from the positive and the negative frequencies reconstructs the time domain signal: contribution from positive frequency ! ½ cos (2B 0.23 n) % ½ j sin(2B 0.23n ) contribution ... much help; one complex expression is equal to another complex expression Nevertheless, a little algebra can rearrange the relation into two other forms: EQUATION 31-3 Euler's relation for sine ... domain signal is periodic, the appropriate section is over any one complete period The equations shown here are written with the integration (or summation) over the period: to T (or to N-1) However,...

Ngày tải lên: 13/09/2012, 10:20

... mentioned in the introduction, systems that belong to this class are extremely common in science and engineering This is because sinusoids and exponentials are solutions to differential equations, ... to know what portions of the s-plane are within the region-of-convergence However, this information is not needed for the applications in this book Only the exact cancellations are of interest ... along the path While your description of the signal might consist of thousands of individual measurements, the conductor's description of the signal will contain only a few parameters To show how...

Ngày tải lên: 13/09/2012, 10:20

... x(n) = Z-1{X(z)}  5.1.2 MIỀN HỘI TỤ CỦA BIẾN ĐỔI Z (ROC) • Miền hội tụ biến đổi Z - ROC (Region Of Convergence) tập hợp tất giá trị Z nằm mặt phẳng phức cho X(z) hội tụ Im(Z) Rx+ • Để tìm ROC ... /z/ /a/ /z/ < /a/ /z/ > /a/ -nan u(-n-1) az (1 − az −1 ) cos( on) u(n) (1-z-1cosωo)/(1-2z-1cosωo+z-2) /z/ >1 sin( on) u(n) (z-1sinωo)/(1-2z-1cosωo+z-2) /z/ >1 /z/ < /a/ 2.3 BIẾN ĐỔI Z NGƯỢC ... thặng dư tất điểm cực hàm X(z)zn-1 : x ( n) = X ( z ) z n−1dz ∫ 2πj C (*) Trong đó: • Zci – điểm cực X(z)zn-1 nằm đường cong C • Res[X(z)zn-1]z=zci - thặng dư X(z)zn-1 điểm cực zci  Tổng cộng thặng...

Ngày tải lên: 13/09/2012, 11:16

... )] : max[ Ri − ] < | z | < min[ Ri + ] Miền hội tụ hàm Y(z) giao miền hội tụ X1(z) X2(z) Đường cong kín C tích phân [2.2-15] phải bao quanh gốc tọa độ thuộc miền hội tụ X1(z) X2(z) mặt phẳng phức...

Ngày tải lên: 13/09/2012, 12:13