blt amp 8211 trapezoidal 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 ... 287 6.3.4 Right-Side (Rectangular) Rule on Numerical Integration 288 6.3.5 Bilinear Transformation (BLT) – Trapezoidal Rule on Numerical Integration 288 6.3.6 ... Continuous-time Continuous-time continuous-amplitude continuous-amplitude discrete-amplitude discrete-amplitude signal signal sampled signal signal xd [n] x (t ) x∗(t ) xd (t ) A/D conversion...

Ngày tải lên: 29/08/2015, 10:44

... 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 ... locations, converting analog filters into digital, etc These operations are carried out by algebra performed in the zdomain, such as: multiplication, addition, and factoring After these operations...

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 ... satisfied 2.6 CONVOLUTION REVISITED In a previous section on convolution, we had shown that the output y(n) of a linear, shift-invariant, discrete-time system is obtained by convolution of x(n) and...

Ngày tải lên: 29/09/2013, 21:20

Ngày tải lên: 24/12/2013, 12:16

... 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 ... 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...

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 ... 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 49 4.3.3 ... following finite duration signals 4.1 Z - transform • Solution 4.1 Z - transform • Example 4.1 Z - transform Recall that 4.1 Z - transform • Example • Solution 4.1 Z - transform • Example • We have...

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

... n=0 n =0 R ( z ) = r ( nT ) z n = z n = + z + z + z + R ( z) = z , z > z 1.2.2 H m ramp H m ramp hay gọi l h m dốc đợc định nghĩa nh sau n>G = tf(1, [1 4]); >>Gz = c2d(G, 0.1) Kết m n hình nh sau Transfer function: 0.08242 -z - 0.6703 Sampling time: 0.1 Điều có nghĩa l biến đổi z h m l G ( z) = 0,08242 z - 0,6703 Ví...

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

... s0[ ] Amplitude Amplitude -1 -1 -2 -2 16 Sample number 24 32 24 32 16 24 32 16 24 32 16 24 32 d s2[ ] Amplitude -1 -1 -2 -2 16 24 32 Sample number Sample number e c10[ ] f s10[ ] Amplitude Amplitude ... Amplitude 16 c c2[ ] Amplitude Sample number -1 -1 -2 -2 16 Sample number 24 32 Sample number g c16[ ] h s16[ ] Amplitude Amplitude 151 -1 -1 -2 -2 16 Sample number 24 32 Sample number FIGURE ... 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:...

Ngày tải lên: 13/09/2012, 09:49

... Solution #1 f = 3, = -B/4 a Samples Amplitude Amplitude -1 -1 -2 -2 16 24 32 Sample number 16 24 32 24 32 Sample number 2 c Solution #2 f = -3, = B/4 d Solution #3 f = 35, = -B/4 Amplitude Amplitude ... of sampling frequency Amplitude Amplitude 0 -1 -1 sample shift = 1/32 cycle sample shift = 1/2 cycle -2 -2 16 Sample number 24 32 16 Sample number 24 32 FIGURE 10-4 The relationship between samples ... a one sample shift is only a small fraction of a full cycle In (b), the sinusoid has a frequency of one-half of the sampling rate, the highest frequency that can exist in sampled data A one sample...

Ngày tải lên: 13/09/2012, 09:49

... c Imaginary part Amplitude Amplitude Amplitude 1 -1 -2 -0.5 -1 16 32 48 Sample number 64 63 -1 Frequency -2 -0.5 0.5 Amplitude Amplitude Amplitude 0 -1 -2 -0.5 -1 16 32 48 Sample number 63 64 ... offending harmonics with an antialias filter before digitization Harmonic aliasing is only a problem when nonlinear operations are performed directly on a discrete signal Even then, the amplitude ... chapters on filter design Chapter 11- Fourier Transform Pairs 2 b Frequencies: & 1 Amplitude Amplitude a Frequencies: 0 -1 -1 256 512 Sample number 768 1023 1024 Amplitude Amplitude 512 Sample...

Ngày tải lên: 13/09/2012, 09:49

... stretches from sample to sample N& , corresponding with to 1.0 times the sampling rate The positive frequencies sit between sample and N/2 , corresponding with to 0.5 The other samples, between ... individual components 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, ... For example, sample (0011) is exchanged with sample number 12 (1100) Likewise, sample number 14 (1110) is swapped with sample number (0111), and so forth The FFT time domain decomposition is...

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 ... real part correspond to a cosine wave with an amplitude of one, and a frequency of 0.23 The two round markers in the imaginary part correspond to a sine wave with an amplitude of one, and a frequency ... 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...

Ngày tải lên: 13/09/2012, 10:20

... equations show that the two poles always lie somewhere on a circle of radius: 1/RC The exact position along the circle depends on the gain of the amplifier As shown in (a), an amplification of ... 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 ... 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,...

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