Create the page "DT" on this wiki! See also the search results found.
- <math>\frac{dx_1}{dt}=f_1(t,x_1,x_2,...x_n)</math> <math>\frac{dx_2}{dt}=f_2(t,x_1,x_2,...x_n)</math>10 KB (1,613 words) - 23:16, 21 November 2017
- ...Transform is defined as <math>Y(s)=L[y(t)]=\int_{0}^{\infty} y(t) e^{-st} dt</math>， which is also time function <math>y(t)</math> expressed in the "c ...\int_{0}^{\infty} e^{(2-s)t} dt=\lim_{b \to \infty} {\int_{0}^{b} e^{2-s}t dt}=\lim_{b \to \infty} {\frac{e^{2-s}t}{2-s} |_{0}^{b}}=\lim_{b \to \infty} {6 KB (1,071 words) - 18:26, 22 November 2017
- ...'' Solve the ODE <math>t^2 (lnt+1) \frac{d^2y}{dt^2} + t(2lnt+1) \frac{dy}{dt} -y=0</math>, one of the solutions is <math>y=\frac{1}{t}</math>. Find a se ...^2y}{dt^2}=\frac{2x}{t^3} - \frac{2\frac{dx}{dt}}{t^2} + \frac{\frac{d^2y}{dt^2}}{t}</math>.7 KB (1,254 words) - 19:49, 22 November 2017
- <math>\frac{dx_1}{dt}=f_1(t,x_1,x_2,...x_n)</math> <math>\frac{dx_2}{dt}=f_2(t,x_1,x_2,...x_n)</math>8 KB (1,377 words) - 04:04, 19 November 2017
- | Table of DT Fourier series properties with proofs (yes! I'm fearless ;D ) and list of c4 KB (618 words) - 12:12, 1 May 2018
- W_E = \sum_{k = 1}^{N} \int v_k i_k \, dt ...\, \textrm{s}</math> and revert to time integrals using <math>\frac{di_1}{dt} = +10 e^{-t} \, \frac{\textrm{A}}{\textrm{s}}</math>.13 KB (2,127 words) - 13:49, 16 January 2018
- ...ll by the Quotient Rule or the Chain Rule + Power Rule that <math>\frac{d}{dt} \frac{a}{\sum_{k=0}^K b_k t^k} = \frac{-a\sum_{k=1}^K k b_k t^{k - 1}}{\le4 KB (701 words) - 18:58, 26 January 2018
- v_1(i, T) &= \frac{d}{dT} \left[\frac{2N^2 \mu_0 w t d i}{2 t g(T) + w c}\right] \\ ...}{dT} \left(2 t g(T) + w c\right) - 2N^2 \mu_0 w t d i \left(2 t \frac{dg}{dT}\right)}{\left(2 t g(T) + w c\right)^2} \\2 KB (353 words) - 23:30, 16 January 2018
- E_{\infty}&=\int_{-\infty}^\infty |\sin(2 \pi t)|^2 dt \\ &=\int_{-\infty}^\infty \sin^2(2 \pi t) dt2 KB (373 words) - 10:09, 22 January 2018
- E_{\infty}&=\int_{-\infty}^\infty |e^{-2\pi jt}|^2 dt \\ &=\int_{-\infty}^\infty e^{-2\pi jt} * e^{2\pi jt} dt \\2 KB (229 words) - 10:22, 22 January 2018
- v_1(t) &= \frac{d}{dt} \frac{1}{2}N^2 \mu_0 \ell (\cancelto{0}{i_1(t)} + i_2(t)) G(g) \\ v_1(t) &= \frac{1}{2}N^2 \mu_0 \ell G(g) \frac{d}{dt} \left[I_2 \cos(\omega_e t)\right] \\2 KB (311 words) - 14:22, 22 January 2018
- v_2(t) &= \frac{\mu_0 w \ell}{3 g} \frac{d}{dt} \left[N_1 N_2 i_1(t) + 2N_2^2 i_2(t)\right] \\ v_2(t) &= \frac{\mu_0 w \ell}{3 g} \frac{d}{dt} \left[N_1 N_2 I_1 \cos(\omega_e t) + 2N_2^2 I_2 \cos(\omega_e t)\right] \\5 KB (867 words) - 16:05, 26 January 2018
- ...{f,j}</math>, then it can be said that <math>W_{e,j} = \int e_{f,j} i_j \, dt</math> since the energy in a circuit is the product of the voltage and curr W_f = \int \sum_{j=1}^J e_{f,j} i_j \, dt - \int f_e \, dx7 KB (1,270 words) - 14:25, 12 February 2018
- | Duality || '''''NO DUALITY IN DT''''' || '''''NO DUALITY IN DT'''''<br />7 KB (1,166 words) - 13:20, 26 March 2018
- ...) and often require conversion from continuous time (CT) to discrete time (DT) for analysis.12 KB (1,702 words) - 20:48, 9 April 2018
- <math>\chi (- \omega ) = \int_{-\infty}^{\infty} x(t) e^{ \jmath (-\omega) t} dt </math> ...hi (- \omega ) = \int_{-\infty}^{\infty} x(-\tau) e^{ \jmath \omega \tau } dt </math>6 KB (1,010 words) - 18:04, 20 April 2018
- ...c_2h(t) = \int_{-\infty}^\infty c_1g(t) dt + \int_{-\infty}^\infty c_2h(t) dt </math><br/> ...y}^\infty g(t)e^{i2\pi ft} dt + c_2 \int_{-\infty}^\infty g(t)e^{i2\pi ft} dt </math><br/>3 KB (669 words) - 22:52, 22 April 2018
- Enjoy this tutorial of DT and CT convolutions (with examples!!!)329 B (47 words) - 10:19, 26 April 2018
- v_1(t) &= L_s \frac{d}{dt} \left[10 \cos\left(\omega_1 t\right) \, \text{A}\right] \\5 KB (816 words) - 15:22, 4 August 2018
- ...k{F}(ax(t) + by(t)) = \int_{-\infty}^{\infty}[ax(t) + by(t)]e^{-j\omega t} dt</math><br /> ...\infty}ax(t)e^{-j\omega t} dt + \int_{-\infty}^{\infty}by(t)e^{-j\omega t} dt</math><br />5 KB (873 words) - 00:52, 15 November 2018
- ...E_\infty</math> and the power <math class="inline">P_\infty</math> of the DT exponential signal below:1 KB (161 words) - 19:48, 1 December 2018
- =CT and DT Convolution Examples= ...course, it is important to know how to do convolutions in both the CT and DT world. Sometimes there may be some confusion about how to deal with certain5 KB (985 words) - 12:38, 30 November 2018
- ..._\infty</math> and the power <math class="inline">P_\infty</math> of this DT signal:1 KB (196 words) - 19:39, 1 December 2018
- <math> F(h(t)) = \int_{-\infty}^{\infty}h(t)e^{-j \omega t} dt </math> <math> \phantom{aaaaaa} = \int_{-\infty}^{\infty} \delta(t-7) e^{-j \omega t} dt </math>5 KB (865 words) - 16:23, 2 December 2018
- E_{\infty} &=\int_{-\infty}^\infty |\cos^2(5t)|^2 dt \\ &=\int_{-\infty}^\infty \frac{1+\cos(10t)}{2} dt \\1 KB (178 words) - 19:48, 1 December 2018
- This model also has a differential form:<math>\frac{dP}{dt}=rP</math>4 KB (599 words) - 22:58, 2 December 2018
- ...Salisbury, 2011, p.62) is given by the cubic growth model, <math>\frac{dN}{dT}=rN(\frac{N}{T}-1)(1-\frac{N}{K})</math> where <math>\frac{dN}{dT}</math> = rate of increase of the population.10 KB (1,532 words) - 22:51, 2 December 2018
- ...d the input audio file. This makes sense from what we know about computing DT convolution.7 KB (1,070 words) - 00:57, 3 December 2018
- <center><big><math>\frac{dN}{dt}=rN(\frac{K-N}{K})</math><br /></big></center>3 KB (463 words) - 23:57, 2 December 2018
- ...to compute some Fourier series coefficients. I have done 3 in both CT and DT, with explanations as to how I got my answers. Hope you can find this helpf ==DT signals==5 KB (951 words) - 21:55, 30 April 2019
- <math>\lambda_n = (\lambda_n^b-\lambda_n^d) e^{-\int_{0}^{x}\mu(t)dt}d)\lambda_n^c</math> <math>\hat{P}_n = \int_{0}^{x}\mu(t)dt= -log(\frac{\lambda_n}{\lambda_n^b-\lambda_n^d})</math>3 KB (575 words) - 03:07, 26 April 2020
- ...^c e^{-\int_{0}^{x}\mu(t)dt} \Longrightarrow \hat{P}_n = \int_{0}^{x}\mu(t)dt= -ln(\frac{\lambda_n}{\lambda_n^c}) = -ln(\frac{\lambda_n}{\lambda_n^b-\lam2 KB (445 words) - 20:45, 9 July 2019
- **[[Table DT Fourier Transforms|DTFT]]4 KB (467 words) - 02:18, 10 December 2019
- *Week 1-2: CT and DT Fourier Transforms == Part 2 (week 9-14): DT Systems and Applications ==10 KB (1,356 words) - 18:52, 20 August 2019
- ...the act of converting a continuous-time (CT) signal into a discrete-time (DT) one. Although it may be easier to mathematically process a CT signal direc ...gnal <math>x[n]</math>, where <math>n</math> is an integer and indexes the DT signal.16 KB (2,611 words) - 14:11, 12 November 2019
- ...^c e^{-\int_{0}^{x}\mu(t)dt} \Longrightarrow \hat{P}_n = \int_{0}^{x}\mu(t)dt= -ln(\frac{\lambda_n}{\lambda_n^c}) = -ln(\frac{\lambda_n}{\lambda_n^b-\lam2 KB (484 words) - 15:45, 25 February 2020
- <math>\frac{1}{t_{2}-t_{1}}\int_{t_{1}}^{t_{2}}g(t)e^{-2\pi ift}dt</math><br /><br /> <math>\int_{-\infty}^{\infty}g(t)e^{-2\pi ift}dt</math><br /><br />12 KB (2,051 words) - 14:20, 5 December 2020
- ...hen the Haar measure is given by <math>\mu (S)=\int _{S}{\frac {1}{|t|}}\,dt</math>730 B (122 words) - 01:04, 7 December 2020
