Create the page "DT" on this wiki! See also the search results found.
- ...f the signal. We then began the second topic: "Spectral representation of DT signals". After giving the formulas for the DTFT and the inverse DTFT, we o *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]3 KB (382 words) - 16:41, 31 August 2015
- '''2)''' Write MATLAB code to play the two DT signals from part a) for 2 seconds. Briefly comment on how each signal "sou2 KB (395 words) - 12:13, 7 September 2015
- a_k=\frac{1}{T_0}\int_{\tau}^{\tau+T_0} x(t)e^{-j\omega_0 kt}dt a_k&=\frac{1}{T_0}\int_{\tau}^{\tau+T_0} x(t)e^{-j\omega_0 kt}dt \\5 KB (812 words) - 13:08, 19 October 2015
- ...in such a way that a band-limited interpolation of the processed (output) DT signal would be the same as y(t)? Answer yes/no. If you answered yes, expla ...ignal in such a way a band-limited interpolation of the processed (output) DT signal would be the same as y(t)? Answer yes/no. If you answered yes, expla3 KB (499 words) - 16:04, 22 September 2015
- 2) Write MATLAB code to play the two DT signals from part a) for 2 seconds. Briefly comment on how each signal "sou4 KB (536 words) - 15:54, 25 September 2015
- The goal of this homework is to get an intuitive understanding on how to DT signals with different sampling frequencies in an equivalent fashion. a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[4n]? (Give the mathematical re5 KB (779 words) - 18:19, 25 September 2015
- INSTRUCTOR'S NOTE: THERE IS A MISTAKE BELOW. THE AMPLITUDE OF THE DT FILTER SHOULD NOT BE MULTIPLIED BY 1/TS. -> Corrected! ...in such a way that a band-limited interpolation of the processed (output) DT signal would be the same as y(t)? Answer yes/no. If you answered yes, expla3 KB (475 words) - 15:23, 20 October 2015
- a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[4n]? (Give the mathematical re b) What is the relationship between the DT Fourier transform of x[n] and that of6 KB (945 words) - 11:40, 19 October 2015
- Consider a DT LTI system described by the following equation Consider a DT LTI system described by the following non-recursive difference4 KB (625 words) - 13:17, 16 November 2015
- ...for |f|>2.5KHz.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?3 KB (449 words) - 11:39, 20 November 2015
- DT – Distance Table,<br /> Initialize DT(s,0) = 0, DT(s,1) = 0, all remaining DT(j,k) = -1<br />14 KB (2,351 words) - 23:21, 24 April 2016
- *DT convolution: 2.3 *DT system stability and causality: 2.28acef526 B (73 words) - 21:35, 20 June 2016
- *DT convolution: 2.21abcd *DT impulse response and convolution: 2.24ab707 B (103 words) - 14:02, 24 June 2016
- * DT signals: 3.28a (subparts a and c), c * DT signals: 3.31abc607 B (86 words) - 00:27, 6 July 2016
- **[[Table DT Fourier Transforms|DTFT]] | Something related to CT or DT Fourier transform4 KB (622 words) - 09:42, 8 January 2017
- *Week 1-2: CT and DT Fourier Transforms == Part 2 (week 9-14): DT Systems and Applications ==10 KB (1,357 words) - 17:02, 14 September 2016
- '''2)''' Write MATLAB code to play the two DT signals from part a) for 3 seconds.2 KB (398 words) - 11:41, 2 September 2016
- *go over the relationship between DT signal processing and CT signal processing (for a simple filter) once more, Let x[n] be a DT signal. Let z[n]=x[2n] be a downsampling of x[n]. Let y[n] be an upsampling4 KB (636 words) - 08:16, 21 September 2016
- Let x[n] be a DT signal of finite duration N and let <math>{\mathcal X}(\omega)</math> be it3 KB (485 words) - 17:11, 27 September 2016
- Consider a DT LTI system described by the following equation Consider a DT LTI system described by the following non-recursive difference3 KB (503 words) - 15:44, 8 November 2016
- ...m of the phoneme. How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?8 KB (1,336 words) - 15:40, 27 November 2016
- ...for |f|>2.5KHz.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?3 KB (460 words) - 13:20, 18 November 2016
- ...of the spectrum.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?7 KB (1,236 words) - 17:19, 29 November 2016
- *Week 1-2: CT and DT Fourier Transforms == Part 2 (week 9-14): DT Systems and Applications ==10 KB (1,357 words) - 09:45, 8 January 2017
- **[[Table DT Fourier Transforms|DTFT]]3 KB (421 words) - 16:18, 10 December 2017
- **[[Table DT Fourier Transforms|DTFT]]3 KB (448 words) - 23:55, 23 April 2017
- :a) understand how to implement a CT system as a DT system through sampling and reconstruction.4 KB (658 words) - 14:50, 1 February 2017
- \end{bmatrix}dt}=e^{\begin{bmatrix}6 KB (742 words) - 07:16, 17 May 2017
- \lambda_x = \lambda_0e^{-\int^x_0\mu(t)dt} <math>\lambda_x = \lambda_0e^{-\int^x_0\mu(t)dt}</math>3 KB (529 words) - 16:42, 18 May 2017
- The linear dynamics around <math>x_e</math> is <math>\frac{d}{dt}f(x)=\begin{bmatrix}7 KB (1,126 words) - 05:45, 22 May 2017
- \nabla^2\bar{E} - \mu\epsilon\big(\frac{d^2E}{dt^2}\big)\\ \cancelto{0}{\nabla^2(E_o\sin(\omega t)\hat{z})} - \mu\epsilon\frac{d^2}{dt^2}[E_o\sin(\omega t)] = 0\\2 KB (352 words) - 21:21, 3 June 2017
- \frac{dz}{dt} = \frac{\triangle \omega}{\triangle \beta}= \bigg(\frac{\partial\beta}{\pa \omega - \beta \frac{dz}{dt} = 0\\5 KB (874 words) - 19:16, 18 June 2017
- \big(\frac{2\pi}{\lambda}\big)\big(\frac{dx}{dt}\big)(-\sin\theta_2-\sin\theta_2) + \triangle \omega &= 0, \beta =\frac{2\p \frac{dx}{dt} = v_p = \frac{\triangle\omega}{2\beta\sin\theta_2} \cong \frac{2\pi\cdot107 KB (1,072 words) - 16:11, 11 June 2017
- \nabla\times\bar{E} = -\frac{d\bar{B}}{dt} = \begin{vmatrix}\hat{x} & \hat{y} & \hat{z}\\\frac{\partial}{\partial y}& -\mu_0\frac{d\bar{H}}{dt} = (-\hat{x})[\beta E_0\sin(10\pi x)\sin(\omega t-\beta z)] + (\hat{z})[E_04 KB (752 words) - 17:19, 11 June 2017
- \frac{dz}{dt} = \frac{\triangle \omega}{\triangle \beta}= \bigg(\frac{\partial\beta}{\pa \omega - \beta \frac{dz}{dt} = 0\\5 KB (795 words) - 17:35, 11 June 2017
- 2)<math>\oint\bar{H}\cdot dl = \int_S(J+\frac{d}{dt}\bar{D})ds\hspace{2cm}\text{ only have } H_z</math>4 KB (642 words) - 10:44, 18 June 2017
- <math>\int_0^{2\pi} \int_0^a D_z rdrd\phi = Q = \int I_0 \cos(\omega t) dt</math>5 KB (834 words) - 11:35, 18 June 2017
- ...\bar{r}\times\bar{F}= RF\sin\theta=RB_0\lambda(\pi a^2)\delta(t)=\frac{dL}{dt}</math> <math>\varepsilon_0(t)= L\frac{di(t)}{dt}+Ri(t)=\varepsilon_0\mu(t)</math>3 KB (476 words) - 11:00, 18 June 2017
- 2) <math>\nabla\times\bar{E} = -\frac{d}{dt}B</math> <math>\oint\bar{E}\cdot dl = - \frac{d}{dt}\int_S\bar{B}\cdot ds = V_{EMF}</math>3 KB (591 words) - 11:21, 18 June 2017
- 2) <math>\nabla\times\bar{E} = -\frac{d}{dt}B</math> <math>\oint\bar{E}\cdot dl = - \frac{d}{dt}\int_S\bar{B}\cdot ds = V_{EMF}</math>3 KB (591 words) - 11:24, 18 June 2017
- F&= \frac{d(\hslash k)}{dt}2 KB (263 words) - 11:02, 6 August 2017
- V(t) = \int_0^t a dt =at=\frac{qE_xt}{m^*}3 KB (457 words) - 10:59, 6 August 2017
- ...{E_F/kT}}{2\pi\alpha}kT\int_0^\infty e^{-t}\cdot (tkT)^{\frac{2}{\alpha}-1}dt\\ ...ot(kt)^{\frac{2}{\alpha}-1}\int_0^\infty e^{-t}\cdot t^{\frac{2}{\alpha}-1}dt\\4 KB (644 words) - 19:34, 30 July 2017
- I_{La}&=qA\int_0^{x_n}\frac{dn}{dt}\cdot dx\\ \frac{dn}{dt} = -R=G_L2 KB (375 words) - 22:19, 5 August 2017
- ...rac{dy}{dx}=y^2+y</math>, <math>k</math> is a parametre || <math>\frac{dh}{dt}=k\frac{d^2h}{dx^2}</math>, <math>k</math> is a parametre | Examples .....|| <math>ü=\frac{d^2u}{dt^2}</math>|| <math>y'=\frac{dy}{dx}</math>6 KB (1,070 words) - 23:06, 21 November 2017
- ''' <big><big><big> 3.1 Separable Equation for <math>\frac{dy}{dt}=f(y)g(t)</math> </big></big></big> ''' ...d form of differential equation to use this method is like <math>\frac{dy}{dt}=f(y)g(t)</math>, where <math>f(y)</math> and <math>g(t)</math> are easy to10 KB (1,764 words) - 14:31, 17 November 2017
- '''·''' Find an explicit solution for <math>\frac{dy}{dt}=f(t)</math>. This is the same thing as finding the integral of <math>f(t)< '''·''' <math>\frac{dy}{dt}=y^2</math>5 KB (852 words) - 22:39, 16 November 2017
- ...n(t)\frac{d^ny}{dt^n}+f_{n-1}\frac{d^{n-1}y}{dt^{n-1}}+...+f_1(t)\frac{dy}{dt}+f_0(t)y=g(t)</math>, where <math>n</math> is the order.2 KB (283 words) - 02:01, 17 November 2017
- ...n(t)\frac{d^ny}{dt^n}+f_{n-1}\frac{d^{n-1}y}{dt^{n-1}}+...+f_1(t)\frac{dy}{dt}+f_0(t)y=g(t)</math>, where <math>n</math> is the order. ...ion look more like a system, we rename <math>y=x_1</math>, <math>\frac{dy}{dt}=x=x_2</math>.4 KB (712 words) - 23:15, 21 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>9 KB (1,504 words) - 23:12, 21 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>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
