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  • Mock up midterm exam with solution
    ...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
  • HW10ECE438F16
    ...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
  • HW10ECE438F16sln
    ...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
  • Lecture Schedule ECE438Spring17 Boutin
    *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
  • 2017 Fall ECE 438 Boutin
    **[[Table DT Fourier Transforms|DTFT]]
    3 KB (421 words) - 16:18, 10 December 2017
  • 2017 Spring ECE 438 Boutin
    **[[Table DT Fourier Transforms|DTFT]]
    3 KB (448 words) - 23:55, 23 April 2017
  • HW4ECE438S17
    :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
  • ECE-QE AC2-2015
    \end{bmatrix}dt}=e^{\begin{bmatrix}
    6 KB (742 words) - 07:16, 17 May 2017
  • CS5 2014 Aug prob1
    \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
  • ECE-QE AC2-2016
    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
  • ECE PhD QE FO2 2013 Problem3.1
    \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
  • ECE PhD QE FO2 2007
    \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
  • ECE PhD QE FO2 2011 Problem1.1
    \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\cdot10
    7 KB (1,072 words) - 16:11, 11 June 2017
  • ECE PhD QE FO2 2008 Problem1.1
    \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_0
    4 KB (752 words) - 17:19, 11 June 2017
  • ECE PhD QE FO2 2007 Problem1.1
    \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
  • ECE PhD QE FO3 2012 1 Problem1.1
    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
  • ECE PhD QE FO3 2011 Problem1.1
    <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
  • ECE PhD QE FO3 2010 Problem1.1
    ...\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
  • ECE PhD QE FO3 2009 Problem1.1
    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
  • ECE PhD QE FO3 2008 Problem1.1
    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
  • ECE PhD QE MN1 2007
    F&= \frac{d(\hslash k)}{dt}
    2 KB (263 words) - 11:02, 6 August 2017
  • ECE PhD QE MN1 2008
    V(t) = \int_0^t a dt =at=\frac{qE_xt}{m^*}
    3 KB (457 words) - 10:59, 6 August 2017
  • ECE PhD QE MN1 2009
    ...{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
  • ECE PhD QE MN2 2010
    I_{La}&=qA\int_0^{x_n}\frac{dn}{dt}\cdot dx\\ \frac{dn}{dt} = -R=G_L
    2 KB (375 words) - 22:19, 5 August 2017
  • Introduction to Differential Equations
    ...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
  • Basic Methods to Solve 1st-Order ODEs
    ''' <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 to
    10 KB (1,764 words) - 14:31, 17 November 2017
  • The Existence and Uniqueness Theorem for Solutions to ODEs
    '''&#183;''' 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)< '''&#183;''' <math>\frac{dy}{dt}=y^2</math>
    5 KB (852 words) - 22:39, 16 November 2017
  • Introduction to Higher-Order ODEs
    ...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
  • Introduction to ODEs in Higher Orders
    ...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
  • Linear Systems of ODEs
    <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
  • Non-Linear Systems of ODEs
    <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
  • Laplace Transforms
    ...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
  • Advanced Methods to Solve 2nd-Order ODEs
    ...'' 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
  • Systems of ODEs
    <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
  • 2018 Spring ECE 301 Boutin
    | Table of DT Fourier series properties with proofs (yes! I'm fearless ;D ) and list of c
    4 KB (618 words) - 12:12, 1 May 2018
  • ECE PhD QE ES 2007 Problem2
    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
  • ECE PhD QE ES1 2008 Problem2
    ...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}}{\le
    4 KB (701 words) - 18:58, 26 January 2018
  • ECE PhD QE ES1 2009 Problem2
    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
  • Signal power energy exercise CT ECE301S18 sin
    E_{\infty}&=\int_{-\infty}^\infty |\sin(2 \pi t)|^2 dt \\ &=\int_{-\infty}^\infty \sin^2(2 \pi t) dt
    2 KB (373 words) - 10:09, 22 January 2018
  • Signal power energy exercise CT ECE301S18 exponential
    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
  • ECE PhD QE PE1 2010 Problem2
    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
  • ECE PhD QE PE1 2011 Problem1
    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
  • ECE PhD QE PE1 2012 Problem1
    ...{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 \, dx
    7 KB (1,270 words) - 14:25, 12 February 2018
  • Discrete Time Fourior Transfrom Properties and Proofs
    | Duality || '''''NO DUALITY IN DT''''' || '''''NO DUALITY IN DT'''''<br />
    7 KB (1,166 words) - 13:20, 26 March 2018
  • Signals, Systems, and Biomedical Engineering
    ...) and often require conversion from continuous time (CT) to discrete time (DT) for analysis.
    12 KB (1,702 words) - 20:48, 9 April 2018
  • ECE301Spring18-DeterminingSignalPropertiesThroughFourierExam
    <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
  • CT Fourier Proofs Pranith Lomada Spring18 Boutin
    ...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
  • ECE301ConvolutionTutorial
    Enjoy this tutorial of DT and CT convolutions (with examples!!!)
    329 B (47 words) - 10:19, 26 April 2018
  • ECE PhD QE PE1 2014 Problem1a
    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
  • CTFT periodic signals ECE301F18
    ...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

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Ryne Rayburn