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- **[[Lecture1 ECE301Fall2008mboutin|Lecture 1]]: Intro; Example of DT signal (text) and system (enigma machine). **[[Lecture19 ECE301Fall2008mboutin|Lecture 19]]: TA Example Session w/ DT Fourier Transforms and inverses3 KB (328 words) - 17:57, 30 November 2018
- Compute the compute the z-transform (including the ROC) of the following DT signal:8 KB (1,313 words) - 15:19, 1 May 2016
- *[[CT_DT_Fourier_transform_ECE438F10|Summary of CT and DT Fourier transform]] ...udent_summary_CT_DT_Fourier_transform_ECE438F09| Student summary of CT and DT Fourier transform]]4 KB (471 words) - 19:34, 9 February 2015
- ...e able to calculate the Fourier series coefficients of a period CT signal (DT Fourier series will NOT be on the exam). (3.28a(subparts abc), 3.22, 3.31,6 KB (765 words) - 13:35, 4 August 2016
- \epsilon_0 = \int_{R_1} f(t|\omega_0)dt = \int_{z_c}^{\infty}\phi(z;0,1)dz \leq .05 \epsilon_0 = \int_{R_1} f(t|\omega_0)dt = \int_{z_c}^{\infty}\phi(z;0,1)dz = .0510 KB (793 words) - 10:46, 22 January 2015
- **[[Table DT Fourier Transforms|DTFT]] | Something related to CT or DT Fourier transform13 KB (1,944 words) - 16:51, 13 March 2015
- ...htarrow F_n = \frac{1}{T}\int\limits_{-T/2}^{T/2}P_T(t)e^{jn\cdot 2\pi t/T}dt</math>4 KB (610 words) - 18:55, 16 March 2015
- ...l{X}(\omega)=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i\omega t} dt</math> | <math>X(f)=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i2\pi ft} dt</math>4 KB (613 words) - 18:51, 16 March 2015
- ...\qquad \qquad \qquad X(f)=\int\limits_{-\infty}^{\infty}x(t)e^{-j2\pi ft} dt </math> <math>X(2\pi f)=\int\limits_{-\infty}^{\infty} x(t)e^{-j2\pi ft} dt </math>3 KB (512 words) - 09:50, 14 March 2015
- <math> {x}_{1}[n] </math> is a DT sampled signal of <math> {x}_{c}(t) </math> with sampling period <math> {T}3 KB (542 words) - 10:00, 14 March 2015
- <math> \frac{\lambda(x)}{\lambda(0)} = e^{-\int_0^x \mu(t)dt}</math> <br /> \int_0^x \mu(t)dt &= -ln(\frac{\lambda_x}{\lambda(0)})\\7 KB (1,072 words) - 19:25, 9 February 2015
- <math>f(t) = \frac{d\phi (t)}{dt}</math><br /> \frac{d\phi(t)}{dt} &= LM(x,y,t) \\14 KB (2,487 words) - 19:26, 9 February 2015
- *Week 1-2: CT and DT Fourier Transforms == Part 2 (week 9-14): DT Systems and Applications ==10 KB (1,356 words) - 13:19, 19 October 2015
- ...t e^{-i\omega t}dt=\alpha\int_{0}^{\infty}e^{-\left(\alpha+i\omega\right)t}dt=\alpha\frac{e^{-\left(\alpha+i\omega\right)t}}{-\left(\alpha+i\omega\right)6 KB (1,002 words) - 01:38, 10 March 2015
- ...ass="inline">isf_{\mathbf{T}_{k}}\left(t\right)=\frac{dF_{\mathbf{T}_{k}}}{dt}=-\sum_{j=0}^{k-1}\frac{\left(-\lambda\right)e^{-\lambda t}\cdot\left(\lamb4 KB (679 words) - 01:58, 10 March 2015
- ...{-\infty}^{\infty}\left(m_{\mathbf{X}}+m_{\mathbf{N}}\right)h\left(t\right)dt=\left(m_{\mathbf{X}}+m_{\mathbf{N}}\right)H\left(0\right)\Rightarrow m_{\ma5 KB (939 words) - 10:37, 10 March 2015
- |<math>F(s)=\int_{0}^\infty f(t) e^{-st}dt, \ s\in {\mathbb C} \ </math> | <math>u_n(t) = \frac{d^{n}\delta (t)}{dt^{n}}</math>29 KB (4,417 words) - 15:53, 12 March 2015
- ...^T | x(t) |^2 dt = \lim_{T\rightarrow \infty} {1 \over {2T}} \int_{-T}^T 4 dt = \lim_{T\rightarrow \infty} {1 \over {2T}} 4t \Big| ^T _{-T} = \lim_{T\rig ...|^2 dt = \lim_{T\rightarrow \infty} {1 \over {2T}} \int_{-\infty}^\infty 4 dt = \lim_{T\rightarrow \infty} {1 \over {2T}} \infty= \frac{\infty}{\infty}=12 KB (290 words) - 15:29, 21 April 2015
- **[[Table DT Fourier Transforms|DTFT]] | Something related to CT or DT Fourier transform6 KB (845 words) - 15:37, 4 November 2016
- It was observed that this sampling yields a DT signal that also sounds like a middle C. Perhaps the most confusing part of3 KB (487 words) - 11:09, 2 September 2015
- ...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
