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- = Limits of Functions = ..., we first consider continuity at a point. Unless otherwise mentioned, all functions here will have domain and range <math>\mathbb{R}</math>, the real numbers.20 KB (3,513 words) - 14:55, 13 May 2014
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- ===Basic Functions===3 KB (436 words) - 12:44, 3 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=574 B (85 words) - 07:19, 14 April 2010
- ...ows the relationship between the complex exponential and the trigonometric functions sine and cosine. The functions ''e''<sup>''x''</sup>, cos ''x'' and sin ''x'' of the (real) vari2 KB (362 words) - 07:05, 11 July 2012
- ==Periodic Functions==1 KB (265 words) - 06:12, 2 February 2011
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= == Periodic Functions in Continuous Time ==1 KB (163 words) - 07:19, 14 April 2010
- Define functions x, y, and z as follows: Define functions x, y, and z as follows:1 KB (226 words) - 06:23, 4 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= == Periodic Functions in CT - The Tangent Function ==1,003 B (148 words) - 07:21, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=1 KB (205 words) - 07:20, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= === Periodic Functions ===1 KB (169 words) - 07:22, 14 April 2010
- ...These values come in very handy when they are shown through sine or cosine functions as imaginary numbers compared to their real counterparts that exist on the524 B (95 words) - 10:50, 4 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=994 B (164 words) - 07:20, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=791 B (117 words) - 07:17, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=742 B (104 words) - 07:23, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=2 KB (279 words) - 07:18, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=491 B (64 words) - 07:24, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=732 B (100 words) - 07:24, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=640 B (106 words) - 07:25, 14 April 2010
- %Transform by x(2t). Replace t in all functions with 2*t4 KB (759 words) - 13:38, 4 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= == Examples of periodic and non-periodic functions ==1 KB (210 words) - 07:25, 14 April 2010
- ==Period Functions==20 B (2 words) - 13:51, 4 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=879 B (140 words) - 07:25, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=883 B (143 words) - 07:24, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=856 B (140 words) - 07:26, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= == Non-Periodic Functions ==779 B (124 words) - 07:27, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= '''Periodic functions'''2 KB (274 words) - 07:27, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=634 B (89 words) - 07:28, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=1 KB (192 words) - 07:28, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= == Periodic Functions ==796 B (137 words) - 07:18, 14 April 2010
- ==Periodic Functions== Periodic functions are functions that repeat over and over for a specific period. More specifically, a func648 B (117 words) - 20:01, 4 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= ==Non Periodic Functions==835 B (141 words) - 07:26, 14 April 2010
- ==Periodic Functions== A great example for demonstrating periodic and non-periodic functions as well as differences between Discrete and Continuous Time is the sine fun873 B (149 words) - 17:24, 4 September 2008
- == Periodic Functions == == Non-periodic Functions ==1 KB (221 words) - 12:21, 5 September 2008
- == Periodic / Non-Periodic Functions ==897 B (156 words) - 05:16, 5 September 2008
- ...a complex number into its real and imaginary parts using the real and imag functions: zr = real(z)1 KB (176 words) - 20:22, 4 September 2008
- ...a complex number into its real and imaginary parts using the real and imag functions: zr = real(z)1 KB (181 words) - 20:27, 4 September 2008
- == Periodic Functions == ==Non-Periodic Functions ==438 B (72 words) - 21:53, 4 September 2008
- Remember that constant functions like Y=2 and the like are periodic for CT and DT.175 B (35 words) - 03:36, 5 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= Remember that constant functions like Y=2 and the like are periodic for CT and DT.685 B (102 words) - 07:16, 14 April 2010
- Signal Energy expended from <math>t_1\!</math> to <math>t_2\!</math> for CT functions is given by the formula <math>E = \int_{t_1}^{t_2} \! |x(t)|^2\ dt</math> For CT functions, the power of a signal from <math>t_1\!</math> to <math>t_2\!</math> is giv2 KB (295 words) - 06:34, 5 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=1 KB (195 words) - 07:20, 14 April 2010
- == Periodic Functions ==831 B (141 words) - 08:17, 5 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=960 B (171 words) - 07:13, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=688 B (106 words) - 07:08, 14 April 2010
- ==Periodic functions== ==Non-Periodic functions==566 B (79 words) - 09:16, 5 September 2008
- == Periodic and Non-Periodic Functions ==563 B (104 words) - 09:23, 5 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=838 B (138 words) - 07:22, 14 April 2010
- *This formula links together the exponential function and the trigonometric functions. ...present cos and sin in terms of e in a way very similar to hyperbolic trig functions, which is why they hyperbolics are named sinh and cosh.2 KB (242 words) - 10:27, 5 September 2008
- Periodic functions are functions that return the same to the same <math>y</math> value after a given interva Non-periodic functions are functions that do not return to the same value after a given interval. An example for597 B (102 words) - 10:11, 5 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=700 B (115 words) - 07:11, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= periodic functions, all with the same period.1 KB (253 words) - 07:04, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=801 B (121 words) - 07:28, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= A plot of f(x) = sin(x) and g(x) = cos(x); both functions are periodic with period 2π.A simple example of a periodic function is the2 KB (291 words) - 07:03, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= ...umbers , so there is no concept analogous to the least period for constant functions.813 B (113 words) - 07:03, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=306 B (40 words) - 07:21, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= == Periodic Functions ==688 B (113 words) - 07:12, 14 April 2010
- =Periodic Functions= ==Functions==942 B (142 words) - 18:30, 5 September 2008
- ...ity to +infinity. Similar to these functions are the inverse trigonometric functions (i.e. cosecant, secant, cotangent) that have different ranges and yet still940 B (153 words) - 18:27, 5 September 2008
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=567 B (81 words) - 07:12, 14 April 2010
- =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=446 B (74 words) - 07:22, 14 April 2010
- ...u[n] would yield Y[n]=u[n-1] since u[n] is simply the sum of shifted delta functions, and linearity dictates that they could be sent through the system (produci2 KB (341 words) - 14:22, 11 September 2008
- [[Image:Periodicshifted_ECE301Fall2008mboutin.jpg|300x300px|multiple functions y = x being put together]]1,021 B (167 words) - 08:08, 10 September 2008
- In layman's terms, that means that a system (call it f) is linear if functions (call them x and y) can be sent through the system in either one of these t Say we take any two functions <math>x_1(t), x_2(t)</math> and any two variables <math>a,b \in \mathbb{C}<3 KB (544 words) - 19:05, 10 September 2008
- Since, in this case, the definition is not true for ''all'' functions and constants (The one above didn't work, for instance.), I can conclude th3 KB (581 words) - 20:22, 10 September 2008
- ...e output. Adding any number of linear combinations of complex numbers and functions of time together does not affect the linearity of the system. ...B*y2(t) .... extendable for any amount of complex numbers (A, B, C...) and functions (x1, x2, x3...)1 KB (232 words) - 09:10, 11 September 2008
- ...sum of shifted delta functions as input will yield a sum of shifted delta functions as output. In this system the fact that the desired step function output be1 KB (219 words) - 09:25, 11 September 2008
- The system seems to work specifically on delta functions, so I take the approach of describing u[n] as an infinite sum of shifted de1 KB (245 words) - 15:10, 12 September 2008
- since u[n] is simply the summation of shifted delta functions we can say that1 KB (230 words) - 15:34, 12 September 2008
- A linear system is a system for which if you can add two functions and multiply them by scalars then pass them through the system, it is equiv2 KB (245 words) - 13:50, 11 September 2008
- ...r this part can be found [[HW1.4 Wei Jian Chan - Periodic and Non periodic Functions _ECE301Fall2008mboutin| here]].1 KB (186 words) - 16:07, 11 September 2008
- ...this means that if the <math>X[n]</math> inputs were changed to unit step functions <math>u[n]</math> , then the output will be a time shifted step function. F753 B (131 words) - 16:23, 11 September 2008
- We have two functions: <math>\,x_1(t), x_2(t)\,</math>. After applying the functions to the system <math>\,s(t)\,</math>, we get:2 KB (302 words) - 19:06, 11 September 2008
- ...definition of <math>u[n]</math>, which is just a sum of many shifted delta functions.869 B (161 words) - 07:37, 12 September 2008
- DT function that was made by repeating nonperiodic CT functions1 KB (183 words) - 09:21, 12 September 2008
- ...d that the unit step function can be shown by a summation of shifted delta functions over a series of - <math>\infty </math> to +<math>\infty</math>.796 B (155 words) - 13:37, 12 September 2008
- a functions output can be shown by a squaring of the x(t) portion of the function, as w893 B (166 words) - 15:53, 14 September 2008
- ...function must not have any memory or foresight. Examples of these types of functions are: ...ends on <math>x(t)\!</math> reaction to a past or future time. Thus, these functions are systems with memory.1 KB (202 words) - 15:42, 19 September 2008
- Given 2 functions x1 and x2, constants a and b, outputs y1 and y2, and system s408 B (87 words) - 07:27, 18 September 2008
- ...se the proprties of linearity - namely, that for constants a and b and for functions x and y, <math>f(ax+by) = af(x)+bf(y)</math> - to find an output given an i5 KB (729 words) - 13:12, 18 September 2008
- The functions z(t) are equal, so the system is time invariant.1 KB (244 words) - 14:40, 18 September 2008
- The functions z(t) are equal, so the system is time invariant.1 KB (244 words) - 14:42, 18 September 2008
- The two functions given to us happen to be part of the breakdown of cos(2t).349 B (68 words) - 06:58, 19 September 2008
- A system is stable if for all bounded input functions x(t)(system approaches +/- infinity) there exists an output y(t) where y(t)481 B (86 words) - 13:51, 19 September 2008
- I take <math>\omega_o \,</math> as <math>\pi \,</math> since both functions have a period based on it.784 B (140 words) - 10:34, 20 September 2008
- I take <math>\omega_o \,</math> as <math>\pi \,</math> since both functions have a period based on it.1 KB (197 words) - 10:59, 16 September 2013
- ===Periodic versus non-periodic functions===2 KB (243 words) - 08:04, 21 November 2008
- x(t) is written as a sum of exponential functions, so take the coefficients of those.2 KB (363 words) - 10:56, 16 September 2013
- ...sure that <math>\,\frac{2\pi }{\omega_0}</math> is a whole number for both functions, so multiply it in this fashion:2 KB (374 words) - 14:27, 25 September 2008
- I contend that the <math>\omega_0=2</math> since both functions are periodic based on it.1 KB (205 words) - 10:56, 16 September 2013
- The following functions can be used to find the system function:842 B (168 words) - 14:55, 26 September 2008
- ...or not a signal is periodic if the signal is written as the sum of shifted functions. A good example of this type of problem would be problem number 1 from the343 B (61 words) - 14:22, 6 October 2008
- The final '''final''' answer comes when we realize the the delta functions multiplied by each of the exponentials are only valid when <math> \omega </8 KB (1,324 words) - 18:59, 8 October 2008
- Since integrating dirac functions is extremely easy one can easily simplify to the following1 KB (184 words) - 12:47, 16 September 2013
- <math>H(z)=1+\frac{1}{z}</math> due to the two step functions.680 B (127 words) - 03:59, 15 October 2008
- ...of partial fraction expansion. Partial fraction expansion allows us to fit functions to the known ones given by the known Fourier Transform pairs table.2 KB (284 words) - 10:14, 24 October 2008
- Since there a u[n] functions in this method, it might be a little easier to set the bounds of the summat1 KB (242 words) - 14:45, 24 October 2008
- Fourier Transform of delta functions860 B (156 words) - 18:26, 24 October 2008
- In other words, the samples are represented by unit-step functions.453 B (65 words) - 13:36, 9 November 2008
- == Interpolation using step functions ==409 B (76 words) - 13:12, 10 November 2008
- ...reconstruct" a signal is by zero-order interpolation which looks like step functions. ...d they asked him if he has ever heard of splines and peace-wise polynomial functions and that is what this is.808 B (160 words) - 16:15, 10 November 2008
- ...until the next sample is taken. A good example of this is a series of step functions. ...s are connected by a straight line. An example of this is a series of ramp functions.951 B (153 words) - 17:14, 10 November 2008
