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- =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
- (3) The theorem is based on signal reconstruction utilizing a series of sinc functions each of which is infinite in time, which in reality must of course be trunc548 B (84 words) - 17:56, 10 November 2008
- A signal can be sampled using piecewise step functions; The sample is extended directly across until the new sample is reached. Th ...t)=x(nT)h_1(t-nT)</math> , which is our result, the shifted piecewise step functions.2 KB (411 words) - 17:16, 17 November 2008
- For functions x(t) and y(t) and constants a and b, <math>L(a*x(t) + b*y(t)) = a*L(x(t)) +542 B (108 words) - 19:40, 23 November 2008
- #The Unit Impulse and Unit Step Functions7 KB (1,017 words) - 10:05, 11 December 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 </2 KB (290 words) - 12:06, 12 December 2008
- ...be an interval containing the point ''a''. Let ''f'', ''g'', and ''h'' be functions defined on ''I'', except possibly at ''a'' itself. Suppose that for every '705 B (130 words) - 06:06, 31 August 2008
- ...,b]. Let F be an antiderivative of f, that is one of the indefinitely many functions such that, for all x in [a,b],317 B (66 words) - 11:22, 2 September 2008
- ...sorder but can someone give me a couple of examples with disjointed cyclic functions.434 B (74 words) - 18:25, 12 October 2008
- 130 is the number of functions from 6 unlabeled points to themselves. 166 is the number of monotone Boolean functions of 4 variables.13 KB (2,062 words) - 13:16, 29 November 2010
- ...)) and some number d (the lcm of the denominators of h(x)), to get two new functions which multiply to give f(x):1,019 B (215 words) - 17:49, 16 November 2008
- ...lanations of the mathematics behind probability, sequences, and generating functions. I really enjoy this book.877 B (141 words) - 07:55, 11 December 2008
- ...wk and feature vector x, which is in n-dimensional space, the discriminant functions g1(x), g2(x), .., gk(x) where g#(x) maps n-dimensional space to real number ...eric property of a class of functions is one that is true of most of those functions, as in the statements, " A generic polynomial does not have a root at zero,31 KB (4,832 words) - 18:13, 22 October 2010
- ...tics of clusters. For well-separated clusters, CIFs are similar to density functions. But, when8 KB (1,173 words) - 12:41, 26 April 2008
- is modeled as a composition of simple functions <math>f_i</math>'s647 B (106 words) - 11:08, 3 April 2008
- '''Useful Matlab Functions''' --stephen.r.rudolph.1, Sun, 10 Feb 2008 21:38:45 -0500 ...ine to sample points from a multivariate normal density, this library of C functions may come in handy ..10 KB (1,594 words) - 11:41, 24 March 2008
- ...e [[Combining Hypersurfaces _Old Kiwi| combined]] by multiplication of the functions which define them, not by intersection.5 KB (737 words) - 08:45, 17 January 2013
- - ''Discriminant Functions'' '''Discriminant Functions''': one way of representing classifiers6 KB (916 words) - 08:47, 17 January 2013
- =Lecture 6- Discriminant Functions= - Discriminant Functions9 KB (1,586 words) - 08:47, 17 January 2013
- * Linear Discriminant Functions == Linear Discriminant Functions ==5 KB (792 words) - 08:48, 17 January 2013
- ...use it to find corresponding kernel. Another method is to construct kernel functions directly by making sure that the function is a valid kernel which means it ..., summing two kernel functions, inserting kernel functions into some other functions and so on.8 KB (1,235 words) - 08:49, 17 January 2013
- [[Kernel Functions_Old Kiwi|Why kernel functions?]] == Kernel Functions ==8 KB (1,354 words) - 08:51, 17 January 2013
- ...ath> is [Dirac delta Function]. We do not want to average over dirac delta functions. Our objective is that <math>p_i(\vec{x_0})</math> should converge to true7 KB (1,212 words) - 08:38, 17 January 2013
- If we denote L as the class of likelihood functions p(x|y), a class P of priors distributions p(y) is a conjugate931 B (161 words) - 08:46, 10 April 2008
- *defining c linear discriminant functions == More on Linear Discriminant Functions ==2 KB (433 words) - 23:11, 10 March 2008
- ...on in the Bayesian estimation yields different estimates. Two popular cost functions are considered below:6 KB (995 words) - 10:39, 20 May 2013
- ...h> and feature vector x, which is in n-dimensional space, the discriminant functions <math>g_1(x), g_2(x), \ldots, g_k(x)</math> where <math>g_\#(x)</math> maps Discriminant functions are used to define [[Decision Surfaces_Old Kiwi]].548 B (89 words) - 09:53, 10 April 2008
- There are several '''tool boxes''' of functions written by people all over the world adding extra functionality to Scilab.3 KB (376 words) - 20:45, 26 March 2008
- ...al of Multivariate Analysis on Bayesian Estimators for Normal Discriminant Functions=== ...PRQ) classifier, in which the nonlinearity is achieved by employing kernel functions. The PRQ classifier generates a Rayleigh quotient based on a set of pairwis39 KB (5,715 words) - 10:52, 25 April 2008
- ==Basics: Systems as "functions that operate on functions"== ...on functions" way of thinking can be extended even further to the "system" functions (such as ``timeshift`` above) to prove things about systems.3 KB (495 words) - 18:39, 16 March 2008
- The Bayes rules to minimize the expected loss([Loss Functions]) or "Risk":8 KB (1,360 words) - 08:46, 17 January 2013
- -defining c linear discriminant functions2 KB (428 words) - 09:12, 7 April 2008
- ...s like me, there is GSL (GNU Scientific Library) available that contains c functions for a variety of scientific computational tasks. The URL is http://www.gnu. Subject: How to call matlab functions from C782 B (110 words) - 17:39, 19 March 2008
- There are several ''tool boxes'' of functions written by people all over the world adding extra functionality to Scilab.3 KB (379 words) - 10:20, 20 March 2008
- convolution is a mathematical operator which takes two functions f and g and produces a third function that, in a sense, represents the amou ...ions results in a new function that is a product of the overlap of the two functions when one is flipped across the x-axis and then shifted from <math>{-\infty}821 B (137 words) - 16:22, 20 March 2008
- I haven't used any additional functions for stacking purposes. I kept track of the stack pointer at an integer "i",3 KB (445 words) - 00:52, 22 March 2008
- where {<math>fj's</math>} are pre-determined class of functions6 KB (1,047 words) - 08:42, 17 January 2013
- And since x(t) can be written as the sum of these sine functions, x(t) can be written in the form x(t) = a(t) + jb(t) Where a(t) is going to2 KB (363 words) - 23:23, 15 April 2008
- The following figure shows above-mentioned impurity functions for a two-category case, as a function of the probability of one of the cat6 KB (1,012 words) - 08:42, 17 January 2013
- ...gorithm is also known as agglomerative methods, which proceed by series of functions of the n objects into groups.987 B (148 words) - 16:01, 6 April 2008
- ...eric property of a class of functions is one that is true of most of those functions, as in the statements, " A generic polynomial does not have a root at zero,576 B (105 words) - 10:15, 7 April 2008
- ...ationally cheaper than the explicit computation of the coordinates. Kernel functions have been introduced for sequence data, text, images, as well as vectors.413 B (65 words) - 10:18, 7 April 2008
- Functions that are linear combinations of x.340 B (63 words) - 01:40, 17 April 2008
- The estimate <math>p_n(x)</math> is an average of (window) functions. Usually the window function has its maximum at the origin and its values b1 KB (194 words) - 01:44, 17 April 2008
- The estimate <math>p_n(x)</math> is an average of (window) functions. Usually the window function has its maximum at the origin and its values b1 KB (194 words) - 01:54, 17 April 2008
- ...particular value of O is, if we know that X has a value x. Two likelihood functions are equivalent if one is a scalar multiple of the other.708 B (126 words) - 01:55, 17 April 2008
- The goal is to find y_i's such that a cost functions is minimized such as the cost function below: Other alternatives of cost functions for the MDS can be found in the DHS book 2nd Ed, page 573. Since the gradie3 KB (582 words) - 12:55, 21 April 2008
- Partial fraction expansion allows us to fit functions to the known ones given by the known Fourier Transform pairs table.4 KB (606 words) - 22:25, 1 May 2008
- ...nded then the output y(t) is also bound because it is the sum of two bound functions. ...und, the function y(t) is also bound since it is the multiple of two bound functions.3 KB (499 words) - 17:51, 16 June 2008
- ...tau-5)} + e^{-3(\tau-3)}</math>. I think you then may need to add the step functions to the answer so that it is general for all cases: <math>y(\tau) = e^{-3(\t1 KB (286 words) - 23:53, 17 June 2008
- NO: The inverse transform of this signal is a set of delta functions that are not periodic. YES: Taking the FT of c(t) we get delta functions at <math>\omega_c</math> and <math>-\omega_c</math>.4 KB (739 words) - 20:48, 30 July 2008
