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Monday October 18, 2010. | Monday October 18, 2010. | ||
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| − | Continuing our practice problems series | + | Continuing our practice problems series, here is [[Practice_Question_2_ECE439F10|a simple question on computing the z-transform]] of a signal |
and a slightly more complicated question on [[Practice_Question_3_ECE439F10|computing the inverse z-transform]]. | and a slightly more complicated question on [[Practice_Question_3_ECE439F10|computing the inverse z-transform]]. | ||
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| + | Today in the lecture, we continued our discussion of systems defined by difference equations with constant coefficients. We reemphasized the fact that boundary conditions need to be given for the system to be uniquely determine, and pointed out that such boundary conditions can either be given by fixing the value of the output y[n] at N different points, or by fixing the value of the unit impulse response h[n] at N different points. We then observed that assuming causality of the system would also uniquely determine the system, as causal systems always have h[n]=0 for n<0. We obtained a general expression for the transfer function of a system defined by a difference equation with constant coefficients, and observed that the ROC of the transfer function must be the outside of a circle if the system is causal. Thus if one is trying to define a causal system for which the frequency response is well defined, then the poles of the transfer function should all be inside the unit circle in the complex plane. | ||
Note: Your friend Clayton was asking in the [[Lecture22ECE438F10|previous lecture blog]] whether some of you want to meet with Prof. Mimi for lunch every week to go over problems. Don't forget [[Lecture22ECE438F10|to answer]]! | Note: Your friend Clayton was asking in the [[Lecture22ECE438F10|previous lecture blog]] whether some of you want to meet with Prof. Mimi for lunch every week to go over problems. Don't forget [[Lecture22ECE438F10|to answer]]! | ||
| + | ---- | ||
| + | Related Rhea pages | ||
| + | *[[ECE_301_Fall_2007_mboutin_Difference_Equation_in_Class_Example| A puzzling question about from a student]] | ||
| + | *[[Tyler_Houlihan_-_Difference_equations_-_a_few_examples_with_Partial_Fraction_Expansion_explanation_ECE301Fall2008mboutin|Related problems posed and solved by a student- ]] | ||
Previous: [[Lecture22ECE438F10|Lecture 22]]; Next: [[Lecture24ECE438F10|Lecture 24]] | Previous: [[Lecture22ECE438F10|Lecture 22]]; Next: [[Lecture24ECE438F10|Lecture 24]] | ||
Latest revision as of 12:04, 18 October 2010
Lecture 23 Blog, ECE438 Fall 2010, Prof. Boutin
Monday October 18, 2010.
Continuing our practice problems series, here is a simple question on computing the z-transform of a signal and a slightly more complicated question on computing the inverse z-transform.
Today in the lecture, we continued our discussion of systems defined by difference equations with constant coefficients. We reemphasized the fact that boundary conditions need to be given for the system to be uniquely determine, and pointed out that such boundary conditions can either be given by fixing the value of the output y[n] at N different points, or by fixing the value of the unit impulse response h[n] at N different points. We then observed that assuming causality of the system would also uniquely determine the system, as causal systems always have h[n]=0 for n<0. We obtained a general expression for the transfer function of a system defined by a difference equation with constant coefficients, and observed that the ROC of the transfer function must be the outside of a circle if the system is causal. Thus if one is trying to define a causal system for which the frequency response is well defined, then the poles of the transfer function should all be inside the unit circle in the complex plane.
Note: Your friend Clayton was asking in the previous lecture blog whether some of you want to meet with Prof. Mimi for lunch every week to go over problems. Don't forget to answer!
Related Rhea pages
Previous: Lecture 22; Next: Lecture 24
