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Jump to [[Lecture1ECE438F13|Lecture 1]], [[Lecture2ECE438F13|2]], [[Lecture3ECE438F13|3]] ,[[Lecture4ECE438F13|4]] ,[[Lecture5ECE438F13|5]] ,[[Lecture6ECE438F13|6]] ,[[Lecture7ECE438F13|7]] ,[[Lecture8ECE438F13|8]] ,[[Lecture9ECE438F13|9]] ,[[Lecture10ECE438F13|10]] ,[[Lecture11ECE438F13|11]] ,[[Lecture12ECE438F13|12]] ,[[Lecture13ECE438F13|13]] ,[[Lecture14ECE438F13|14]] ,[[Lecture15ECE438F13|15]] ,[[Lecture16ECE438F13|16]] ,[[Lecture17ECE438F13|17]] ,[[Lecture18ECE438F13|18]] ,[[Lecture19ECE438F13|19]] ,[[Lecture20ECE438F13|20]] ,[[Lecture21ECE438F13|21]] ,[[Lecture22ECE438F13|22]] ,[[Lecture23ECE438F13|23]] ,[[Lecture24ECE438F13|24]] ,[[Lecture25ECE438F13|25]] ,[[Lecture26ECE438F13|26]] ,[[Lecture27ECE438F13|27]] ,[[Lecture28ECE438F13|28]] ,[[Lecture29ECE438F13|29]] ,[[Lecture30ECE438F13|30]] ,[[Lecture31ECE438F13|31]] ,[[Lecture32ECE438F13|32]] ,[[Lecture33ECE438F13|33]] ,[[Lecture34ECE438F13|34]] ,[[Lecture35ECE438F13|35]] ,[[Lecture36ECE438F13|36]] ,[[Lecture37ECE438F13|37]] ,[[Lecture38ECE438F13|38]] ,[[Lecture39ECE438F13|39]] ,[[Lecture40ECE438F13|40]] ,[[Lecture41ECE438F13|41]] ,[[Lecture42ECE438F13|42]] ,[[Lecture43ECE438F13|43]] ,[[Lecture44ECE438F13|44]] | Jump to [[Lecture1ECE438F13|Lecture 1]], [[Lecture2ECE438F13|2]], [[Lecture3ECE438F13|3]] ,[[Lecture4ECE438F13|4]] ,[[Lecture5ECE438F13|5]] ,[[Lecture6ECE438F13|6]] ,[[Lecture7ECE438F13|7]] ,[[Lecture8ECE438F13|8]] ,[[Lecture9ECE438F13|9]] ,[[Lecture10ECE438F13|10]] ,[[Lecture11ECE438F13|11]] ,[[Lecture12ECE438F13|12]] ,[[Lecture13ECE438F13|13]] ,[[Lecture14ECE438F13|14]] ,[[Lecture15ECE438F13|15]] ,[[Lecture16ECE438F13|16]] ,[[Lecture17ECE438F13|17]] ,[[Lecture18ECE438F13|18]] ,[[Lecture19ECE438F13|19]] ,[[Lecture20ECE438F13|20]] ,[[Lecture21ECE438F13|21]] ,[[Lecture22ECE438F13|22]] ,[[Lecture23ECE438F13|23]] ,[[Lecture24ECE438F13|24]] ,[[Lecture25ECE438F13|25]] ,[[Lecture26ECE438F13|26]] ,[[Lecture27ECE438F13|27]] ,[[Lecture28ECE438F13|28]] ,[[Lecture29ECE438F13|29]] ,[[Lecture30ECE438F13|30]] ,[[Lecture31ECE438F13|31]] ,[[Lecture32ECE438F13|32]] ,[[Lecture33ECE438F13|33]] ,[[Lecture34ECE438F13|34]] ,[[Lecture35ECE438F13|35]] ,[[Lecture36ECE438F13|36]] ,[[Lecture37ECE438F13|37]] ,[[Lecture38ECE438F13|38]] ,[[Lecture39ECE438F13|39]] ,[[Lecture40ECE438F13|40]] ,[[Lecture41ECE438F13|41]] ,[[Lecture42ECE438F13|42]] ,[[Lecture43ECE438F13|43]] ,[[Lecture44ECE438F13|44]] | ||
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| − | Today we | + | Today we introduced the z-transform formula and observed its similarity to the DTFT formula. More precisely, we noticed that the DTFT is a restriction of the z-transform to the unit circle. We then computed a couple of z-transforms as examples. It was observed that there may be values of z for which the z-transform does not exist. Even though we did not see the formula for the inverse z-transform, we were able to invert a z-transform simply by comparing the expression for the given z-transform to the formula for the z-transform. As we will see later, this trick will be very handy for inverting z-transforms in general. |
| + | ==Relevant Rhea links== | ||
| + | *[[Z_Transform_table|Table of z-transform pairs and properties]] | ||
| + | *[[Geometric_Series_Explanation|Tutorial on the geometric series]], by [[user:amcgail | Alec McGail]], member of [[Math_squad | Rhea's Math Squad]]. | ||
==Action Items== | ==Action Items== | ||
Revision as of 06:03, 4 September 2013
Lecture 7 Blog, ECE438 Fall 2013, Prof. Boutin
Wednesday September 4, 2013 (Week 3) - See Course Outline.
Jump to Lecture 1, 2, 3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12 ,13 ,14 ,15 ,16 ,17 ,18 ,19 ,20 ,21 ,22 ,23 ,24 ,25 ,26 ,27 ,28 ,29 ,30 ,31 ,32 ,33 ,34 ,35 ,36 ,37 ,38 ,39 ,40 ,41 ,42 ,43 ,44
Today we introduced the z-transform formula and observed its similarity to the DTFT formula. More precisely, we noticed that the DTFT is a restriction of the z-transform to the unit circle. We then computed a couple of z-transforms as examples. It was observed that there may be values of z for which the z-transform does not exist. Even though we did not see the formula for the inverse z-transform, we were able to invert a z-transform simply by comparing the expression for the given z-transform to the formula for the z-transform. As we will see later, this trick will be very handy for inverting z-transforms in general.
Relevant Rhea links
- Table of z-transform pairs and properties
- Tutorial on the geometric series, by Alec McGail, member of Rhea's Math Squad.
Action Items
- Solve the following practice problems and share your answer to get feedback. It will help you get full credit on the second homework and on the test.
Previous: Lecture 6 Next: Lecture 8
