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Friday October 22, 2010.  
 
Friday October 22, 2010.  
 
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We presented a simple method to obtain a causal FIR filter from an ideal filter using time shifting and windowing in the time domain. It is important to understand how the filter obtained in this fashion differs from the original ideal filter (in the frequency domain). Note: the picture of filter I draw should have been repeated periodically with period <math>2 \pi</math>. It is important to remember this for any filter in discrete-time. In the last part of the lecture, we saw how the heat equation for an infinite length rod can be used to define an LTI system (by letting the heat evolve for a fixed amount of time), and we observed that the frequency response of this system has low-pass characteristics. We then discretized this differential equation by approximating each derivative using a standard numerical scheme. This gave us a simple discrete-time LTI system defined by a constant coefficient difference equation (but not causal).  
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We presented a simple method to obtain a causal FIR filter from an ideal filter using time shifting and windowing in the time domain. It is important to understand how the filter obtained in this fashion differs from the original ideal filter (in the frequency domain). Note: the picture of filter I drew should have been repeated periodically with period <math>2 \pi</math>. It is important to remember this for any filter in discrete-time. In the last part of the lecture, we saw how the heat equation for an infinite length rod can be used to define an LTI system (by letting the heat evolve for a fixed amount of time), and we observed that the frequency response of this system has low-pass characteristics. We then discretized this differential equation by approximating each derivative using a standard numerical scheme. This gave us a simple discrete-time LTI system defined by a constant coefficient difference equation (but not causal).  
  
 
'''Related Rhea page previously created by students:''' (Feel free correct/comment, expand on them, or simply write new pages on the subject)
 
'''Related Rhea page previously created by students:''' (Feel free correct/comment, expand on them, or simply write new pages on the subject)

Latest revision as of 11:42, 22 October 2010

Lecture 25 Blog, ECE438 Fall 2010, Prof. Boutin

Friday October 22, 2010.


We presented a simple method to obtain a causal FIR filter from an ideal filter using time shifting and windowing in the time domain. It is important to understand how the filter obtained in this fashion differs from the original ideal filter (in the frequency domain). Note: the picture of filter I drew should have been repeated periodically with period $ 2 \pi $. It is important to remember this for any filter in discrete-time. In the last part of the lecture, we saw how the heat equation for an infinite length rod can be used to define an LTI system (by letting the heat evolve for a fixed amount of time), and we observed that the frequency response of this system has low-pass characteristics. We then discretized this differential equation by approximating each derivative using a standard numerical scheme. This gave us a simple discrete-time LTI system defined by a constant coefficient difference equation (but not causal).

Related Rhea page previously created by students: (Feel free correct/comment, expand on them, or simply write new pages on the subject)

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