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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 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 equations by approximating each derivative using a standard numerical scheme. This gave us a simple discrete-time system (defined by a constant coefficient difference equation) with low-pass characteristics. |
'''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) | ||
Revision as of 11:24, 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 draw 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 equations by approximating each derivative using a standard numerical scheme. This gave us a simple discrete-time system (defined by a constant coefficient difference equation) with low-pass characteristics.
Related Rhea page previously created by students: (Feel free correct/comment, expand on them, or simply write new pages on the subject)
- Ideal filter types in continuous-time: do not forget to repeat periodically every $ 2 \pi $ when considering discrete-time filters.
- Fourier transform of a DT window function
- How to solve differential equations iteratively
Previous: Lecture 24; Next: Lecture 26
