- #31
FrogPad
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T.Engineer said:
More detail than what rbj posted?
What Are the Key Challenges in Understanding Convolution in Signal Processing?
- Thread starter WolfOfTheSteps
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- Convolution
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Discussion Overview
The discussion revolves around the challenges of understanding convolution in signal processing, focusing on both discrete and continuous time cases. Participants explore the mathematical foundations, properties, and implications of convolution, as well as the concepts of impulse response and the sifting property.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant expresses confusion about the sifting property, questioning its usefulness and logic, suggesting it seems circular.
- Another participant raises a question regarding the nature of the impulse function \(\delta(t-t_0)\), asking whether it is 1 or infinity at time \(t_0\) and how a system can respond to an infinite input.
- A participant discusses the impulse response and its significance, stating that knowing the impulse response allows for understanding the system's behavior to any arbitrary input.
- There is a suggestion to approach the topic from a discrete-time perspective first, as it may simplify understanding before extending to continuous time.
- One participant shares a detailed explanation of linearity and time-invariance in systems, providing mathematical definitions and properties related to discrete signals and convolution.
Areas of Agreement / Disagreement
Participants express various viewpoints and questions, indicating that there is no consensus on the understanding of convolution, the sifting property, or the nature of the impulse response. The discussion remains unresolved with multiple competing views and ongoing exploration of the concepts.
Contextual Notes
Some limitations include the potential confusion surrounding the definitions of the impulse function and the implications of linearity and time-invariance in systems. There are also unresolved mathematical steps in the discussion of convolution.
Who May Find This Useful
This discussion may be useful for students and individuals studying signals and systems, particularly those seeking to deepen their understanding of convolution and its applications in signal processing.
More detail than what rbj posted?
- #32
WolfOfTheSteps
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Frogpad is right, you probably aren't going to find a better explanation that is as concise and to the point as what rbj posted. But here are some links anyway:
- http://cnx.org/content/m11541/latest/" of computing the convolution of two signals.
- A pretty cool http://www.jhu.edu/~signals/convolve/index.html" helping you gain a good visual intuition of the convolution. (continuous time)
- Same "slider" for the http://www.jhu.edu/~signals/discreteconv2/index.html"
- You can also check out the EE 20 and EE 120 Lectures on the http://webcast.berkeley.edu/courses.php?semesterid=22" (I'm not sure exactly where in the videos he talks about the convolution, though.)
- And of course there are the http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-003Fall-2003/CourseHome/index.htm" at the MIT Open Courseware site. (The homework solutions are exceptionally well written!)
But for a great derivation, I've found nothing better than what rbj posted here!
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- #33
trickae
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this is an amazing tutorial - thanks a lot rbj
wolf of the steps - haven't i seen you somewhere? :P
wolf of the steps - haven't i seen you somewhere? :P
- #34
WolfOfTheSteps
- 134
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trickae said:
Who me? You must be thinking of someone else.
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