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LTI Image Interpretation

Started by laurito April 9, 2013
How would you interpretate this image about LTI systems and convolution?:
[img]http://i.imgur.com/JAlHsYs.jpg[/img]


On Tue, 09 Apr 2013 15:08:43 -0500, laurito wrote:

> How would you interpretate this image about LTI systems and > convolution?: [img]http://i.imgur.com/JAlHsYs.jpg[/img]
It looks like a fair representation of a system responding to a signal, unless "flipping" is a bowlderized swear word, in which case there _is flipping too_ an impulse response. (However, I assume that "flipping impulse response" means "an impulse response that does not change sign"). -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
> On Tue, 09 Apr 2013 15:08:43 -0500, laurito wrote: > How would you interpretate this image about LTI systems and > convolution?: [img]http://i.imgur.com/JAlHsYs.jpg[/img]
I'm not sure I'd like to see it shown that way for 2 or 3 dimensions. It might start to look like a Jackson Pollock painting. And the term LTI won't be applicable for some image/physics/other problems. Contrast the 'no flipping' (ie: 'no time reversal') approach to the Wiki article, where the flipping concept is used (eg: 'Visual explanations of convolution'): http://en.wikipedia.org/wiki/Convolution As usual, the answer to: �which way is best?� probably depends on who you're trying to teach, and what you want them to learn. I've often used hardware shift register/multiply/add descriptions when describing convolution/correlation, but that may not be the best way for some people to learn. Kevin
On Apr 9, 4:08&#2013266080;pm, "laurito" <94889@dsprelated> wrote:
> How would you interpretate this image about LTI systems and convolution?: > [img]http://i.imgur.com/JAlHsYs.jpg[/img]
From the definition of Linear Time Invariant system, this makes the most sense to me. An input sequence consists of a sequence discrete impulses. Each weighted input impulse produces a corresponding weighted impulse response. The final output is the sum of these output responses. The advantage of calculating the output this way is it gives you all the output samples i.e. for y(1), y(2), ... y(n). When you want to calculate a specific output sample i.e. y(3), then idea of using the flipped impulse response comes into play. Cheers, Dave
On Tue, 09 Apr 2013 21:11:19 -0700, kevin wrote:

>> On Tue, 09 Apr 2013 15:08:43 -0500, laurito wrote: How would you >> interpretate this image about LTI systems and convolution?: >> [img]http://i.imgur.com/JAlHsYs.jpg[/img] > > I'm not sure I'd like to see it shown that way for 2 or 3 dimensions. It > might start to look like a Jackson Pollock painting. And the term LTI > won't be applicable for some image/physics/other problems. > > Contrast the 'no flipping' (ie: 'no time reversal') approach to the Wiki > article, where the flipping concept is used (eg: 'Visual explanations of > convolution'): > > http://en.wikipedia.org/wiki/Convolution > > As usual, the answer to: &ldquo;which way is best?&rdquo; probably depends on who > you're trying to teach, and what you want them to learn. I've often > used hardware shift register/multiply/add descriptions when describing > convolution/correlation, but that may not be the best way for some > people to learn.
Oh! Convolution! Flipping! (Sound of forehead smacking). Now that I understand the point of the picture, yes, it would be confusing for multi-dimensional images. But it does get the point across about how convolution "really" works in the time domain -- the whole "flip and sum" thing is really just a mathematical convenience for finding the value of the convolved sequences at a single point. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
On Tue, 09 Apr 2013 21:11:19 -0700, kevin wrote:

>> On Tue, 09 Apr 2013 15:08:43 -0500, laurito wrote: How would you >> interpretate this image about LTI systems and convolution?: >> [img]http://i.imgur.com/JAlHsYs.jpg[/img] > > I'm not sure I'd like to see it shown that way for 2 or 3 dimensions. It > might start to look like a Jackson Pollock painting. And the term LTI > won't be applicable for some image/physics/other problems.
<< snip >> I don't like the term "LTI" for sampled systems at any rate. I prefer "linear shift invariant" -- it helps newbies remember that they're in sampled time, and it helps to prevent them from starting to think of a sampled-time system as time invariant. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
Do you think everything in the image is clear and correct? Is it easy to
understand what you have to multiply and add together? (y[0]=..., y[1]=...,
etc) What would happen if you change 'Y[3]' to 'X[1]h[2] + X[2]h[1] +
X[3]h[0]'?
Do you think that the input (x[n]) is time reversed?