Why should one use convolution ?

[ng]

hello

Why shud one use convolution ?Inorder to get the state transition matrix
from
x'=Ax+Bu

x(t)=exp(at)x(0) + integral[exp(a(t-tau)) bu(tau) dtau

where tau is the variable of convolution.
i have read that convolution is used when integration is reqd,for instance,in capacitors and inductors which don't respond to an input immediately...but can someone PLEASEEEEEEEEEE help me understand how convolution really works?

Thanks for any help always!

 

[berkeman]

Hi ng, My Stremler textbook on "Introduction to Communication Systems" has a pretty good explanation of convolution and why it is used as a way to work with linear systems. See if your library has a copy of the book, and check out section 3.6, "Properties of the Fourier Transform". It has a mathematical justification and development, as well as the traditional graphical convolution method (mirror and slide).

You would most often use convolution to help determine input/output behavior of a linear system, once you've derived the impulse response for the system. Convolution in the time domain is like multiplication in the frequency domain, which is why the Fouier transform is so handy.

My favorite DSP book by Williams, "Designing Digital Filters" also has a brief description of convolution in the digital domain in section 1.5, "Interesting Responses".

Hope that helps some.

 

[ng]

hi berkeman

Thanku for the response.I am actually learning control systems now and came across this DSP stuff in it.
As far as i know DSP is way too hifi to begin in this priliminary stage.Is it not?So i tot i wud stick with understanding Control systems then move on to DSP.I have heard its interesting too.
thanu so much.

 

[berkeman]

hi berkeman

Thanku for the response.I am actually learning control systems now and came across this DSP stuff in it.
As far as i know DSP is way too hifi to begin in this priliminary stage.Is it not?So i tot i wud stick with understanding Control systems then move on to DSP.I have heard its interesting too.
thanu so much.

No way bud. DSP is so cool when it's taught/explained well. Plus it's the way you will do 90% of your work in the real world. Well, that really depends on the chips and systems you're working on. The chip that I'm on the design team for right now (intense, 24/7 actually) is about 60% analog signal processing and 40% DSP, all in one mixed-signal chip. That's how you get the costs down and sell millions of chips...

Anyway, I'd highly recommend that you buy the DSP book that I mentioned above in this thread. It is well worth the money. Excellent textbooks are rare, especially when you are looking for them and buying them for yourself as a working engineer. It's not like it's a class requirement or anything anymore -- I want the info and I want it presented in a practical way that I can understand right now (with some intense study -- that's okay), and I want practical examples that I can test on my office PC with SPICE or Mathematica or MathCAD or Excel right now.

I built some really cool Excel recursive spreadsheets after reading the first couple chapters of that DSP textbook that showed LPF, HPF and BPF responses, and I had a lot better feeling for Eigenfunctions and Eigenvalues after reading this textbook cover to cover.

Check it out. You'll definitely like it. -Mike-

 

[ng]

hi mike
i am really new to dsp and control systems etc.and there is actually no one who can sit down and explain all this stuff to me.So u see its more of a self study.I am much dependent on the forum and replies from people like you.
i shall see if i can get hold the book u mentioned.I am learning the basics.
Once again thanku for ur help and time.

 

[mmwave]

more about why convolution

I think the question merits more discussion.

First, you have to use convolution to learn it and get through your classes. But what about after that?

The only reason to use convolution instead of the frequency domain is when the tranform of the signal or the system is too hard to calculate. I can't remember ever doing a convolution after my BS that wasn't done by a computer.

The frequency domain seems much more intuitive for electrical engineering problems.

Comments?