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| achuttys... |
 Posted: Tue Oct 27, 2009 8:08 pm |
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Guest
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Hi all
Please help...
I have some doubts on LTI systems. Recently I read the second chapter of
Digital Signal Processing by John G Proakis. In the second chapter, it
gives a method to charecterize LTI system by LCCDE(Linear Constant
Coefficient Differential Equation). The differential equation is solved to
find the system parameters. Once the system parameters are found, one can
find the response of an LTI system for any arbitary signal.
The response of an LTI system can also be found by knowing the impulse
response of the system through Convolution method.
Why does one need LCCDE method when Convolution method is there to find
the response of an LTI system? Is it because Convolution cannot be applied
to recursive systems?
On computation efficiency, is LCCDE better than Convolution?
Thanks in Advance |
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| Rune Allnor... |
| Posted: Tue Oct 27, 2009 8:08 pm |
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Guest
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On 27 Okt, 17:08, "achuttys" <subhish_ku... at (no spam) yahoo.co.in> wrote:
Quote: Hi all
Please help...
I have some doubts on LTI systems. Recently I read the second chapter of
Digital Signal Processing by John G Proakis. In the second chapter, it
gives a method to charecterize LTI system by LCCDE(Linear Constant
Coefficient Differential Equation). The differential equation is solved to
find the system parameters. Once the system parameters are found, one can
find the response of an LTI system for any arbitary signal.
The response of an LTI system can also be found by knowing the impulse
response of the system through Convolution method.
Why does one need LCCDE method when Convolution method is there to find
the response of an LTI system? Is it because Convolution cannot be applied
to recursive systems?
On computation efficiency, is LCCDE better than Convolution?
There are a number of different but equivalent (formally,
although not necessarily practically) representations of the LTI
system. Which one is 'best' depends on what information or
assumptions you start out from, and what you want to achieve.
If you have the LCCDE, then work from that POV. If you don't,
but instead have the impulse response, then work from that POV.
I have noticed that entry-level DSP classes often start with
the case of the known difference equations, and the question is
to work out frequency responses, impulse responses, and so on.
On medium to advanced levels, the problem is often to work
out the diffence equation from measured impulse responses or
transfer functions.
Rune |
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| Jerry Avins... |
| Posted: Tue Oct 27, 2009 9:06 pm |
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Guest
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achuttys wrote:
Quote: Hi all
Please help...
I have some doubts on LTI systems. Recently I read the second chapter of
Digital Signal Processing by John G Proakis. In the second chapter, it
gives a method to charecterize LTI system by LCCDE(Linear Constant
Coefficient Differential Equation). The differential equation is solved to
find the system parameters. Once the system parameters are found, one can
find the response of an LTI system for any arbitary signal.
The response of an LTI system can also be found by knowing the impulse
response of the system through Convolution method.
Why does one need LCCDE method when Convolution method is there to find
the response of an LTI system? Is it because Convolution cannot be applied
to recursive systems?
On computation efficiency, is LCCDE better than Convolution?
Thanks in Advance
LCCDE systems can also be solved with Laplace transformations.
Personally, I would rather, when working by hand, solve the differential
equation than work out a convolution integral.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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| Tim Wescott... |
| Posted: Tue Oct 27, 2009 10:43 pm |
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On Tue, 27 Oct 2009 10:46:04 -0700, Rune Allnor wrote:
Quote: On 27 Okt, 17:08, "achuttys" <subhish_ku... at (no spam) yahoo.co.in> wrote:
Hi all
Please help...
I have some doubts on LTI systems. Recently I read the second chapter
of Digital Signal Processing by John G Proakis. In the second chapter,
it gives a method to charecterize LTI system by LCCDE(Linear Constant
Coefficient Differential Equation). The differential equation is solved
to find the system parameters. Once the system parameters are found,
one can find the response of an LTI system for any arbitary signal.
The response of an LTI system can also be found by knowing the impulse
response of the system through Convolution method.
Why does one need LCCDE method when Convolution method is there to find
the response of an LTI system? Is it because Convolution cannot be
applied to recursive systems?
On computation efficiency, is LCCDE better than Convolution?
There are a number of different but equivalent (formally, although not
necessarily practically) representations of the LTI system. Which one is
'best' depends on what information or assumptions you start out from,
and what you want to achieve. If you have the LCCDE, then work from that
POV. If you don't, but instead have the impulse response, then work from
that POV.
I have noticed that entry-level DSP classes often start with the case of
the known difference equations, and the question is to work out
frequency responses, impulse responses, and so on. On medium to advanced
levels, the problem is often to work out the diffence equation from
measured impulse responses or transfer functions.
Rune
And if you're designing control systems you must do both -- first you
predict your plant behavior with differential and difference equations,
then you design a controller with differential equations, then once the
plant is built you verify your model by measurement (and usually adjust
it), then you tweak the controller's difference equations yet again.
Toss in the need to quantify the system's behavior in the frequency
domain and you'll be doing plenty of different kinds of analysis.
--
www.wescottdesign.com |
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| Tim Wescott... |
| Posted: Wed Oct 28, 2009 12:54 am |
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Guest
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On Tue, 27 Oct 2009 11:08:20 -0500, achuttys wrote:
Quote: Hi all
Please help...
I have some doubts on LTI systems. Recently I read the second chapter of
Digital Signal Processing by John G Proakis. In the second chapter, it
gives a method to charecterize LTI system by LCCDE(Linear Constant
Coefficient Differential Equation). The differential equation is solved
to find the system parameters. Once the system parameters are found, one
can find the response of an LTI system for any arbitary signal.
The response of an LTI system can also be found by knowing the impulse
response of the system through Convolution method.
Why does one need LCCDE method when Convolution method is there to find
the response of an LTI system? Is it because Convolution cannot be
applied to recursive systems?
On computation efficiency, is LCCDE better than Convolution? Thanks in
Advance
I'll more or less rephrase what Rune said:
There are a number of different ways to do this, each one completely
valid, each one fitting a given problem differently. Knowing a variety
of methods lets you choose the method that fits your problem well, and
makes your work lighter.
--
www.wescottdesign.com |
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