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why should I apply a transform ?

Started by frier April 4, 2009
hi...,


=> DFT, DCT, DWT,
=> Z-transform, Laplace transform..etc

and the list goes on......

keep all this aside for 10 min
for the sake of discussion

Lets talk...about..,

Q) Why should I transform any signal ?

this is the question which is bothering me a lot..

Excluding these reasons any other new stuff
from you people

1) to reduce Redundancy
2) to perform the job of filters

thnx a lot
for the help;

Any book advise or web-links on
Video and Music compression
{ I'm want very very advanced ones }
_____
Why should I refuse a good dinner
simply because I don't understand
the digestive processes involved?

         Oliver Heaviside


frier wrote:

> Q) Why should I transform any signal ?
Usually because some operations or analysis is easier or better done on the transformed signal. bye, -- piergiorgio
On 4 Apr, 10:06, frier <azeez...@gmail.com> wrote:

> Q) Why should I transform any signal ?
Because it's useful, somehow. If it isn't useful, no need to do it.
> 1) to reduce Redundancy
This might be one reason, e.g. in data compression schemes, but it is not the only one.
> 2) to perform the job of filters
Not do the job of filters (filters can be implemented directly in time domain), but designing filters. The filters most common in DSP are designed in terms of their frequency responses. That's a very good reason to study filters in terms of Fourier transforms. Rune
On Sat, 4 Apr 2009 04:09:23 -0700 (PDT), Rune Allnor
<allnor@tele.ntnu.no> wrote:

>On 4 Apr, 10:06, frier <azeez...@gmail.com> wrote: >> 2) to perform the job of filters > >Not do the job of filters (filters can be implemented >directly in time domain),
But at a much higher cost (for large enough N). Frequency domain filtering can have a huge computational benefit (at a higher latency cost). Muzaffer Kal DSPIA INC. ASIC/FPGA Design Services http://www.dspia.com
frier wrote:
> hi..., > > > => DFT, DCT, DWT, > => Z-transform, Laplace transform..etc > > and the list goes on...... > > keep all this aside for 10 min > for the sake of discussion > > Lets talk...about.., > > Q) Why should I transform any signal ?
A transform is a mathematical operation. Cross multiplying, integrating differentiating, and counting are other operations. Each is used when it is a step toward the solution you want.
> this is the question which is bothering me a lot..
It's a tool to accomplish something. If you don't know what the tool does or how it acts on the material, you will be bothered a lot. Even a hammer can puzzle the uninitiated.
> Excluding these reasons any other new stuff > from you people > > 1) to reduce Redundancy > 2) to perform the job of filters > > thnx a lot > for the help; > > Any book advise or web-links on > Video and Music compression > { I'm want very very advanced ones }
I don't think you're ready for than. Start with simpler material for background. _____
> Why should I refuse a good dinner > simply because I don't understand > the digestive processes involved? > > Oliver Heaviside
I like that quote. Heaviside introduced Laplace transforms into the mathematics of electrical engineering under the name of "operational calculus". Others faulted him for lack of rigor, and the quote was a response. Then Laplace transforms were first reinvented and later rediscovered, and they turned out to be the same thing. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On Apr 4, 3:09&#2013266080;am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 4 Apr, 10:06, frier <azeez...@gmail.com> wrote: > > > Q) Why should I transform any signal ? > > Because it's useful, somehow. If it isn't useful, > no need to do it.
=> this is the line; I want to hear from you people. thnx a lot to all others too, who helped me with their valuable suggestions. _____ frier<=>Nimo {sorry for the correction} ______ some interesting lines of the day:- Throughout this immersion in physics, Hilbert worked on putting rigor into the mathematics of physics. While highly dependent on higher math, the physicist tended to be "sloppy" with it. To a "pure" mathematician like Hilbert, this was both "ugly" and difficult to understand. As he began to understand the physics and how the physicists were using mathematics, he developed a coherent mathematical theory for what he found, most importantly in the area of integral equations. When his colleague Richard Courant wrote the now => "classic Methods of Mathematical Physics" including some of Hilbert's ideas, he added Hilbert's name as author even though Hilbert had not directly contributed to the writing. => Hilbert said "Physics is too hard for physicists", implying that the necessary mathematics was generally beyond them; the Courant-Hilbert book made it easier for them. by David Hilbert
> > 1) to reduce Redundancy > > This might be one reason, e.g. in data > compression schemes, but it is not the > only one. > > > 2) to perform the job of filters > > Not do the job of filters (filters can be implemented > directly in time domain), but designing filters. > The filters most common in DSP are designed > in terms of their frequency responses. That's a > very good reason to study filters in terms of Fourier > transforms. > > Rune
On Apr 4, 1:06&#2013266080;pm, frier <azeez...@gmail.com> wrote:
> hi..., > > => DFT, DCT, DWT, > => Z-transform, Laplace transform..etc > > and the list goes on...... > > keep all this aside for 10 min > for the sake of discussion > > Lets talk...about.., > > Q) Why should I transform any signal ? > > this is the question which is bothering me a lot.. > > Excluding these reasons any other new stuff > from you people > > 1) to reduce Redundancy > 2) to perform the job of filters > > thnx a lot > for the help; > > Any book advise or web-links on > Video and Music compression > { I'm want very very advanced ones } > _____ > Why should I refuse a good dinner > simply because I don't understand > the digestive processes involved? > > &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080;Oliver Heaviside
We use transforms to more information out of our signal/system. If you have a time domain FM signal, it is difficult to see the frequency content of the signal, difficult to measure that. But if you transform your point of view from time-domain to frequency domain, you'll set a better understanding i.e. now it would be much easier to look at the frequency content of the signal. And this true for all transforms, they give you oppurtunity to extract more information by looking at something from different point of view. Other examples include Laplace or Z-transforms, which provide for you an easy way to look at system stability and so on. Also, sometimes processing in one domain is easier/less-complicated than processing in another domain. I wont go into details of that, as it has been already mentioned here Happy learning ------------------------------------------------------------------------------------------------ groups.yahoo.com/group/telecom_research
> > Q) Why should I transform any signal ? > > this is the question which is bothering me a lot.. > > Excluding these reasons any other new stuff > from you people > > 1) to reduce Redundancy > 2) to perform the job of filters
>
First, it might be useful to examine just a little what most of these transforms *are*. Generally, they are operations that *map* a function or sequence into another domain. And, generally, the mappings are 1:1 meaning that they can be reversed. The most obvious use, to me, is that such transforms allow us to do some mathematical operations easier: Calculus becomes algebra. Examples are the Laplace and Z transforms in solving ordinary linear differential / difference equations with constant coefficients. A ready example with the Fourier Transform is trading convolution for multiplication. Many useful operations can be done using well-known transform pairs to avoid doing any transformations at all. Gate and Sync are one of those pairs. So, why transform? Generally to make your job easier. Sometimes to help in analysis (e.g. spectral), etc. Fred