LTI systems? (non-HW non-test questions...)

Hi all,


Is a Foureir Transformer an LTI system?

(input x(t), output the foureir transform of the input x(t))

Is a Hilbert Transformer an LTI system?

(input x(t), output the hilbert transform of the input x(t))

are these systems stable?

Thanks a lot!

lucy wrote:
> Hi all,
> 
> 
> Is a Foureir Transformer an LTI system?
> 
> (input x(t), output the foureir transform of the input x(t))
> 
> Is a Hilbert Transformer an LTI system?
> 
> (input x(t), output the hilbert transform of the input x(t))
> 
> are these systems stable?

You know, the "non-HW non-test" in the subject are just words;
putting it does not necessarily give you a license to ask
whatever HW-style questions and expect everyone to naively
answer them.

That said (and taking into account the possibility that these
might indeed NOT be homework), why don't you try to answer
them based on what you know?

Think about the definition of a LTI system -- what are the
conditions?  Does the Fourier transform meet the conditions?
Id the Fourier transform of f(t) + g(t) equal to the sum of
the Fourier transforms of f and g?  What if you take a linear
combination?  a*f(t) + b*g(t) -- is the Fourier transform of
that equal to a*F(f(t)) + b*F(g(t)) ??  (use the definition
of Fourier transform).

If you can not answer the above, then this is definitely
homework (or entirely hopeless).

For the TI part, it's a bit trickier, but you'd definitely
have to be able to answer the equivalent questions, if you
are given an exact definition of what is a Fourier
*transformER*and how exactly it operates.

HTH,

Carlos
--

lucy wrote:
> Hi all,
> 
> Is a Foureir Transformer an LTI system?
> (input x(t), output the foureir transform of the input x(t))
> Is a Hilbert Transformer an LTI system?
> (input x(t), output the hilbert transform of the input x(t))
> are these systems stable?

Are you reading this on your own? Do you have an instructor or a tutor?

As far as I l know, there's no "Fourier /note spelling/ transformer" 
(but see http://zapatopi.net/kelvin/papers/harmonic_analyzer.html for a 
harmonic analyzer).

As for stability, if the Hilbert transform exists and is finite, then 
any system that produces it must be stable. I know that DSP is both deep 
and broad, but you learn about it by finding ways to *understand* its 
parts. You can't find your way about it the way a taxi driver finds her 
way around a city, by memorizing maps and routes.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Unfortunately I don't have instructor or tutor.

I am an amateur DSPer and hopefully amateur mathmatician...

I try to think of problems myself,

and answer them myself,

if I am not sure about my thinking,

I ask you guys...

So please help! I do appreciate your help greatly!

On 8 Oct 2005 00:23:36 -0700, "lucy" <losemind@yahoo.com> wrote:

>Unfortunately I don't have instructor or tutor.
>
>I am an amateur DSPer and hopefully amateur mathmatician...
>
>I try to think of problems myself,
>
>and answer them myself,
>
>if I am not sure about my thinking,
>
>I ask you guys...
>
>So please help! I do appreciate your help greatly!

Hi Lucy,

   having someone here answer your homework 
problems for you DOES NOT help you.
You probably do not believe me, but it's true.

Study, read, learn, study, read, learn.

[-Rick-]

That's misunderstanding... the problem itself was thought out by
myself...

How come it is a HW problem? I guess I confused you guys to think that
it is a HW problem... I am sorry about that.

lucy wrote:
> That's misunderstanding... the problem itself was thought out by
> myself...
> 
> How come it is a HW problem? I guess I confused you guys to think that
> it is a HW problem... I am sorry about that.

It's unusual to have someone doing self study to the depth that you try 
to. The truth is that our filter for such posts id fairly good, there is 
evidently a lot of aliasing here. Here is a proposition: instead of just 
asking for answers to problems that puzzle you, tell us also what 
thoughts you had and why you rejected or mistrusted them. That's all we 
usually ask of classroom students, anyway.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������