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From: fisico32 on 8 May 2010 10:19
hello Forum,

I know that a continous time sinusoids can have any radian frequency
w=2pi/T, therefore any period T.

A discrete time sinusoids has a radian frequency equal to 2pi/N (where N is
the number of samples). No matter what N is, a discre-time sinusoid, if
periodic, will always be periodic with period=2pi in the frequency domain.


I am reading a book (modern spectrum analysis of time series by Naidu).
Very good book. But the author uses a "continous time radian frequency
that is confined from -pi to pi.... Why?
Is that only a convection? What advantage does it bring?

thanks
fisico32
From: dbd on 8 May 2010 11:16
On May 8, 7:19 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com>
wrote:
> hello Forum,
>
> I know that a continous time sinusoids can have any radian frequency
> w=2pi/T, therefore any period T.
>
> A discrete time sinusoids has a radian frequency equal to 2pi/N (where N is
> the number of samples). No matter what N is, a discre-time sinusoid, if
> periodic, will always be periodic with period=2pi in the frequency domain.
>
> I am reading a book (modern spectrum analysis of time series by Naidu).
> Very good book. But the author uses  a "continous time radian frequency
> that is confined from -pi to pi.... Why?
> Is that only a convection? What advantage does it bring?
>
> thanks
> fisico32

The book you mention is intended as a graduate level text. It requires
but does not discuss or supply at least an undergraduate level
understanding of DSP concepts including sampling. Your question in his
thread is easily answered from a basic undergraduate understanding of
sampling. I suggest that you add a book including such topics to your
consideration. An example is:

Discrete-Time Signal Processing
Alan V. Oppenheim
Ronald W. Schafer

There are many others. You may have noticed that there are few in this
forum who are interested in discussing graduate level concepts that
appear to be parroted by someone who seems to lack the basic tools
required for the discussion. Sometimes that means you may get no
reply. Sometimes that means that the responses you get will wander
from the question.

Dale B.Dalrymple
From: John Monro on 8 May 2010 20:22
dbd wrote:
> On May 8, 7:19 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com>
> wrote:
>> hello Forum,
>>
>> I know that a continous time sinusoids can have any radian frequency
>> w=2pi/T, therefore any period T.
>>
>> A discrete time sinusoids has a radian frequency equal to 2pi/N (where N is
>> the number of samples). No matter what N is, a discre-time sinusoid, if
>> periodic, will always be periodic with period=2pi in the frequency domain.
>>
>> I am reading a book (modern spectrum analysis of time series by Naidu).
>> Very good book. But the author uses a "continous time radian frequency
>> that is confined from -pi to pi.... Why?
>> Is that only a convection? What advantage does it bring?
>>
>> thanks
>> fisico32
>
> The book you mention is intended as a graduate level text. It requires
> but does not discuss or supply at least an undergraduate level
> understanding of DSP concepts including sampling. Your question in his
> thread is easily answered from a basic undergraduate understanding of
> sampling. I suggest that you add a book including such topics to your
> consideration. An example is:
>
> Discrete-Time Signal Processing
> Alan V. Oppenheim
> Ronald W. Schafer
>
> There are many others. You may have noticed that there are few in this
> forum who are interested in discussing graduate level concepts that
> appear to be parroted by someone who seems to lack the basic tools
> required for the discussion. Sometimes that means you may get no
> reply. Sometimes that means that the responses you get will wander
> from the question.
>
> Dale B.Dalrymple

Fisico32,
The clue lies in the expressions you quoted:
"... periodic with period=2pi in the frequency domain" and
"... confined from -pi to pi."

The range -pi to pi covers the positive and negative
frequencies up to 1/2 the sample frequency. There is
probably no point considering a frequency range greater than
this because the spectrum only repeats again.

Regards,
John

From: robert bristow-johnson on 8 May 2010 22:09
On May 8, 10:19 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com>
wrote:
> hello Forum,
>
> I know that a continous time sinusoids can have any radian frequency
> w=2pi/T, therefore any period T.
>
> A discrete time sinusoids has a radian frequency equal to 2pi/N (where N is
> the number of samples). No matter what N is, a discre-time sinusoid, if
> periodic, will always be periodic with period=2pi in the frequency domain.
>
> I am reading a book (modern spectrum analysis of time series by Naidu).
> Very good book. But the author uses  a "continous time radian frequency
> that is confined from -pi to pi.... Why?
> Is that only a convention? What advantage does it bring?
>

i don't have the book, but i might surmise that it's a convention
that, even in the C.T. domain, the unit of time is defined to be the
same as the sampling period of an associated physical discrete-time
system. we are free to do this in C.T. because, in the classical
physical world, no particular time is preferred to by nature. so if
you choose the unit time to be the same as the sampling period, you
lose an extraneous parameter (T), then z=e^s, and small-case omega is
directly comparable to capital Omega.

it's just a convention. possibly a handy one if you're not worried
about connecting your digital system to a real analog system with
capacitors and resistors (but it wouldn't be fatal if that were the
case, you would just need the correct conversion factors).

r b-j
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