effects of derivative on frequency

Greetings,

What is the effect of derivative operator on a signal's frequency
representation? Do I lose low frequency components for example?
Basically what kind of a filter is the derivative operator (taking
derivative with respect to time)?

Thanks

On Nov 6, 6:24&#4294967295;am, Cagdas Ozgenc <cagdas.ozg...@gmail.com> wrote:
> Greetings,
>
> What is the effect of derivative operator on a signal's frequency
> representation? Do I lose low frequency components for example?
> Basically what kind of a filter is the derivative operator (taking
> derivative with respect to time)?
>
> Thanks

I would suggest you look at a table of Fourier transforms and
mathematical operators/operations, and understand each entry.

Maurice Givens

Dnia 06-11-2009 o 13:24:30 Cagdas Ozgenc <cagdas.ozgenc@gmail.com>  
napisa&#4294967295;(a):

(...)
>  Do I lose low frequency components for example?
> Basically what kind of a filter is the derivative operator (taking
> derivative with respect to time)?


It is a philosophical question.
When you look on the sun through a color filter
what do you expect to see.
You want to emphasize one colour from many.

The same is with other operators.
You use them to emphasize some property
among others.

Deriviation emphasize (draws out, makes more visible)
fast changes.
Complementary, slow changes are weakly visible
after such operation.


-- 
Mikolaj

Cagdas Ozgenc <cagdas.ozgenc@gmail.com> writes:

> Greetings,
>
> What is the effect of derivative operator on a signal's frequency
> representation? Do I lose low frequency components for example?
> Basically what kind of a filter is the derivative operator (taking
> derivative with respect to time)?

Try this thought experiment to see if you can intuitively answer your
second question: If you put DC into a differentiator, what do you get
out?
-- 
Randy Yates                      % "Though you ride on the wheels of tomorrow,
Digital Signal Labs              %  you still wander the fields of your
mailto://yates@ieee.org          %  sorrow."
http://www.digitalsignallabs.com % '21st Century Man', *Time*, ELO

On Nov 6, 7:24&#4294967295;am, Cagdas Ozgenc <cagdas.ozg...@gmail.com> wrote:
> Greetings,
>
> What is the effect of derivative operator on a signal's frequency
> representation? Do I lose low frequency components for example?
> Basically what kind of a filter is the derivative operator (taking
> derivative with respect to time)?
>
> Thanks

a derivative or integration operation (lets say adding an inductor or
capacitor to a circuit) does exactly two things to the steady state
response of a given input frequency.
1. It will alter the phase of the input frequency.
2. It will alter the amplitude of the imput frequency.

It will not alter the frequency itself.

Any linear system simply alters the amplitude or phase of each input
frequency (in steady state conditions).

A filter has a different changes on phase and amplitude of each
frequency.  For instance, a low pass filter tends to reduce the
amplitude of high frequencies, while not affecting the amplitude of
the low frequencies (very much)

Remember, the system does not alter the frequeny of the input signal,
just phase and amplitude.

If you go to the differential  equations of forcing functions of
orinary differential equations, the only solution to a forcing
function of frequeny : f1, are sine and cosine functions of
frequency : f1.

"Cagdas Ozgenc" <cagdas.ozgenc@gmail.com> wrote in message 
news:01ec1f54-a2f6-419d-a063-6531f0f57648@d21g2000yqn.googlegroups.com...
> What is the effect of derivative operator on a signal's frequency
> representation?

Go back to your school mathematics ...

If y = sin(wt)

then dy/dt = w sin(wt)

therefore, for w less than 1 rad/sec, the response is attenuation
and for w above 1 rad/sec, the response is an hf filter of ever
increasing output.

> Do I lose low frequency components for example?

As shown above, there is progressive attenuation for w below 1 rad/sec.

At w = 0, which as you know is DC, there is no output.

> Basically what kind of a filter is the derivative operator (taking
> derivative with respect to time)?

Because the output is proportional to w, it is a high pass filter.

However, it's probably not the one you want, because a monotonic
rising output with respect to frequenct most certainly is not flat.

On 6 Nov., 16:39, "Phil O. Sopher" <inva...@invalid.invalid> wrote:
> "Cagdas Ozgenc" <cagdas.ozg...@gmail.com> wrote in message
>
> news:01ec1f54-a2f6-419d-a063-6531f0f57648@d21g2000yqn.googlegroups.com...
>
> > What is the effect of derivative operator on a signal's frequency
> > representation?
>
> Go back to your school mathematics ...
>
> If y = sin(wt)
>
> then dy/dt = w sin(wt)

Perhaps you should also go back to your school mathematics ... :-)

"Andor" <andor.bariska@gmail.com> wrote in message 
news:7f9c62d0-9fd9-4675-8a80-e86846acf07f@v36g2000yqv.googlegroups.com...
> On 6 Nov., 16:39, "Phil O. Sopher" <inva...@invalid.invalid> wrote:
>> "Cagdas Ozgenc" <cagdas.ozg...@gmail.com> wrote in message
>> news:01ec1f54-a2f6-419d-a063-6531f0f57648@d21g2000yqn.googlegroups.com...
>>
>> > What is the effect of derivative operator on a signal's frequency
>> > representation?
>> Go back to your school mathematics ...
>> If y = sin(wt)
>> then dy/dt = w sin(wt)
> Perhaps you should also go back to your school mathematics ... :-)

Oops! :-)

 then dy/dt = w cos(wt)

On Nov 6, 5:59�pm, Mikolaj
<sterowanie_komputerowe@_haha_poczta.onet.pl> wrote:
> Dnia 06-11-2009 o 13:24:30 Cagdas Ozgenc <cagdas.ozg...@gmail.com> &#4294967295;
> napisa&#4294967295;(a):
>
> (...)
>
> > &#4294967295;Do I lose low frequency components for example?
> > Basically what kind of a filter is the derivative operator (taking
> > derivative with respect to time)?
>
> It is a philosophical question.
> When you look on the sun through a color filter
> what do you expect to see.
> You want to emphasize one colour from many.
>
> The same is with other operators.
> You use them to emphasize some property
> among others.
>
> Deriviation emphasize (draws out, makes more visible)
> fast changes.
> Complementary, slow changes are weakly visible
> after such operation.
>
> --
> Mikolaj


Hmm. So this filter is actually keeping the noise in general, and
losing the low frequency dynamics (I understand that noise can be in
low frequency too, but information theoretically it is more likely to
be in the high frequency). In that case differentiating a signal
generated by an I(1) process for signal estimation should not be such
a good idea, however it is common practice and part of ARIMA
framework. What's the catch here?

On 2009-11-06 12:02:59 -0400, Cagdas Ozgenc <cagdas.ozgenc@gmail.com> said:

> On Nov 6, 5:59&#4294967295;pm, Mikolaj
> <sterowanie_komputerowe@_haha_poczta.onet.pl> wrote:
>> Dnia 06-11-2009 o 13:24:30 Cagdas Ozgenc <cagdas.ozg...@gmail.com> &#4294967295;
>> napisa&#4294967295;(a):
>> 
>> (...)
>> 
>>> &#4294967295;Do I lose low frequency components for example?
>>> Basically what kind of a filter is the derivative operator (taking
>>> derivative with respect to time)?
>> 
>> It is a philosophical question.
>> When you look on the sun through a color filter
>> what do you expect to see.
>> You want to emphasize one colour from many.
>> 
>> The same is with other operators.
>> You use them to emphasize some property
>> among others.
>> 
>> Deriviation emphasize (draws out, makes more visible)
>> fast changes.
>> Complementary, slow changes are weakly visible
>> after such operation.
>> 
>> --
>> Mikolaj
> 
> 
> Hmm. So this filter is actually keeping the noise in general, and
> losing the low frequency dynamics (I understand that noise can be in
> low frequency too, but information theoretically it is more likely to
> be in the high frequency). In that case differentiating a signal
> generated by an I(1) process for signal estimation should not be such
> a good idea, however it is common practice and part of ARIMA
> framework. What's the catch here?

Look carefully at the acronym. What is the I in ARIMA for? AR is for
autoregressive and MA is for moving average.

Hint: What is the opposite of differentiation and starts with an I?