Estimate the amplitude of SIN(t*f(t))

Hi guys,

Assume I have a sweeping sine wave, with KNOWN sweeping frequency f(t)
which is a parameter of time, what is the best approach to estimate
the amplitude of this "sine wave"?

James

Sorry, more on this: The signal can be characterized by SIN(t*f(t)) as
its fundemental frequency. There are also harmonics associated with
this signal. I also would like to estimate the amplitude of its
harmonics, i.e., the amplitude at
SIN(t*f(t)) ,SIN(2t*f(t)) ,SIN(3t*f(t)) ...

Any good idea?

Thanks a lot.

James

DigitalSignal wrote:
> Sorry, more on this: The signal can be characterized by SIN(t*f(t)) as
> its fundemental frequency. There are also harmonics associated with
> this signal. I also would like to estimate the amplitude of its
> harmonics, i.e., the amplitude at
> SIN(t*f(t)) ,SIN(2t*f(t)) ,SIN(3t*f(t)) ...

What constrains the amplitude? Can you turn a knob and make it bigger?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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Good question. The amplitude(s) can change. A typical example is when
the sweeping frequency goes through a frequency range between 100Hz to
200Hz in 5 seconds, the amplitude(s) of the signal can go up and down
by 20dB.

DigitalSignal wrote:
> Good question. The amplitude(s) can change. A typical example is when
> the sweeping frequency goes through a frequency range between 100Hz to
> 200Hz in 5 seconds, the amplitude(s) of the signal can go up and down
> by 20dB.

You need to explain what's going on in more detail. amplitude is not set 
by anything you mentioned so far. You seem to be looking at a special 
case and looking for a general truth.

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

DigitalSignal wrote:

> Sorry, more on this: The signal can be characterized by SIN(t*f(t)) as
> its fundemental frequency. There are also harmonics associated with
> this signal. I also would like to estimate the amplitude of its
> harmonics, i.e., the amplitude at
> SIN(t*f(t)) ,SIN(2t*f(t)) ,SIN(3t*f(t)) ...
> 
> Any good idea?

What is known about f(t) ?


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

DigitalSignal wrote:
(context restored -- this is USENET, fer crying out loud!)
 >> Assume I have a sweeping sine wave, with KNOWN sweeping frequency f(t)
 >> which is a parameter of time, what is the best approach to estimate
 >> the amplitude of this "sine wave"?
 >>
 >> James
> Sorry, more on this: The signal can be characterized by SIN(t*f(t)) as
> its fundemental frequency. There are also harmonics associated with
> this signal. I also would like to estimate the amplitude of its
> harmonics, i.e., the amplitude at
> SIN(t*f(t)) ,SIN(2t*f(t)) ,SIN(3t*f(t)) ...
> 
If you know f(t), and if it's rate of change is slow compared to it's 
value, then modulate your signal by sin(t*f(t)), cos(t*f(t)), 
sin(2t*f(t)), etc., and average the results (averaging over one whole 
period nicely nulls out the 2f content).  Then you have enough 
information to get both amplitude and phase of all your components.

If you control f(t) don't sweep it -- step it through your desired 
range, collect your points all at one frequency, get your data, then 
change the frequency and do it again.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

Tim, beautiful! We now just changed the kernel of Fourier transform to
a time variant function. I know your method works well. It can be
interpreted as tracking filter plus DFT. In fact I am awaiting for
this answer so I can ask the next one: Is there a fast transform to
calculate 1024 amplitudes relative to this changing frequency?

Jerry, the application background is more like when a sweeping sine
excitation goes through a network with sharp resonance, we want to
estimate the changing amplitude of the response accurately. The
harmonics are of interest as well.

James

DigitalSignal wrote:
> Jerry, the application background is more like when a sweeping sine
> excitation goes through a network with sharp resonance, we want to
> estimate the changing amplitude of the response accurately. The
> harmonics are of interest as well.

So it's not amplitude you want, but relative amplitude with the input as 
reference. I hope you realize that the results will depend on the speed 
of the sweep. (It takes time to excite a resonance and for it to decay.) 
Unless the sweep speed is slow enough so that slowing it further won't 
materially alter the outcome, calculating the outcome is very difficult. 
So is interpreting a measured result. A DFT assumes a stationary signal, 
which a fast sweep assuredly is not. The frequency must change very 
little during the time needed to collect enough samples for a meaningful 
result.

Why do you include harmonics in the swept waveform? Where does your 
driving waveform originate?

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