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From: Rune Allnor on 3 Mar 2010 11:56
On 3 Mar, 17:14, "Mark Shore" <msh...(a)magmageosciences.ca> wrote:
> Rune Allnor <all...(a)tele.ntnu.no> wrote in message <09bb2565-f34d-44b4-9a16-d2f2a4282...(a)z4g2000yqa.googlegroups.com>...
>
> > There are very, very few applications - I am not aware of a single
> > one - where determining the amplitude of a sinusoidal makes any
> > sort of sense.
>
> > > My problem in short: I would like to determine the amplitude of a signal
>
> > I would like to win the lottery.
>
> > The fact that one would like to do something, does not mean it
> > is neither useful, wise, or even possible.
>
> > Rune
>
> With all respect, I don't understand these statements at all. This is a common practice in geophysical signal processing.

To estimate the amplitude of *sinusoidals*? Could you
please provide references?

> And coincidentally or not, here is the first paragraph of a paper (Wu & Hong, Five-Point Amplitude Estimation of Sinusoidal Signals: With Application to LVDT Signal Conditioning) in the March 2010 IEEE Transactions on Measurement and Instrumentation:
>
> "AMPLITUDE estimation of sinusoidal signals is a crucial
> issue in many tasks of measurement and instrumentation,
> e.g., system identification [1], demodulation of amplitude modulated
> (AM) signals, and signal conditioning for linear
> variable differential transformers (LVDT) or the related differential
> variable reluctance transducers [2]. Sinusoidal signal
> amplitude estimation is also important in the evaluation of
> multifrequency signal parameters, e.g., the root-mean-square
> (RMS) value, signal-to-noise ratio (SNR), and total harmonic
> distortion (THD). There are many techniques available for
> amplitude estimation, including the least square method [1],
> [3], the adaptive state observers [4], [5], and the well-known
> fast Fourier transform (FFT)."
>
> Perhaps the OP could refer to this paper and the references therein, as well as to look at the undesired artifacts of typical FIR and IIR filters and how these can be mitigated.

The OP would be wise not to.

The quoted section only shows that the authors of the paper
have no idea what they are talking about:

- "system identification": The key is to estimate the frequency
domain transfer function for the system. This is usually
done with broad-band data; be it frequency chirps, pulses
or random noise. To what extent sinusoidals are used at all,
it is the ratio of amplitudes of input and output that is
important; not the amplitudes as such.

- "demodulation of amplitude modulated (AM) signals": Sinusoidal
estimation have nothing to do with this. All one needs is
a mizer and a low-pass filter. The fact that the authors
of the quoted paper even mentiones AM as an application
for sinusoidal estimation, suggests that they have looked
for terms that *sound* relevant but in fact are not.

- "Sinusoidal signal amplitude estimation is also important
in the evaluation of multifrequency signal parameters, e.g.,
the root-mean-square (RMS) value, signal-to-noise ratio (SNR)":
This is plain BS. What on earth is "the RMS vale"? Is the term
"SNR" invalid for broadband signals? Again, another clue that
the authors are only making noises without understanding
semantics.

- "There are many techniques available for amplitude estimation,
including ... the well-known fast Fourier transform (FFT)":
These guys don't even know the basics. Allow me to demonstrate:

N = 8;
f = 3/16;
A = 1; % Amplitude
x = sin((0:(N-1))*2*pi*f);
X = fft(x)/sqrt(N);
clf
stem((0:(N-1)),abs(X))
hold on
plot([0,N],0.5*A*[1,1],'r')
axis([0,N-1,0,1])

In this plot the red line denotes the expected amplitude of the
FT of a sinusoidal with unit time-domain amplitide.

Where, in this plot, do you recognize that amplitude?
Where, in this plot, do you recognize the fact that
the time-domain signal is in fact a sinusoidal?

The authors of the quoted paper are probably nothing more than
a couple of students or research assistants who are desperate
to get some publication on their CV, and thus have chosen a
subject that sound straight-forward but that they in reality
know nothing about.

Rune
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