🚀 go-pugleaf

In order to determine the location of components known to be sinusoidal
in noise, I recommend looking at S. Lawrence Marple, Jr.'s book
_Digital Spectral Analysis with Applications_,
Englewood Cliffs, N.J.: Prentice-Hall, which discusses an unusually
wide range of spectral analysis techniques, including techniques for
high-resolution identification of components of known type in noise.
The eigen-analysis based frequency estimation techniques discussed
in Chapter 13 are probably what you want.

In article <3575@syma.sussex.ac.uk> paulr@syma.sussex.ac.uk (Paul T Russell) writes:
]I would appreciate any suggestions on practical methods
]for extracting spectral information from a noisy signal.
]In particular I need to measure the amplitude of
]one sinusoidal component (whose frequency is known in
]advance) where the amplitude of the component is
]close to the noise level. My first thought was to use
]an FFT to estimate the power spectrum and then try to
]identify the peak, but I feel sure that there must be
]a better way. Maybe digital filtering or some other
]means of power spectrum estimation (such as the Maximum
]Entropy Method) ? Or perhaps I should be doing something
]in the time domain, such as autocorrelation + averaging ?

I have an application where I need phase, rather than amplitude, but
the problem is similar. In that case, I compute:

  for i = 0 through a bunch
   I = sum(sinwt*sample[i])
   Q = sum(coswt*sample[i])

  A = sqrt(I*I + Q*Q)
  P = arctan(I/Q)
  
This is equivalent to computing just one line of the PSD from the DFT.
I do this in real time with an 8 bit uP running at .25 itty-bitty-Mips.

I suspect autocorrelation would work even better, if you really know the
frequency, and you don't care about the phase. 

Given that you know the frequency, I don't think you require anything
fancier than this. The algorithm shown above is simple enough that it
can be done in real time (on audio) with most microprocessor chips.
No need for a DSP or even a real fast micro (unless you are sampling
real fast and going for high precision/dynamic range).


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On finding a sine wave of known frequency buried in noise ...
 
If you know the phase of the sine, how about summing it for some
tens or even thousands of cycles ?  If you do not know the phase,
how about programming a PLL (Phase Locked Loop) ?  PLL is good
at finding the signal, if the signal is stable in frequency and
phase. If your signal is variable, try to filter it out of the noise.
 

 
-- 
Sakari M. Mattila    71307.1525@CompuServe.COM
                     mattila@tik.vtt.fi    Sakari Mattila@3:663*371.0.FNET

>
>I have an application where I need phase, rather than amplitude, but
>the problem is similar. In that case, I compute:
>
>  for i = 0 through a bunch
>   I = sum(sinwt*sample[i])
>   Q = sum(coswt*sample[i])
>
>  A = sqrt(I*I + Q*Q)
>  P = arctan(I/Q)
>  
>This is equivalent to computing just one line of the PSD from the DFT.
>I do this in real time with an 8 bit uP running at .25 itty-bitty-Mips.
>

This will work even better if the time interval from 0 to 'a bunch' covers
an integral number of cycles of sin(wt). 
---

					Bob Cutler
					KE7ZJ
					Lake Stevens Instrument Division
 					Hewlett-Packard
					Everett, WA

In article <9360012@hplsla.HP.COM> bobc@hplsla.HP.COM (Bob Cutler) writes:
>>
>>I have an application where I need phase, rather than amplitude, but
>>the problem is similar. In that case, I compute:
>>
>>  for i = 0 through a bunch
>>   I = sum(sinwt*sample[i])
>>   Q = sum(coswt*sample[i])

I believe that this is called the Geotzel method, and should be documented	in good DSP texts.  It is much more costly to compute an entire spectrum in 
this manner, but I would guess that it works just fine with single line 
spectra.  I wonder if you could use a window on it.  I wonder if you could
process a wigner kernel in this manner.  I believe that using this method
you create a tuned filter.  I wonder how to handle non-stationary cases.

Score:  3 wonders, 3 tidbits of info.

Greg

> We don't know the absolute phase of the signal but we do know the
> exact frequency. We are generating two sine waves at frequencies
> f1 and f2 and trying to measure the distortion product at 2f1 - f2.
> The signal is swamped by the two much larger components at f1 and
> f2, and is close to the noise level. 

That might even be better.  If you have f1 and f2 as separate components,
you can generate 2*(f1-f2) directly from them by multiplying the instant
values of the squares of f1 and f2 generating 2*(f1-f2).  No sin/cos
calculations or tables; just some multiplies.  You will need to subtract
out the DC from those multiplications.  If f1 and f2 are of stable amplitude
(and hence no sidebands to crossmodulate) then removing the DC should be
easy.

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