🚀 go-pugleaf

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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