Averaging incoherent (noncoherent?) samples

dcarr66 wrote:
> >So, it reduces to the problem "is frequency X periodic at sampling rate Y,
>
> >and what is the period if it is periodic?" that we were posed with in the
>
> >DSP intro lectures?
>
> Yes, that's a better statement of the problem.
>
> >I'd suppose the next questions would be "how good an an average do you
> >need?", and "how good is the average you are getting now?"
>
> I'm working with a 10-bit ADC that is digitizing a spread-spectrum signal
> and need to determine the adjacent channel power ratio. I need to improve
> the SNR by at least 6 dB, preferably by 10 dB.
>
> >In other terms, what do you mean by "didn't work"?
>
> The SNR didn't improve. I experimented with coherent sinusoids generated
> in Matlab, and the SNR increases by 3 dB for every doubling of the number
> of averages.
>
> Dave

Coherent averaging will improve the SNR since the signal power gain is
N^2 while the noise gain (assuming white noise) is N.

Incoherent averaging (summing magnitude or magnitude squared) does not
improve the SNR  - it only reduces the variance of the noise estimate.
If you look at a sinusoid in noise and take a look at 1 FFT the noise
floor jumps around quite a bit. When you start averaging the FFTs
together the noise floor tends to smooth out and become more stable.
This is because the variance of the noise estimate (not the variance of
the noise itself) is reduced. This assumes that the noise is a wide
sense stationary process.

The only way to improve the SNR is to do more coherent integration
which in my example would mean taking a longer FFT.

For details you should look at the detection and estimation books:
Whalen - "Detection of Signals in Noise"
Steven Kay - has a couple of books out
Van Trees - Vol. I and Vol. III in his series discuss this.

Cheers,
Dave

>Coherent averaging will improve the SNR since the signal power gain is
>N^2 while the noise gain (assuming white noise) is N.
>
>Incoherent averaging (summing magnitude or magnitude squared) does not
>improve the SNR  - it only reduces the variance of the noise estimate.
>If you look at a sinusoid in noise and take a look at 1 FFT the noise
>floor jumps around quite a bit. When you start averaging the FFTs
>together the noise floor tends to smooth out and become more stable.
>This is because the variance of the noise estimate (not the variance of
>the noise itself) is reduced. This assumes that the noise is a wide
>sense stationary process.
>
>The only way to improve the SNR is to do more coherent integration
>which in my example would mean taking a longer FFT.
>
>For details you should look at the detection and estimation books:
>Whalen - "Detection of Signals in Noise"
>Steven Kay - has a couple of books out
>Van Trees - Vol. I and Vol. III in his series discuss this.
>
>Cheers,
>Dave
>
>

Thanks to everyone for the suggestions. I think have a better handle on
the problem and definitely have some reading to do.

Dave

dcarr66 wrote:
> I'm testing an A/D converter and need to average several acquired data sets
> to improve SNR. I've done this in the past with coherently sampled data,
> but in this case the data is not coherent and I'm not sure how to proceed.
> I've tried windowing the data sets individually then averaging, but that
> didn't work.
>
> I don't have sufficient control over the instrumentation to force coherent
> sampling. Thanks in advance for any assistance.

You have not made clear what your goal is in 'improving SNR'. If you
are trying to detect spurious tones, incoherent averaging will reduce
the false alarm rate at a given detection threshold by reducing the
variance of the averaged noise background. A classic reference on this
is:

TITLE: THE DETECTION PERFORMANCE OF FFT PROCESSORS FOR NARROWBAND
SIGNALS
PERSONAL AUTHOR: Walker, R.S.
CORPORATE AUTHOR: Defence Research Establishment Atlantic, Dartmouth NS
(CAN)
ABSTRACT: The report analyses the detection performance of the Fast
Fourier Transform (FFT) type signal processor for narrowband signals in
white Gaussian noise. Sinusoidal and narrowband Gaussian signals are
considered. The signal processor structure is based on the short-time
averaged periodogram approach to spectral estimation. Processor
parameters considered in the study include time-bandwidth product, data
windowing, periodogram overlap, FFT zeroes extension and data
normalization. A building-block approach is adopted, whereby the
effects of each parameter on the detection threshold can be determined.
Results are presented in graphical form. Hence, for a selected set of
processor parameters, the appropriate detection threshold can be
readily obtained. A thorough mathematical treatment of the problem is
presented in the Appendices.
DESCRIPTORS: Detection;Detection probability;Signal to noise
ratio;Signal processing;Narrowband;White noise;Random noise;Fast
fourier transforms
REPORT NUMBER: DREA-TM-82-A; Technical Memorandum 	REPORT DATE: 15 Feb
1982 	NUMBER OF PAGES : 107

This is downloadable for free from the Canadian DREA by searching at:
http://pubs.drdc-rddc.gc.ca/BASIS/pcandid/www/engpub/SF

Try searching by author last name in the author field. This paper comes
up in the results. And did I say what the price is?

Dale B. Dalrymple
http://dbdimages.com