This question concerns estimating the PDF of noise, based upon observations of a data stream consisting of noise embedded with transient signals. I would like to know if my(adsbygoogle = window.adsbygoogle || []).push({}); Proposed Solutionis a correct approach.

Suppose I have "long" stream of seismic data, consisting of noise, and with some occasional pulses of transient signals; we can make assumptions about the time-bandwidth product. I DO assume the that the time-width of each signal pulse is very small relative to the length of the data stream.

Objective: Estimate the noise in the data.

Question:

How much of my data stream can be signal in order for my estimate of the noise variance to be correct within Δσ?

Proposed Solution:

(1) Perform a hypothesis testH_{0}: pure noise,H_{1}: is a signal plus noise, with unknown variance.

(2) Form a maximum likelihood ratio.

(3) If the probability of a missed detection--the probability of choosingH_{0}overH_{1}whenH_{1}is true, is sufficiently large--then that means my data is mostly noise.

(4) How to estimate the error, or uncertainty Δσ?

Thanks! I am sure this is easy for you DSP types?

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# Estimate of noise statistics within some error

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