Signal to Noise Ratio: Definition & Wiener Filter Calculation

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Discussion Overview

The discussion centers around the concept of signal to noise ratio (SNR) and its calculation using the Wiener filter. Participants explore the definitions, applications, and methodologies related to SNR and the Wiener filter in signal processing.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant asks for a definition of signal to noise ratio and its calculation using the Wiener filter.
  • Another participant suggests that understanding the input signal and noise characteristics is essential for calculating the output SNR after filtering.
  • A question is raised about the purpose of using the Wiener filter, specifically whether it is intended to calculate the improvement in SNR.
  • A participant describes a specific signal model and asks if the output SNR can be calculated by processing the signal through the Wiener filter taps.
  • One participant confirms that applying the filter to both the signal and noise will yield insights into the output SNR.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the Wiener filter and its application to SNR calculations. There is no consensus on the specific methodology for calculating the output SNR, as questions remain about the approach and assumptions involved.

Contextual Notes

Participants do not fully agree on the definitions or methods for calculating SNR, and there are unresolved questions about the specific characteristics of the signal and noise being processed.

Who May Find This Useful

This discussion may be useful for individuals interested in signal processing, particularly those looking to understand the application of Wiener filters in relation to signal to noise ratio calculations.

cutesteph
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What is signal to noise ratio ? And how do I calculate it with the wiener filter?
 
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You need to know how the signal and the noise look like at the filter input and calculate what they will be at the output.
Usually a signal has a narrow spectrum, while the noise has a broad (almost flat) spectrum.
Apply a filter to that and see how much power is in signal and how much is in noise at the output of the filter.
 
What are you using the filter to do? Since a wiener filter can be used to improve signal to noise, are you actually trying to calculate the signal to noise ratio improvement by your filter?

Do you understand wiener design? Do you understand this? http://en.wikipedia.org/wiki/Wiener_filter
 
I am using it to process a signal say x(n) = sin(nw+theta) +w(n) where w(n) is random noise and say I use a 2 and 3 tap and get wiener values …. [.5 ; -.4] and [-6 ; 15; -5] (note: these are not actual values). I want to calculate the SNR of the interference and SNR of the output. Is the SNR of the output just processing x(n) through each filter i.e. 1/(1-.5z^-1) and then 1/(z-.4z^-1)?
 
Yes, apply the filter on the signal (sin(...)) and the noise (w) and see what happens.
 

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