noises gets added therefore it is additive
which make me think that noises are not destructive
simple thought experiment: You flip a fair coin $X$ (Head = -1 / Tail = 1) and tell me the result. The entropy here is 1 bit, i.e. the (expected) information ($I(X=\xi) = -\log_2 \left[P(X=\xi)\right]$) of each outcome is 1 bit.
The SNR is simply the mean-square of a demodulated symbol divided by the variance of the signal, or in dB:
A typical metric for this in receiver equipment is the Error Vector Magnitude (EVM) where an "error vector" is the Euclidean distance from the ...
OP clarified that the question in the comments as follows:
If we ignore any modulation for now and assume that we are receiving
pure tones plus the band limited noise and we try to improve the SNR
in post processing how much improvement can we expect by oversampling
and is there a limit to it? My original question was about this
First consider the ...
If sensor A has a defect, the clear answer is to only use sensor B.
A preferred solution to minimize noise would be to do a weighted average based on the quality of each sensor, when that can be actively characterized. This can be easily done for the case the OP has presented of taking a reading from a single rotating axis.
The optimum combining for the ...
It's always better to have one more sensor, even if it's a lot noiser or distorted etc., provided that you can sufficiently model its characteristics, and the added circuit complexity is of no concern.
If you cannot mathematically characterise how bad the added sensor is, and instead treat it as if it was good one, then you will degrade your performance, ...
To complement Marcus' answer:
Say you have a resistor (nothing is connected to it) at a certain temperature above absolute zero. The heat causes electrons to move around at random, creating a random current. This current through the resistor creates a random voltage.
If you connect a sensitive-enough voltmeter to the resistor, you can detect this voltage -- ...
Poisson noise estimation can be complicated. I remember two papers, doing that in a wavelet domain. I still have some Matlab code for the oldest one, if needed:
Poisson Intensity Estimation Based on Wavelet Domain Hypothesis Testing (2006)
In this paper, we present the estimation of Poisson intensity based on
hypothesis testing in the wavelet domain for any ...
Here are two papers that deal with generic sensor fusion under unknown statistics:
Multiple sensor fusion under unknown distributions, Journal of the Franklin Institute, 1999
On fusers that perform better than best sensor, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001
Since your domain for the parameters is limited (Only 9 options) the best way for White Noise would be going through them and pick then one with the least Mean Squared Error (MSE) which is the parameter to minimize for AWGN.
in MATLAB it will be something like:
function [ paramAlpha, paramBeta ] = EstimateModelParameters( vT, vY )
vParamAlpha = [1, 2, 3];
Let's not get too in the weeds of using bits or noise densities to determine your minimum detectable signal (MDS) just yet. What you're asking is a more fundamental question about determining what value (in terms of SNR) you need to declare a detection. The answer to the question "What SNR do I need in order to detect a signal in noise?" is ...
My suggestion: find the center, calculate the distance of each pixel to the center. If a given distance is too (above threshold) different from the neighborhood then it's a defect.
Other possibility is to fit a figure model if you always have the same shape and then calculate the error.
Couple of approaches come to mind: you could pick an arbitrary "first" red pixel, then take a square of say 5×5 pixels around it, and simply figure out which quadratic function is a best fit for these, and infer the curvature from that.
Pick an arbitrary direction to start from that point and pick the next pixels; calculate the curvature of the 5×5 ...
You need to invert the filter, i.e. flip the poles and zeros.
The implementation that you reference is fairly awkward and will require a decent amount of math work to invert: you need to write the Z-transform for each first order section, add all the fractions into a single fraction and calculate the zeros of numerator polynomial.
An easier way would be to ...
It's just a matter of finding out the assumptions behind the equation. Sometimes, unfortunately, those assumptions are not made explicit.
For the first equation you present, the one you have issues with, the assumptions are (off the top of my head):
Orthogonal, ideal sinc pulses are used as pulse shape.
The signals involved are strictly baseband, or, if ...
The simplest approach would be to implement a filter using scipy.signal.lfilter, where plenty of documentation exists in python on how to use that function.
To do this effectively you need to first define the signal bandwidth of interest relative to the sampling rate. As long as the sampling rate is sufficiently more than twice the bandwidth, there will be ...
When referring to the SNR achieved by oversampling, we have to be careful in using the term "SNR". There are essentially two SNR's to consider:
The SNR that is the signal-to-quantization-noise ratio.
The SNR that is your signal-to-noise ratio. Here the noise is produced by your system. For simplicity this can be modeled by the kTB relation that ...