Wire-Cell Noise Model
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Table of Contents
1. Overview
WCT provides a “sampled spectrum noise model” which is parametererized by two types of information:
- A set of “median noise spectra”.
- An associative mapping between channel and spectrum.
The WCT implementation is structured into two layers.
- A “model” component provides a median noise spectrum given a key (channel or group).
- An “adder” component generates a noise waveform and associates it to one or more channels.
2. Noise generation
The kernel of the noise generation returns a fluctuated noise waveform given a real-valued median amplitude spectrum. Median and not mean is the proper statistic to supply. The sampling of the distribution characterized by the median spectrum has two steps.
- Each frequency bin of the median spectrum is fluctuated to produce a complex amplitude sample.
- An inverse discrete Fourier transform is applied to the spectrum of samples to produce the noise waveform.
The fluctuation at each frequency is produced by twice sampling a Gaussian distribution of mean zero and sigma equal to the median. These samples form the real and imaginary part of a complex valued spectral sample. Equivalently, such samples have Rayleigh-distributed complex amplitude and uniform-distributed complex phase. This sampling motivates supplying a median and not a mean spectrum.
3. Noise adders
There are two types of noise adders:
IncoherentAddNoise- adds an independent noise waveform to each channel. The
AddNoisetype is an alias for this type. CoherentAddNoise- adds an independent noise waveform to each in a group of channels.
4. Noise spectrum models
There are two types of noise spectrum models:
4.1. EmpiricalNoiseModel
This spectral model associates an initial median spectrum and a set of post-hoc transformations of that spectrum to a channel. It expects as input a set of initial median spectra each of which are identified by a plane number and a wire length and summary information. The post-hoc transformations are the following:
- The initial spectrum for a given channel is formed as the interpolation between provided spectra based on their total wire lengths and that of the channel.
- An additional white-noise component may be specified for each input spectrum, this too is subject to wire-length interpolation.
- A pair of gain and shaping time values may be associated with an input spectrum and a different pair with each channel and the spectrum will be transformed accordingly.
The EmpiricalNoiseModel spectrum model may only be used with the IncoherentAddNoise noise adder.
4.2. GroupNoiseModel
This spectral model associates a channel to a group and a group to a spectrum. No post-hoc wire-length interpolations nor any transformations are performed on the input spectra.
This spectrum model may be used with IncoherentAddNoise and CoherentAddNoise