QuantizedNoise

This package provide the function randqn that generate random values from the normal distribution 𝒩(μ,σ²) quantized to Integer and Complex{<:Integer>} types. Usage is pretty much the same as Base.randn except for the addition of σ and µ keyword arguments for the desired standard deviation and mean. If unspecified, σ defaults to 1.0 and µ defaults to 0.0. The keywords std and mean may be used instead of σ and µ, respectively.

randqn([rng,] T::Type{<:Integer}, dims::Integer...; σ=1.0, µ=0.0)
randqn([rng,] T::Type{<:Integer}, dims::Integer...; std=1.0, mean=0.0)
randqn([rng,] ::Type{<:Complex{T}}, dims::Integer...; σ=1.0, µ=0.0) where T<:Integer
randqn([rng,] ::Type{<:Complex{T}}, dims::Integer...; std=1.0, mean=0.0) where T<:Integer

Generate samples from the normal distribution 𝒩(μ,σ²) quantized and clamped to the Integer subtype T. Note that the σ and μ are properties of the distribution from which the samples are drawn. They are not necessarily properties of the returned samples. For example, quantization will alter the standard deviation of the output values, so std(randqn(Int8, 10^6, std=x)) may be quite different from x, especially as x approaches (and exceeds) typemax(T). Keyword arguments std and mean may be used instead of σ and μ, resp. If both forms are used, the single character keyword argument takes precedence.

For complex types, the standard deviation σ or std may be given as a Real or Complex. If σ is given as a Real, it specifies the standard deviation of the complex values (i.e. each real/imaginary component will have a standard deviarion of σ/sqrt(2)). If given as a Complex, each real/imaginary component of σ will be the standard deviation of the corresponding components of the output. Note that σ=1.0 is equivalent to σ=(1+1im)/sqrt(2). Likewise, if µ is a Real, the complex mean will be µ+µ*im.

julia> using QuantizedNoise

julia> randqn(Int8, std=13)
25

julia> randqn(Int8, 2, 3, σ=13)
2×3 Matrix{Int8}:
  97  108  89
 100   97  98

julia> randqn(Int8, 2, 3, σ=10, µ=100)
2×3 Matrix{Int8}:
 104  101  99
  83   94  94

julia> randqn(Complex{Int8}, 2, 3, σ=30)
2×3 Matrix{Complex{Int8}}:
   6-17im  -29-48im  -19+11im
 -31+18im    1+9im   -37+22im

Until this becomes part of Julia's global registry, this package can be installed from the Julia REPL by:

using Pkg
Pkg.add("https://github.com/david-macmahon/QuantizedNoise.jl")

...or...

]add https://github.com/david-macmahon/QuantizedNoise.jl