paalon/waveforms.jl

Waveform functions for Julia.

Waveforms

Waveform functions for Julia.

Documentations	Build Status	Code Coverage	License

Waveform functions library. Following functions are supported:

• Square wave

• Sawtooth wave

• Triangle wave

Installation

(@v1.9) pkg> add Waveforms

Usage

See documentations for the detail.

Waveform	2π-periodic	1-periodic
Square	squarewave	squarewave1
Sawthooth	sawtoothwave	sawtoothwave1
Triangle	trianglewave	trianglewave1

julia> using Waveforms

julia> squarewave(0.4)
1.0

julia> sawtoothwave(0.4)
0.12732395447351627

julia> trianglewave(0.4)
0.2546479089470326

julia> using UnicodePlots

julia> lineplot([squarewave, sin], -π/2, 2π)
           ┌────────────────────────────────────────┐
         1 │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢉⠟⠉⠉⢫⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ squarewave(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠊⠀⠀⠀⠀⠣⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ sin(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢱⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
   f(x)    │⠤⠤⠤⠤⠤⠤⠤⠤⢼⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤│
           │⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⡸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⡸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⡰⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣄⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀│
        -1 │⠀⢀⣀⣜⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣈⣦⣀⣠⣜⣀⣀⣀⣀⣀⠀⠀⠀│
           └────────────────────────────────────────┘
           ⠀-2⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀7⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

julia> lineplot([sawtoothwave, sin], -π/2, 2π)
           ┌────────────────────────────────────────┐
         1 │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠞⠉⠉⢢⠀⠀⠀⡰⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ sawtoothwave(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠊⠀⠀⠀⠀⠣⡠⠚⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ sin(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇⠀⠀⠀⠀⣠⠎⢱⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡜⠀⠀⠀⢀⠖⠁⠀⠀⢧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢀⠜⠁⠀⠀⠀⠀⠘⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠇⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
   f(x)    │⠤⠤⠤⠤⠤⠤⠤⠤⣼⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤│
           │⠀⠀⠀⠀⠀⠀⣠⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠇⠀⠀⠀│
           │⠀⠀⠀⠀⢠⠎⠀⡸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⡸⠀⠀⠀⠀│
           │⠀⠀⣀⠞⠁⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠀⠀⠀⠀⠀⣠⠚⠁⠀⢠⠃⠀⠀⠀⠀│
           │⠀⠐⠁⠀⠀⠀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠀⢠⠔⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⡸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣆⠴⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⡰⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡔⠛⣄⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀│
        -1 │⠀⢀⣀⠜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠋⠀⠀⠈⢦⣀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀│
           └────────────────────────────────────────┘
           ⠀-2⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀7⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

julia> lineplot([trianglewave, sin], -π/2, 2π)
           ┌────────────────────────────────────────┐
         1 │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⢞⠝⢏⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ trianglewave(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠊⡜⠀⠈⢇⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ sin(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇⡼⠀⠀⠀⠈⡆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡜⡸⠀⠀⠀⠀⠀⠈⢆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡰⠁⠀⠀⠀⠀⠀⠀⠘⣜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
   f(x)    │⠤⠤⠤⠤⠤⠤⠤⠤⢼⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤│
           │⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀│
           │⠀⠀⠀⠀⠀⠀⢠⡻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⠀⠀⠀⠀│
           │⠀⠀⠀⠀⠀⢠⢊⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢣⡀⠀⠀⠀⠀⠀⠀⢠⢣⠃⠀⠀⠀⠀│
           │⠀⠀⠀⠀⢀⠎⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢣⠀⠀⠀⠀⠀⢠⠎⡎⠀⠀⠀⠀⠀│
           │⠀⠀⠀⢀⠎⡸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢳⠀⠀⠀⢀⠇⡸⠀⠀⠀⠀⠀⠀│
           │⠀⠀⠀⡎⡰⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢣⠀⢀⠎⡜⠁⠀⠀⠀⠀⠀⠀│
        -1 │⠀⢀⣎⠜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣦⣮⠜⠀⠀⠀⠀⠀⠀⠀⠀│
           └────────────────────────────────────────┘
           ⠀-2⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀7⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

waveforms.jl's Issues

add to Registry?

a nice and convenient package. maybe add it to the General Registry?

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I'll open a PR within a few hours, please be patient!

soft transition squarewave

function squarewave1_smooth( x::Real, θ::Real) 0 ≤ θ ≤ 1 || throw( DomainError( θ, "squarewave1(x, θ) is only defined for 0 ≤ θ ≤ 1.")) ifelse( mod( x, 1) < θ, 1.0, ifelse( mod( x, 1) == θ, 0, -1.0 ) ) end

Apologies for the formatting...

Here is a squarewave1 that has a smoothed transition. This tends to be better behaved in the Fourier domain. It is a periodic rect function.

https://en.wikipedia.org/wiki/Rectangular_function

If interest I can do a pull request with squarewave_smooth and squarewave1_smooth.