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//@version=5
indicator('DFT', overlay=true)
import jdehorty/KernelFunctions/2 as kernel
// INPUTS
N = input.int(10,"Fourier Period")
xval = input.source(close,"Fourier X Series",tooltip = "i.e. the source of the discrete Fourier"+
" transform (with the Y Series being the bars through time.)")
highlighting = input.bool(true,"Highlighting")
smoothing = input.int(10,"Kernel Smoothing")
DFT(x, y, Nx, _dir) =>
float _arg = 0.0
float _cos = 0.0
float _sin = 0.0
float xArr_i = 0.0
float yArr_i = 0.0
xArr = array.new_float(array.size(x))
yArr = array.new_float(array.size(y))
for i = 0 to Nx - 1 by 1
xArr_i := 0.0
yArr_i := 0.0
kx = float(i) / float(Nx)
_arg := -_dir * 2 * math.pi * kx
for k = 0 to Nx - 1 by 1
_cos := math.cos(k * _arg)
_sin := math.sin(k * _arg)
xArr_i += array.get(x, k) * _cos - array.get(y, k) * _sin
yArr_i += array.get(x, k) * _sin + array.get(y, k) * _cos
yArr_i
array.set(xArr, i, xArr_i)
array.set(yArr, i, yArr_i)
if _dir == 1
for i = 0 to Nx - 1 by 1
array.set(x, i, array.get(xArr, i) / float(Nx))
array.set(y, i, array.get(yArr, i) / float(Nx))
else
for i = 0 to Nx - 1 by 1
array.set(x, i, array.get(xArr, i))
array.set(y, i, array.get(yArr, i))
// CALCULATIONS
// Fourier transform
x = array.new_float(N, 0.0)
y = array.new_float(N, 0.0)
for i = 0 to N - 1
array.set(x, i, xval[i])
array.set(y, i, 0.0)
DFT(x, y, N, 1)
mag = array.new_float(N, 0.0)
for i = 0 to N - 1
mag_i = math.sqrt(math.pow(array.get(x, i), 2) + math.pow(array.get(y, i), 2))
array.set(mag, i, mag_i)
dft = array.get(mag,0)
dfts = kernel.rationalQuadratic(dft,25,1,smoothing)
// DISPLAY
ft = plot(dft, "DFT", color= color.white)
fts = plot(dfts, "Smoothing", color = dfts > dft ? color.red : color.lime)
fill(ft,fts,color = highlighting and dfts > dft ? color.new(color.red,75) : highlighting and dfts < dft ? color.new(color.lime,75) : na)
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2025-10-27 14:42:24