John F. Ehlers - Convolution: Free TradingView Indicator (Pine Script)

Add It to Your TradingView Chart

1Copy the scriptPress Copy script above, or the copy button on the code below.
2Open the Pine EditorOpen a TradingView chart and choose Pine Editor at the bottom of the screen.
3Paste over the templateCreate a new indicator, select all of the template text and paste. Press Save and give it a name.
4Add it to the chartPress Add to chart, then adjust the settings with the gear icon next to its name.

Source Code

170 lines of Pine Script v5 from indicator/convolution.pine, published under MPL-2.0 (file header). Keep the author's credit and licence lines when you reuse it.

convolution.pine

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © palitoj_endthen

//@version=5
indicator(title = 'John F. Ehlers - Convolution', shorttitle = 'convolution', overlay = false)

// input
src = input.source(defval = ohlc4, title = 'Source', group = 'Options', tooltip = 'Determines the source of input data', inline = 'f')
apply_hp = input.bool(defval = false, title = 'High-Pass Filter', group = 'Options', tooltip = 'Determines whether to apply High-Pass filter', inline = 'f')


// variable
shortest_period = 40
longest_period = 80
alpha1 = 0.00
hp = 0.00
a1 = 0.00
b1 = 0.00
c1 = 0.00
c2 = 0.00
c3 = 0.00
filt = 0.00
x = 0.00
y = 0.00
sx = 0.00
sy = 0.00
sxx = 0.00
syy = 0.00
sxy = 0.00


// array
var corr = array.new_float(50)
var slope = array.new_float(50)
var convolution = array.new_float(50)


// convolution
// high-pass filter cyclic components whose periods are shorter than 48 bars
alpha1 := (math.cos(1.414*360/longest_period)+math.sin(1.414*360/longest_period)-1)/math.cos(1.414*360/longest_period)
hp := (1-alpha1/2)*(1-alpha1/2)*(src-2*src[1]+src[2])+2*(1-alpha1)*nz(hp[1])-(1-alpha1)*(1-alpha1)*nz(hp[2])

// smooth with super smoother filter
pi = 2*math.asin(1)
a1 := math.exp(-1.414*pi/shortest_period)
b1 := 2*a1*math.cos(1.414*180/shortest_period)
c2 := b1
c3 := -a1*a1
c1 := 1-c2-c3
filt := c1*((apply_hp?hp:src)+(apply_hp?hp[1]:src[1]))/2+c2*nz(filt[1])+c3*nz(filt[2])

// convolution
for i = 1 to 48
    sx := 0.0
    sy := 0.0
    sxx := 0.0
    syy := 0.0
    sxy := 0.0
    for ii = 1 to i
        x := filt[ii-1]
        y := filt[i-ii]
        sx := sx+x
        sy := sy+y
        sxx := sxx+x*x
        sxy := sxy+x*y
        syy := syy+y*y
    if (i*sxx-sx*sx)*(i*syy-sy*sy) > 0
        array.set(corr, i, ((i*sxy-sx*sy) /math.sqrt((i*sxx-sx*sx)*(i*syy-sy*sy))))
    array.set(slope, i, 1)
    if filt[.5*i] < filt
        array.set(slope, i, -1)
    array.set(convolution, i, (1+math.exp(3*nz(array.get(corr, i))))-1/(math.exp(3*nz(array.get(corr, i))-1))/2)


// visualize as heatmap
// color condition
col(n)=>
    if array.get(slope, n) > 0
        color.rgb((255*array.get(convolution, n)), 0, 0)
    else if array.get(slope, n) < 0
        color.rgb(0, (255*array.get(convolution, n)), 0)

// plot
n = 0
n := 2
plot(n, title = 'n2', color = col(n), linewidth = 8)

n := 3
plot(n, title = 'n3', color = col(n), linewidth = 8)

n := 4
plot(n, title = 'n4', color = col(n), linewidth = 8)

n := 6
plot(n, title = 'n6', color = col(n), linewidth = 8)

n := 8
plot(n, title = 'n8', color = col(n), linewidth = 8)

n := 10
plot(n, title = 'n10', color = col(n), linewidth = 8)

n := 11
plot(n, title = 'n11', color = col(n), linewidth = 8)

n := 12
plot(n, title = 'n12', color = col(n), linewidth = 8)

n := 14
plot(n, title = 'n14', color = col(n), linewidth = 8)

n := 16
plot(n, title = 'n16', color = col(n), linewidth = 8)

n := 18
plot(n, title = 'n18', color = col(n), linewidth = 8)

n := 20
plot(n, title = 'n20', color = col(n), linewidth = 8)

n := 21
plot(n, title = 'n21', color = col(n), linewidth = 8)

n := 22
plot(n, title = 'n22', color = col(n), linewidth = 8)

n := 24
plot(n, title = 'n24', color = col(n), linewidth = 8)

n := 26
plot(n, title = 'n26', color = col(n), linewidth = 8)

n := 28
plot(n, title = 'n28', color = col(n), linewidth = 8)

n := 30
plot(n, title = 'n30', color = col(n), linewidth = 8)

n := 31
plot(n, title = 'n31', color = col(n), linewidth = 8)

n := 32
plot(n, title = 'n32', color = col(n), linewidth = 8)

n := 34
plot(n, title = 'n34', color = col(n), linewidth = 8)

n := 36
plot(n, title = 'n36', color = col(n), linewidth = 8)

n := 38
plot(n, title = 'n38', color = col(n), linewidth = 8)

n := 40
plot(n, title = 'n40', color = col(n), linewidth = 8)

n := 41
plot(n, title = 'n41', color = col(n), linewidth = 8)

n := 42
plot(n, title = 'n42', color = col(n), linewidth = 8)

n := 44
plot(n, title = 'n44', color = col(n), linewidth = 8)

n := 46
plot(n, title = 'n46', color = col(n), linewidth = 8)

n := 48
plot(n, title = 'n48', color = col(n), linewidth = 8)

Overview

Ehlers' convolution algorithm to detect cyclic components across multiple periods. The script processes price data using a SuperSmoother filter with an optional high-pass filter to remove low-frequency trends. It computes cross-correlations across up to 48 lookback bars and renders the output as a multi-tier heatmap in a separate pane, where red and green intensities reflect convolution magnitude and directional slope.

John Ehlers convolution algorithm
SuperSmoother filter smoothing
Optional high-pass filter toggle
Multi-period heatmap visualization

Details

Published by

palitojendthen on GitHub

Type

Indicator, Pine Script v5

Draws

Separate pane below the chart

Markets

Any symbol

Timeframes

Any timeframe

Risk Notes

No repainting, lookahead or stacked entries were found in its code or README. That says nothing about how well it works: test it first.

File

indicator/convolution.pine

Repository

github.com/palitojendthen/pinescript. See its other scripts in the library

Topics

indicatortechnical-analysispinescripttrading-algorithms

Settings

The inputs you can change from the gear icon on the chart. Defaults are the author's.

Setting	Type	Default	Variable
Source	`source`	`ohlc4`	`src`
High-Pass Filter	`bool`	`false`	`apply_hp`

Third-party code. ForexR did not write, test or endorse this script, and the summary above was generated automatically from its code and README. Indicators describe the past, and a strategy's backtest can look better than live trading, especially when a script repaints. Check it in the Strategy Tester and on a demo account before you rely on it.

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