PINE LIBRARY

aprox

Updated

Library "aprox"
It's a library of the aproximations of a price or Series float it uses Fourier transform and
Euler's Theoreum for Homogenus White noice operations. Calling functions without source value it automatically take close as the default source value.

Copy this indicator to see how each approximations interact between each other.
https://www.tradingview.com/x/PWkSg4Qo/

Pine Script®

DFT3(xval, _dir)
Parameters:
xval (float)
_dir (int)

Pine Script®

DFT2(xval, _dir)
Parameters:
xval (float)
_dir (int)

Pine Script®

FFT(xval)
FFT: Fast Fourier Transform
Parameters:
xval (float)
Returns: Aproxiated source value

Pine Script®

DTF32(xval)
DTF32: Combined Discrete Fourier Transforms
Parameters:
xval (float)
Returns: Aproxiated source value

Pine Script®

whitenoise(indic_, _devided, minEmaLength, maxEmaLength, src)
whitenoise: Ehler's Universal Oscillator with White Noise, without extra aproximated src
Parameters:
indic_ (float)
_devided (int)
minEmaLength (int)
maxEmaLength (int)
src (float)
Returns: Smoothed indicator value

Pine Script®

whitenoise(indic_, dft1, _devided, minEmaLength, maxEmaLength, src)
whitenoise: Ehler's Universal Oscillator with White Noise and DFT1
Parameters:
indic_ (float)
dft1 (float)
_devided (int)
minEmaLength (int)
maxEmaLength (int)
src (float)
Returns: Smoothed indicator value

Pine Script®

smooth(dft1, indic__, _devided, minEmaLength, maxEmaLength, src)
smooth: Smoothing source value with help of indicator series and aproximated source value
Parameters:
dft1 (float)
indic__ (float)
_devided (int)
minEmaLength (int)
maxEmaLength (int)
src (float)
Returns: Smoothed source series

Pine Script®

smooth(indic__, _devided, minEmaLength, maxEmaLength, src)
smooth: Smoothing source value with help of indicator series
Parameters:
indic__ (float)
_devided (int)
minEmaLength (int)
maxEmaLength (int)
src (float)
Returns: Smoothed source series

Pine Script®

vzo_ema(src, len)
vzo_ema: Volume Zone Oscillator with EMA smoothing
Parameters:
src (float)
len (simple int)
Returns: VZO value

vzo_sma(src, len)
vzo_sma: Volume Zone Oscillator with SMA smoothing
Parameters:
src (float)
len (int)
Returns: VZO value

vzo_wma(src, len)
vzo_wma: Volume Zone Oscillator with WMA smoothing
Parameters:
src (float)
len (int)
Returns: VZO value

alma2(series, windowsize, offset, sigma)
alma2: Arnaud Legoux Moving Average 2 accepts sigma as series float
Parameters:
series (float)
windowsize (int)
offset (float)
sigma (float)
Returns: ALMA value

Wavelet(src, len, offset, sigma)
Wavelet: Wavelet Transform
Parameters:
src (float)
len (int)
offset (simple float)
sigma (simple float)
Returns: Wavelet-transformed series

Pine Script®

Wavelet_std(src, len, offset, mag)
Wavelet_std: Wavelet Transform with Standard Deviation
Parameters:
src (float)
len (int)
offset (float)
mag (int)
Returns: Wavelet-transformed series

Pine Script®

Release Notes

v2

Added:
DFT32(xval)
DFT32 Combined Discrete Fourier Transforms of DFT3 and DTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
Parameters:
xval (float): Array of input values
Returns: Aproxiated source value

Updated:
DFT3(xval, _dir)
DFT3 Discrete Fourier Transform with last 3 points
Parameters:
xval (float)
_dir (int): Direction parameter
Returns: Aproxiated source value

DFT2(xval, _dir)
DFT2 Discrete Fourier Transform with last 2 points
Parameters:
xval (float)
_dir (int): Direction parameter
Returns: Aproxiated source value

FFT(xval)
FFT Fast Fourier Transform once. It aproximates usig last 3 points.
Parameters:
xval (float): Array of input values
Returns: Aproxiated source value

whitenoise(indic_, dft1, _devided, minEmaLength, maxEmaLength, src)
whitenoise Ehler's Universal Oscillator with White Noise and DFT1.
It uses src and sproxiated src (dft1) to clearly define white noice.
It uses dinamic EMA to aproximate indicator and thus reducing noise.
Parameters:
indic_ (float): Input series for the indicator values to be smoothed
dft1 (float): Aproximated src value for white noice calculation
_devided (int): Divisor for oscillator calculations
minEmaLength (int): Minimum EMA length
maxEmaLength (int): Maximum EMA length
src (float): Source series
Returns: Smoothed indicator value

smooth(indic__, _devided, minEmaLength, maxEmaLength, src)
smooth Smoothing source value with help of indicator series
It uses dinamic EMA to aproximate src and thus reducing noise.
Parameters:
indic__ (float): Optional input for indicator to help smooth dft1 (default is FFT)
_devided (int): Divisor for smoothing calculations
minEmaLength (int): Minimum EMA length
maxEmaLength (int): Maximum EMA length
src (float): Source series
Returns: Smoothed src series

vzo_ema(src, len)
vzo_ema Volume Zone Oscillator with EMA smoothing
Parameters:
src (float): Source series
len (simple int): Length parameter for EMA
Returns: VZO value

vzo_sma(src, len)
vzo_sma Volume Zone Oscillator with SMA smoothing
Parameters:
src (float): Source series
len (int): Length parameter for SMA
Returns: VZO value

vzo_wma(src, len)
vzo_wma Volume Zone Oscillator with WMA smoothing
Parameters:
src (float): Source series
len (int): Length parameter for WMA
Returns: VZO value

alma2(series, windowsize, offset, sigma)
alma2 Arnaud Legoux Moving Average 2 accepts sigma as series float
Parameters:
series (float): Input series
windowsize (int): Size of the moving average window
offset (float): Offset parameter
sigma (float): Sigma parameter
Returns: ALMA value

Wavelet(src, len, offset, sigma)
Wavelet Wavelet Transform
Parameters:
src (float): Source series
len (int): Length parameter for ALMA
offset (simple float)
sigma (simple float)
Returns: Wavelet-transformed series

Wavelet_std(src, len, offset, mag)
Wavelet_std Wavelet Transform with Standard Deviation
Parameters:
src (float): Source series
len (int): Length parameter for ALMA
offset (float): Offset parameter for ALMA
mag (int): Magnitude parameter for standard deviation
Returns: Wavelet-transformed series

Removed:
DTF32(xval)
DTF32: Combined Discrete Fourier Transforms

Release Notes

v3

Added:
DTF32(xval)
DFT32: Combined Discrete Fourier Transforms of DFT3 and DTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
Parameters:
xval (float): Array of input values
Returns: Aproxiated source value

Updated:
DFT3(xval, _dir)
DFT3: Discrete Fourier Transform with last 3 points
Parameters:
xval (float)
_dir (int): Direction parameter
Returns: Aproxiated source value

DFT2(xval, _dir)
DFT2: Discrete Fourier Transform with last 2 points
Parameters:
xval (float)
_dir (int): Direction parameter
Returns: Aproxiated source value

FFT(xval)
FFT: Fast Fourier Transform once. It aproximates usig last 3 points.
Parameters:
xval (float): Array of input values
Returns: Aproxiated source value

DFT32(xval)
DFT32: Combined Discrete Fourier Transforms of DFT3 and DTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
Parameters:
xval (float): Array of input values
Returns: Aproxiated source value

whitenoise(indic_, dft1, _devided, minEmaLength, maxEmaLength, src)
whitenoise: Ehler's Universal Oscillator with White Noise and DFT1.
It uses src and sproxiated src (dft1) to clearly define white noice.
It uses dinamic EMA to aproximate indicator and thus reducing noise.
Parameters:
indic_ (float): Input series for the indicator values to be smoothed
dft1 (float): Aproximated src value for white noice calculation
_devided (int): Divisor for oscillator calculations
minEmaLength (int): Minimum EMA length
maxEmaLength (int): Maximum EMA length
src (float): Source series
Returns: Smoothed indicator value

smooth(indic__, _devided, minEmaLength, maxEmaLength, src)
smooth: Smoothing source value with help of indicator series
It uses dinamic EMA to aproximate src and thus reducing noise.
Parameters:
indic__ (float): Optional input for indicator to help smooth dft1 (default is FFT)
_devided (int): Divisor for smoothing calculations
minEmaLength (int): Minimum EMA length
maxEmaLength (int): Maximum EMA length
src (float): Source series
Returns: Smoothed src series

vzo_ema(src, len)
vzo_ema: Volume Zone Oscillator with EMA smoothing
Parameters:
src (float): Source series
len (simple int): Length parameter for EMA
Returns: VZO value

vzo_wma(src, len)
vzo_wma: Volume Zone Oscillator with WMA smoothing
Parameters:
src (float): Source series
len (int): Length parameter for WMA
Returns: VZO value

alma2(series, windowsize, offset, sigma)
alma2: Arnaud Legoux Moving Average 2 accepts sigma as series float
Parameters:
series (float): Input series
windowsize (int): Size of the moving average window
offset (float): Offset parameter
sigma (float): Sigma parameter
Returns: ALMA value

Wavelet(src, len, offset, sigma)
Wavelet Wavelet Transform: aproxiates srt using Discrete wavelet transform.
Parameters:
src (float): Source series
len (int): Length parameter for ALMA
offset (simple float)
sigma (simple float)
Returns: Wavelet-transformed series

Wavelet_std(src, len, offset, mag)
Wavelet_std: aproxiates srt using Discrete wavelet transform with standard deviation as a magnitude.
Parameters:
src (float): Source series
len (int): Length parameter for ALMA
offset (float): Offset parameter for ALMA
mag (int): Magnitude parameter for standard deviation
Returns: Wavelet-transformed series

AutomatedTradingAlgorithms

Automated Trading Algorithms: discord.gg/xuKHyhPKS6
Tutorials-YouTube: youtube.com/channel/UCJH8wJ8Ab_O-HTb0wrrtAKQ

Mathematical papers:
algoalert.net/pdfs/fourier.pdf
algoalert.net/pdfs/IEEEwavelet.pdf

Pine library

In true TradingView spirit, the author has published this Pine code as an open-source library so that other Pine programmers from our community can reuse it. Cheers to the author! You may use this library privately or in other open-source publications, but reuse of this code in a publication is governed by House rules.

Disclaimer

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