AIS Ind Basic Window Functions

Various window functions can be used to smooth time series. Window functions can be quite different from each other in their characteristics - the level of smoothing, noise suppression, etc. This indicator allows you to implement the main window functions and evaluate their performance on financial time series.

Indicator parameters:

• iPeriod – indicator period. iPeriod >= 2
• iCenter is the index of the reference where the center of the window function will be located. By default, this parameter is 0 - the center of the window coincides with the center of the indicator. With 1 <= iCenter <= iPeriod, the center of the window function will be shifted, as a result of which some characteristics of the indicator will change. In Figure 1, you can see how the choice of the center affects the window function and the display of the indicator. This parameter can be changed in increments of 0.5.

Some window functions use additional parameters - ParameterA and ParameterB. They affect the window weights. Because of this, the characteristics of the indicator change. The table shows the window functions and the limits for changing parameters if they are used. The distribution of window function weights for given parameters can be estimated using the script https://www.mql5.com/ru/market/product/72156

Window	Parameter A	Parameter B
Bartlett - Hann window
Blackman window
Blackman window exact
Blackman – Harris window
Blackman – Harris window approx.
Blackman – Harris window corr.
Blackman - Harris window opt.
Blackman – Harris window ref.
Blackman - Nuttall window
Bohman window
Cauchy window	0 <= ParameterA
Connes window	1 < = ParameterA
Cosine gen. window 1st	0 <= ParameterA <= 100
Cosine gen. window 2nd	0 <= ParameterA <= 100
Dolph - Chebyshev window	0 <= ParameterA
Flat Top window
Flat Top window approx.
Gauss window	1 < = ParameterA <= 2*iPeriod
Gauss window approx.	1 < = ParameterA <= 2*(iPeriod+1)
Gauss window conf.	1 < = ParameterA <= 2*(iPeriod+1)
Gauss window gen.	1 < = ParameterA <= 2*iPeriod	0 <= ParameterB
Hamming window
Hamming window opt.
Hann window
Hann double window
Hann - Poisson window	0 <= ParameterA
Hyperbolic tangent window	0 <= ParameterA	0 <= ParameterB
Kaiser window	0 <= ParameterA
Kaiser - Bessel window	0 <= ParameterA
Kaiser – Bessel window approx.
Karre window
Lanczos window
Lanczos kernel window	1 <= ParameterA
Log window	1 <= ParameterA
Logistic window
Modified cosine window
Nuttall's window
Parzen window
Planck - Bessel window	0 < = ParameterA <= iPeriod/2	0 <= ParameterB
Plank-taper window	0 < = ParameterA <= iPeriod/2
Poisson window	0 <= ParameterA
Rectangular window
Rife – Vincent 3rd window
Rife – Vincent 4th window
Silverman window	1 <= ParameterA
Sinusoidal windows	0 <= ParameterA
Smoothed rectangular window	0 < = ParameterA <= iPeriod/2
Stepped window	0 <= ParameterA
Triangular window	0 < = ParameterA
Tukey window	0 < = ParameterA <= iPeriod/2
Welch window	1 <= ParameterA