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STD/C-Filtered, Power-of-Cosine FIR Filter [Loxx]

STD/C-Filtered, Power-of-Cosine FIR Filter [Loxx] is a Discrete-Time, FIR Digital Filter that uses Power-of-Cosine Family of FIR filters. This indicator also includes a clutter and standard deviation filter.

Amplitudes

What are FIR Filters?
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several window functions can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multipying the given sampled signal by the window function. For trading purposes, these FIR filters act as advanced weighted moving averages.

What is Power-of-Sine Digital FIR Filter?

Also called Cos^alpha Window Family. In this family of windows, changing the value of the parameter alpha generates different windows.

f(n) = math.cos(alpha) * (math.pi * n / N) , 0 ≤ |n| ≤ N/2

where alpha takes on integer values and N is a even number

General expanded form:

alpha0 - alpha1 * math.cos(2 * math.pi * n / N)
+ alpha2 * math.cos(4 * math.pi * n / N)
- alpha3 * math.cos(4 * math.pi * n / N)
+ alpha4 * math.cos(6 * math.pi * n / N)
- ...

Special Cases for alpha:

alpha = 0: Rectangular window, this is also just the SMA (not included here)
alpha = 1: MLT sine window (not included here)
alpha = 2: Hann window (raised cosine = cos^2)
alpha = 4: Alternative Blackman (maximized roll-off rate)

For this indicator, I've included alpha values from 2 to 16

What is a Standard Devaition Filter?
If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering.

What is a Clutter Filter?
For our purposes here, this is a filter that compares the slope of the trading filter output to a threshold to determine whether to shift trends. If the slope is up but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. If the slope is down but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. Alternatively if either up or down slope exceeds the threshold then the trend turns green for up and red for down. Fro demonstration purposes, an EMA is used as the moving average. This acts to reduce the noise in the signal.

Included