STD/C-Filtered, Power-of-Cosine FIR Filter [Loxx]STD/C-Filtered, Power-of-Cosine FIR Filter 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
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
Clutter
STD/C-Filtered, Truncated Taylor Family FIR Filter [Loxx]STD/C-Filtered, Truncated Taylor Family FIR Filter is a FIR Digital Filter that uses Truncated Taylor Family of Windows. Taylor functions are obtained by adding a weighted-cosine series to a constant (called a pedestal). A simpler form of these functions can be obtained by dropping some of the higher-order terms in the Taylor series expansion. If all other terms, except for the first two significant ones, are dropped, a truncated Taylor function is obtained. This is a generalized window that is expressed as:
(1 + K) / 2 + (1 - K) / 2 * math.cos(2.0 * math.pi *n / N) where 0 ≤ |n| ≤ N/2
Here k can take the values in the range 0≤k≤1. We note that the Hann 0 ≤ |n| ≤ window is a special case of the truncated Taylor family with k = 0 and Rectangular 0 ≤ |n| ≤ window (SMA) is a special case of the truncated Taylor family with k = 1.
Truncated Taylor Family of Windows amplitudes for this indicator with K = 0.5
This indicator also includes Standard Deviation and Clutter filtering.
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
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
STD/Clutter-Filtered, Kaiser Window FIR Digital Filter [Loxx]STD/Clutter-Filtered, Kaiser Window FIR Digital Filter is an is FIR digital filter using Kaiser Windowing. I've also included a clutter filter to reduce signal noise.
What is a Kaiser Window?
The Kaiser window, also known as the Kaiser–Bessel window, was developed by James Kaiser at Bell Laboratories. It is a one-parameter family of window functions used in finite impulse response filter design and spectral analysis. The Kaiser window approximates the DPSS window which maximizes the energy concentration in the main lobe but which is difficult to compute. Kaiser windowing strikes a balance among the various conflicting goals of amplitude accuracy, side lobe distance, and side lobe height. Choosing this window will often reveal signals close to the noise floor that other windows may obscure. For this reason, many spectrum analyzers default to this window. For our purposes here, we use a the Kaiser–Bessel-derived (KBD) window, which is designed to be suitable for use with the modified discrete cosine transform (MDCT).
You can read more here: The Io-sinh function, calculation of Kaiser windows and design of FIR filters
Kaiser Window Amplitudes (not the default settings)
What is a Finite Impulse Response Filter?
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
Ultra Low Lag Moving Average's weights are designed to have MAXIMUM possible smoothing and MINIMUM possible lag compatible with as-flat-as-possible phase response.
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
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
Realed Indicators
STD/Clutter Filtered, One-Sided, N-Sinc-Kernel, EFIR Filt
STD- and Clutter-Filtered, Non-Lag Moving Average
Clutter-Filtered, D-Lag Reducer, Spec. Ops FIR Filter
STD-Filtered, Ultra Low Lag Moving Average
STD/Clutter Filtered, One-Sided, N-Sinc-Kernel, EFIR Filt [Loxx]STD/Clutter Filtered, One-Sided, N-Sinc-Kernel, EFIR Filt is a normalized Cardinal Sine Filter Kernel Weighted Fir Filter that uses Ehler's FIR filter calculation instead of the general FIR filter calculation. This indicator has Kalman Velocity lag reduction, a standard deviation filter, a clutter filter, and a kernel noise filter. When calculating the Kernels, the both sides are calculated, then smoothed, then sliced to just the Right side of the Kernel weights. Lastly, blackman windowing is used for our purposes here. You can read about blackman windowing here:
Blackman window
Advantages of Blackman Window over Hamming Window Method for designing FIR Filter
The Kernel amplitudes are shown below with their corresponding values in yellow:
This indicator is intended to be used with Heikin-Ashi source inputs, specially HAB Median. You can read about this here:
Moving Average Filters Add-on w/ Expanded Source Types
What is a Finite Impulse Response Filter?
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
Ultra Low Lag Moving Average's weights are designed to have MAXIMUM possible smoothing and MINIMUM possible lag compatible with as-flat-as-possible phase response.
Ehlers FIR Filter
Ehlers Filter (EF) was authored, not surprisingly, by John Ehlers. Read all about them here: Ehlers Filters
What is Normalized Cardinal Sine?
The sinc function sinc (x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms.
In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by
sinc x = sinx / x
In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by
sinc x = sin(pi * x) / (pi * x)
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.
What is a Dual Element Lag Reducer?
Modifies an array of coefficients to reduce lag by the Lag Reduction Factor uses a generic version of a Kalman velocity component to accomplish this lag reduction is achieved by applying the following to the array:
2 * coeff - coeff
The response time vs noise battle still holds true, high lag reduction means more noise is present in your data! Please note that the beginning coefficients which the modifying matrix cannot be applied to (coef whose indecies are < LagReductionFactor) are simply multiplied by two for additional smoothing .
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
STD- and Clutter-Filtered, Non-Lag Moving Average [Loxx]STD- and Clutter-Filtered, Non-Lag Moving Average is a Weighted Moving Average with a minimal lag using a damping cosine wave as the line of weight coefficients. The indicator has two filters. They are static (in points) and dynamic (expressed as a decimal). They allow cutting the price noise giving a stepped shape to the Moving Average. Moreover, there is the possibility to highlight the trend direction by color. This also includes a standard deviation and clutter filter. This filter is a FIR filter.
What is a Generic or Direct Form FIR Filter?
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
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.
What is a Dual Element Lag Reducer?
Modifies an array of coefficients to reduce lag by the Lag Reduction Factor uses a generic version of a Kalman velocity component to accomplish this lag reduction is achieved by applying the following to the array:
2 * coeff - coeff
The response time vs noise battle still holds true, high lag reduction means more noise is present in your data! Please note that the beginning coefficients which the modifying matrix cannot be applied to (coef whose indecies are < LagReductionFactor) are simply multiplied by two for additional smoothing .
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
Clutter-Filtered, D-Lag Reducer, Spec. Ops FIR Filter [Loxx]Clutter-Filtered, D-Lag Reducer, Spec. Ops FIR Filter is a FIR filter moving average with extreme lag reduction and noise elimination technology. This is a special instance of a static weight FIR filter designed specifically for Forex trading. This is not only a useful indictor, but also a demonstration of how one would create their own moving average using FIR filtering weights. This moving average has static period and weighting inputs. You can change the lag reduction and the clutter filtering but you can't change the weights or the numbers of bars the weights are applied to in history.
Plot of weighting coefficients used in this indicator
These coefficients were derived from a smoothed cardinal sine weighed SMA on EURUSD in Matlab. You can see the coefficients in the code.
What is Normalized Cardinal Sine?
The sinc function sinc (x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms.
In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by
sinc x = sinx / x
In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by
sinc x = sin(pi * x) / (pi * x)
What is a Generic or Direct Form FIR Filter?
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
Ultra Low Lag Moving Average's weights are designed to have MAXIMUM possible smoothing and MINIMUM possible lag compatible with as-flat-as-possible phase response.
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.
What is a Dual Element Lag Reducer?
Modifies an array of coefficients to reduce lag by the Lag Reduction Factor uses a generic version of a Kalman velocity component to accomplish this lag reduction is achieved by applying the following to the array:
2 * coeff - coeff
The response time vs noise battle still holds true, high lag reduction means more noise is present in your data! Please note that the beginning coefficients which the modifying matrix cannot be applied to (coef whose indecies are < LagReductionFactor) are simply multiplied by two for additional smoothing .
Things to note
Due to the computational demands of this indicator, there is a bars back input modifier that controls how many bars back the indicator is calculated on. Because of this, the first few bars of the indicator will sometimes appear crazy, just ignore this as it doesn't effect the calculation.
Related Indicators
STD-Filtered, Ultra Low Lag Moving Average
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
Clutter Fitler [Loxx]Clutter Fitler is a simple indicator to demonstrate a clutter filter. The purpose of this technique is to filter useless noise.
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 filtering technique will be used for future indicators.
Included
Bar coloring
EMA Ribbon - low clutter, configurable [aspiers]This script improves on many of the existing EMA ribbon scripts out there:
Reduces visual clutter with shorter labels / titles, and thinner, transparent lines which don't obscure the actual price chart
Two beautiful color gradients for up and down trends
All colors and EMA periods are fully configurable, using the new input grouping / inline features
Uses Pine Script v4, which makes it more future-proof and allows new functionality, e.g.
It allow configurable period resolution, e.g. so user can fix at day resolution even when chart is being viewed at hour or minute resolution (this is the default)
Code clean-up: remove redundant ternary conditionals, improve variable names
Allow smoothing threshold for changes in trend direction to be configurable
