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GKD-C STD-Filtered, Truncated Taylor FIR Filter [Loxx]

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Giga Kaleidoscope GKD-C STD-Filtered, Truncated Taylor Family FIR Filter is a Confirmation module included in Loxx's "Giga Kaleidoscope Modularized Trading System".

█ GKD-C STD-Filtered, Truncated Taylor Family FIR Filter

Exploring the Truncated Taylor Family FIR Filter with Standard Deviation Filtering

Filters play a vital role in signal processing, allowing us to extract valuable information from raw data by removing unwanted noise or highlighting specific features. In the context of financial data analysis, filtering techniques can help traders identify trends and make informed decisions. Below, we delve into the workings of a Truncated Taylor Family Finite Impulse Response (FIR) Filter with standard deviation filtering applied to the input and output signals. We will examine the code provided, breaking down the mathematical formulas and concepts behind it.

The code consists of two main sections: the design function that calculates the FIR filter coefficients and the stdFilter function that applies standard deviation filtering to the input signal.

design(int per, float taylorK)=>
    float[] coeffs = array.new<float>(per, 0)
    float coeffsSum = 0
    float _div = per + 1.0
    float _coeff = 1
    for i = 0 to per - 1 
        _coeff := (1 + taylorK) / 2 - (1 - taylorK) / 2  * math.cos(2.0 * math.pi * (i + 1) / _div)
        array.set(coeffs,i, _coeff)
        coeffsSum += _coeff
    [coeffs, coeffsSum]

stdFilter(float src, int len, float filter)=>
    float price = src
    float filtdev = filter * ta.stdev(src, len)
    price := math.abs(price - nz(price[1])) < filtdev ? nz(price[1]) : price
    price

Design Function
The design function takes two arguments: an integer 'per' representing the number of coefficients for the FIR filter, and a floating-point number 'taylorK' to adjust the filter's characteristics. The function initializes an array 'coeffs' of length 'per' and sets all elements to 0. It also initializes variables 'coeffsSum', '_div', and '_coeff' to store the sum of the coefficients, a divisor for the cosine calculation, and the current coefficient, respectively.

A for loop iterates through the range of 0 to per-1, calculating the FIR filter coefficients using the formula:

_coeff := (1 + taylorK) / 2 - (1 - taylorK) / 2 * math.cos(2.0 * math.pi * (i + 1) / _div)

The calculated coefficients are stored in the 'coeffs' array, and their sum is stored in 'coeffsSum'. The function returns both 'coeffs' and 'coeffsSum' as a list.

stdFilter Function
The stdFilter function takes three arguments: a floating-point number 'src' representing the input signal, an integer 'len' for the standard deviation calculation period, and a floating-point number 'filter' to adjust the standard deviation filtering strength.

The function initializes a 'price' variable equal to 'src' and calculates the filtered standard deviation 'filtdev' using the formula:

filtdev = filter * ta.stdev(src, len)

The 'price' variable is then updated based on whether the absolute difference between the current price and the previous price is less than 'filtdev'. If true, 'price' is set to the previous price, effectively filtering out noise. Otherwise, 'price' remains unchanged.

Application of Design and stdFilter Functions
First, the input signal 'src' is filtered using the stdFilter function if the 'filterop' variable is set to "Both" or "Price", and 'filter' is greater than 0.

Next, the design function is called with the 'per' and 'taylorK' arguments to calculate the FIR filter coefficients and their sum. These values are stored in 'coeffs' and 'coeffsSum', respectively.

A for loop iterates through the range of 0 to per-1, calculating the filtered output 'dSum' using the formula:

dSum += nz(src) * array.get(coeffs, k)

The output signal 'out' is then computed by dividing 'dSum' by 'coeffsSum' if 'coeffsSum' is not equal to 0; otherwise, 'out' is set to 0.

Finally, the output signal 'out' is filtered using the stdFilter function if the 'filterop' variable is set to "Both" or "Truncated Taylor FIR Filter", and 'filter' is greater than 0. The filtered signal is stored in the 'sig' variable.

The Truncated Taylor Family FIR Filter with Standard Deviation Filtering combines the strengths of two powerful filtering techniques to process financial data. By first designing the filter coefficients using the Taylor family FIR filter and then applying standard deviation filtering, the algorithm effectively removes noise and highlights relevant trends in the input signal. This approach allows traders and analysts to make more informed decisions based on the processed data.

In summary, the provided code effectively demonstrates how to create a custom FIR filter based on the Truncated Taylor family, along with standard deviation filtering applied to both input and output signals. This combination of filtering techniques enhances the overall filtering performance, making it a valuable tool for financial data analysis and decision-making processes. As the world of finance continues to evolve and generate increasingly complex data, the importance of robust and efficient filtering techniques cannot be overstated.

█ Giga Kaleidoscope Modularized Trading System

Core components of an NNFX algorithmic trading strategy
The NNFX algorithm is built on the principles of trend, momentum, and volatility. There are six core components in the NNFX trading algorithm:

1. Volatility - price volatility; e.g., Average True Range, True Range Double, Close-to-Close, etc.
2. Baseline - a moving average to identify price trend
3. Confirmation 1 - a technical indicator used to identify trends
4. Confirmation 2 - a technical indicator used to identify trends
5. Continuation - a technical indicator used to identify trends
6. Volatility/Volume - a technical indicator used to identify volatility/volume breakouts/breakdown
7. Exit - a technical indicator used to determine when a trend is exhausted

What is Volatility in the NNFX trading system?
In the NNFX (No Nonsense Forex) trading system, ATR (Average True Range) is typically used to measure the volatility of an asset. It is used as a part of the system to help determine the appropriate stop loss and take profit levels for a trade. ATR is calculated by taking the average of the true range values over a specified period.

True range is calculated as the maximum of the following values:

-Current high minus the current low
-Absolute value of the current high minus the previous close
-Absolute value of the current low minus the previous close

ATR is a dynamic indicator that changes with changes in volatility. As volatility increases, the value of ATR increases, and as volatility decreases, the value of ATR decreases. By using ATR in NNFX system, traders can adjust their stop loss and take profit levels according to the volatility of the asset being traded. This helps to ensure that the trade is given enough room to move, while also minimizing potential losses.

Other types of volatility include True Range Double (TRD), Close-to-Close, and Garman-Klass

What is a Baseline indicator?
The baseline is essentially a moving average, and is used to determine the overall direction of the market.

The baseline in the NNFX system is used to filter out trades that are not in line with the long-term trend of the market. The baseline is plotted on the chart along with other indicators, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR).

Trades are only taken when the price is in the same direction as the baseline. For example, if the baseline is sloping upwards, only long trades are taken, and if the baseline is sloping downwards, only short trades are taken. This approach helps to ensure that trades are in line with the overall trend of the market, and reduces the risk of entering trades that are likely to fail.

By using a baseline in the NNFX system, traders can have a clear reference point for determining the overall trend of the market, and can make more informed trading decisions. The baseline helps to filter out noise and false signals, and ensures that trades are taken in the direction of the long-term trend.

What is a Confirmation indicator?
Confirmation indicators are technical indicators that are used to confirm the signals generated by primary indicators. Primary indicators are the core indicators used in the NNFX system, such as the Average True Range (ATR), the Moving Average (MA), and the Relative Strength Index (RSI).

The purpose of the confirmation indicators is to reduce false signals and improve the accuracy of the trading system. They are designed to confirm the signals generated by the primary indicators by providing additional information about the strength and direction of the trend.

Some examples of confirmation indicators that may be used in the NNFX system include the Bollinger Bands, the MACD (Moving Average Convergence Divergence), and the MACD Oscillator. These indicators can provide information about the volatility, momentum, and trend strength of the market, and can be used to confirm the signals generated by the primary indicators.

In the NNFX system, confirmation indicators are used in combination with primary indicators and other filters to create a trading system that is robust and reliable. By using multiple indicators to confirm trading signals, the system aims to reduce the risk of false signals and improve the overall profitability of the trades.

What is a Continuation indicator?
In the NNFX (No Nonsense Forex) trading system, a continuation indicator is a technical indicator that is used to confirm a current trend and predict that the trend is likely to continue in the same direction. A continuation indicator is typically used in conjunction with other indicators in the system, such as a baseline indicator, to provide a comprehensive trading strategy.

What is a Volatility/Volume indicator?
Volume indicators, such as the On Balance Volume (OBV), the Chaikin Money Flow (CMF), or the Volume Price Trend (VPT), are used to measure the amount of buying and selling activity in a market. They are based on the trading volume of the market, and can provide information about the strength of the trend. In the NNFX system, volume indicators are used to confirm trading signals generated by the Moving Average and the Relative Strength Index. Volatility indicators include Average Direction Index, Waddah Attar, and Volatility Ratio. In the NNFX trading system, volatility is a proxy for volume and vice versa.

By using volume indicators as confirmation tools, the NNFX trading system aims to reduce the risk of false signals and improve the overall profitability of trades. These indicators can provide additional information about the market that is not captured by the primary indicators, and can help traders to make more informed trading decisions. In addition, volume indicators can be used to identify potential changes in market trends and to confirm the strength of price movements.

What is an Exit indicator?
The exit indicator is used in conjunction with other indicators in the system, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR), to provide a comprehensive trading strategy.

The exit indicator in the NNFX system can be any technical indicator that is deemed effective at identifying optimal exit points. Examples of exit indicators that are commonly used include the Parabolic SAR, the Average Directional Index (ADX), and the Chandelier Exit.

The purpose of the exit indicator is to identify when a trend is likely to reverse or when the market conditions have changed, signaling the need to exit a trade. By using an exit indicator, traders can manage their risk and prevent significant losses.

In the NNFX system, the exit indicator is used in conjunction with a stop loss and a take profit order to maximize profits and minimize losses. The stop loss order is used to limit the amount of loss that can be incurred if the trade goes against the trader, while the take profit order is used to lock in profits when the trade is moving in the trader's favor.

Overall, the use of an exit indicator in the NNFX trading system is an important component of a comprehensive trading strategy. It allows traders to manage their risk effectively and improve the profitability of their trades by exiting at the right time.

How does Loxx's GKD (Giga Kaleidoscope Modularized Trading System) implement the NNFX algorithm outlined above?
Loxx's GKD v1.0 system has five types of modules (indicators/strategies). These modules are:

1. GKD-BT - Backtesting module (Volatility, Number 1 in the NNFX algorithm)
2. GKD-B - Baseline module (Baseline and Volatility/Volume, Numbers 1 and 2 in the NNFX algorithm)
3. GKD-C - Confirmation 1/2 and Continuation module (Confirmation 1/2 and Continuation, Numbers 3, 4, and 5 in the NNFX algorithm)
4. GKD-V - Volatility/Volume module (Confirmation 1/2, Number 6 in the NNFX algorithm)
5. GKD-E - Exit module (Exit, Number 7 in the NNFX algorithm)

(additional module types will added in future releases)

Each module interacts with every module by passing data between modules. Data is passed between each module as described below:

GKD-B => GKD-V => GKD-C(1) => GKD-C(2) => GKD-C(Continuation) => GKD-E => GKD-BT

That is, the Baseline indicator passes its data to Volatility/Volume. The Volatility/Volume indicator passes its values to the Confirmation 1 indicator. The Confirmation 1 indicator passes its values to the Confirmation 2 indicator. The Confirmation 2 indicator passes its values to the Continuation indicator. The Continuation indicator passes its values to the Exit indicator, and finally, the Exit indicator passes its values to the Backtest strategy.

This chaining of indicators requires that each module conform to Loxx's GKD protocol, therefore allowing for the testing of every possible combination of technical indicators that make up the six components of the NNFX algorithm.

What does the application of the GKD trading system look like?
Example trading system:
  • Backtest: Strategy with 1-3 take profits, trailing stop loss, multiple types of PnL volatility, and 2 backtesting styles
  • Baseline: Hull Moving Average
  • Volatility/Volume: Hurst Exponent
  • Confirmation 1: STD-Filtered, Truncated Taylor Family FIR Filter as shown on the chart above
  • Confirmation 2: Williams Percent Range
  • Continuation: Fisher Transform
  • Exit: Rex Oscillator

Each GKD indicator is denoted with a module identifier of either: GKD-BT, GKD-B, GKD-C, GKD-V, or GKD-E. This allows traders to understand to which module each indicator belongs and where each indicator fits into the GKD protocol chain.

Giga Kaleidoscope Modularized Trading System Signals (based on the NNFX algorithm)
Standard Entry
1. GKD-C Confirmation 1 Signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees

Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
6. GKD-C Confirmation 1 signal was less than 7 candles prior

Volatility/Volume Entry
1. GKD-V Volatility/Volume signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-B Baseline agrees
6. GKD-C Confirmation 1 signal was less than 7 candles prior

Continuation Entry
1. Standard Entry, Baseline Entry, or Pullback; entry triggered previously
2. GKD-B Baseline hasn't crossed since entry signal trigger
3. GKD-C Confirmation Continuation Indicator signals
4. GKD-C Confirmation 1 agrees
5. GKD-B Baseline agrees
6. GKD-C Confirmation 2 agrees

1-Candle Rule Standard Entry
1. GKD-C Confirmation 1 signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
Next Candle:
1. Price retraced (Long: close < close or Short: close > close)
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees

1-Candle Rule Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 1 signal was less than 7 candles prior
Next Candle:
1. Price retraced (Long: close < close or Short: close > close)
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume Agrees

1-Candle Rule Volatility/Volume Entry
1. GKD-V Volatility/Volume signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 1 signal was less than 7 candles prior
Next Candle:
1. Price retraced (Long: close < close or Short: close > close)
2. GKD-B Volatility/Volume agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-B Baseline agrees

PullBack Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is beyond 1.0x Volatility of Baseline
Next Candle:
1. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
2. GKD-C Confirmation 1 agrees
3. GKD-C Confirmation 2 agrees
4. GKD-V Volatility/Volume Agrees

]█ Setting up the GKD
The GKD system involves chaining indicators together. These are the steps to set this up.

Use a GKD-C indicator alone on a chart
1. Inside the GKD-C indicator, change the "Confirmation Type" setting to "Solo Confirmation Simple"

Use a GKD-V indicator alone on a chart
**nothing, it's already useable on the chart without any settings changes

Use a GKD-B indicator alone on a chart
**nothing, it's already useable on the chart without any settings changes

Baseline (Baseline, Backtest)
1. Import the GKD-B Baseline into the GKD-BT Backtest: "Input into Volatility/Volume or Backtest (Baseline testing)"
2. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "Baseline"

Volatility/Volume (Volatility/Volume, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Solo"
2. Inside the GKD-V indicator, change the "Signal Type" setting to "Crossing" (neither traditional nor both can be backtested)
3. Import the GKD-V indicator into the GKD-BT Backtest: "Input into C1 or Backtest"
4. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "Volatility/Volume"
5. Inside the GKD-BT Backtest, a) change the setting "Backtest Type" to "Trading" if using a directional GKD-V indicator; or, b) change the setting "Backtest Type" to "Full" if using a directional or non-directional GKD-V indicator (non-directional GKD-V can only test Longs and Shorts separately)
6. If "Backtest Type" is set to "Full": Inside the GKD-BT Backtest, change the setting "Backtest Side" to "Long" or "Short
7. If "Backtest Type" is set to "Full": To allow the system to open multiple orders at one time so you test all Longs or Shorts, open the GKD-BT Backtest, click the tab "Properties" and then insert a value of something like 10 orders into the "Pyramiding" settings. This will allow 10 orders to be opened at one time which should be enough to catch all possible Longs or Shorts.

Solo Confirmation Simple (Confirmation, Backtest)
1. Inside the GKD-C indicator, change the "Confirmation Type" setting to "Solo Confirmation Simple"
1. Import the GKD-C indicator into the GKD-BT Backtest: "Input into Backtest"
2. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "Solo Confirmation Simple"

Solo Confirmation Complex without Exits (Baseline, Volatility/Volume, Confirmation, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Chained"
2. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
3. Inside the GKD-C indicator, change the "Confirmation Type" setting to "Solo Confirmation Complex"
4. Import the GKD-V indicator into the GKD-C indicator: "Input into C1 or Backtest"
5. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "GKD Full wo/ Exits"
6. Import the GKD-C into the GKD-BT Backtest: "Input into Exit or Backtest"

Solo Confirmation Complex with Exits (Baseline, Volatility/Volume, Confirmation, Exit, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Chained"
2. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
3. Inside the GKD-C indicator, change the "Confirmation Type" setting to "Solo Confirmation Complex"
4. Import the GKD-V indicator into the GKD-C indicator: "Input into C1 or Backtest"
5. Import the GKD-C indicator into the GKD-E indicator: "Input into Exit"
6. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "GKD Full w/ Exits"
7. Import the GKD-E into the GKD-BT Backtest: "Input into Backtest"

Full GKD without Exits (Baseline, Volatility/Volume, Confirmation 1, Confirmation 2, Continuation, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Chained"
2. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
3. Inside the GKD-C 1 indicator, change the "Confirmation Type" setting to "Confirmation 1"
4. Import the GKD-V indicator into the GKD-C 1 indicator: "Input into C1 or Backtest"
5. Inside the GKD-C 2 indicator, change the "Confirmation Type" setting to "Confirmation 2"
6. Import the GKD-C 1 indicator into the GKD-C 2 indicator: "Input into C2"
7. Inside the GKD-C Continuation indicator, change the "Confirmation Type" setting to "Continuation"
8. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "GKD Full wo/ Exits"
9. Import the GKD-E into the GKD-BT Backtest: "Input into Exit or Backtest"

Full GKD with Exits (Baseline, Volatility/Volume, Confirmation 1, Confirmation 2, Continuation, Exit, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Chained"
2. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
3. Inside the GKD-C 1 indicator, change the "Confirmation Type" setting to "Confirmation 1"
4. Import the GKD-V indicator into the GKD-C 1 indicator: "Input into C1 or Backtest"
5. Inside the GKD-C 2 indicator, change the "Confirmation Type" setting to "Confirmation 2"
6. Import the GKD-C 1 indicator into the GKD-C 2 indicator: "Input into C2"
7. Inside the GKD-C Continuation indicator, change the "Confirmation Type" setting to "Continuation"
8. Import the GKD-C Continuation indicator into the GKD-E indicator: "Input into Exit"
9. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "GKD Full w/ Exits"
10. Import the GKD-E into the GKD-BT Backtest: "Input into Backtest"

Baseline + Volatility/Volume (Baseline, Volatility/Volume, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Baseline + Volatility/Volume"
2. Inside the GKD-V indicator, make sure the "Signal Type" setting is set to "Traditional"
3. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
4. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "Baseline + Volatility/Volume"
5. Import the GKD-V into the GKD-BT Backtest: "Input into C1 or Backtest"
6. Inside the GKD-BT Backtest, change the setting "Backtest Type" to "Full". For this backtest, you must test Longs and Shorts separately
7. To allow the system to open multiple orders at one time so you can test all Longs or Shorts, open the GKD-BT Backtest, click the tab "Properties" and then insert a value of something like 10 orders into the "Pyramiding" settings. This will allow 10 orders to be opened at one time which should be enough to catch all possible Longs or Shorts.

Requirements
Inputs
Confirmation 1: GKD-V Volatility / Volume indicator
Confirmation 2: GKD-C Confirmation indicator
Continuation: GKD-C Confirmation indicator
Solo Confirmation Simple: GKD-B Baseline
Solo Confirmation Complex: GKD-V Volatility / Volume indicator
Solo Confirmation Super Complex: GKD-V Volatility / Volume indicator
Stacked 1: None
Stacked 2+: GKD-C, GKD-V, or GKD-B Stacked 1

Outputs
Confirmation 1: GKD-C Confirmation 2 indicator
Confirmation 2: GKD-C Continuation indicator
Continuation: GKD-E Exit indicator
Solo Confirmation Simple: GKD-BT Backtest
Solo Confirmation Complex: GKD-BT Backtest or GKD-E Exit indicator
Solo Confirmation Super Complex: GKD-C Continuation indicator
Stacked 1: GKD-C, GKD-V, or GKD-B Stacked 2+
Stacked 2+: GKD-C, GKD-V, or GKD-B Stacked 2+ or GKD-BT Backtest

Additional features will be added in future releases.
Versionshinweise:
Additional notes on Truncated Taylor Family FIR Filters.

A Truncated Taylor Family FIR (Finite Impulse Response) Filter is a specialized type of digital filter used in signal processing for various applications like communication systems, audio processing, and control systems. It is based on the Taylor series expansion, which is a method for approximating a continuous function using a series of polynomials.

In the context of FIR filters, the Truncated Taylor Family refers to a group of filters designed using a truncated version of the Taylor series expansion. The coefficients of the filter are determined by selecting a certain number of terms from the Taylor series, which helps to approximate the desired filter characteristics.

The primary advantage of using a Truncated Taylor Family FIR filter is that it allows for better control of the filter's characteristics, such as passband and stopband performance, phase response, and group delay. This is because the coefficients derived from the Taylor series expansion can be adjusted to meet specific design requirements. As a result, these filters can provide better performance in terms of selectivity, phase linearity, and amplitude response compared to traditional FIR filter designs.

To design a Truncated Taylor Family FIR filter, a designer needs to:
1. Choose the desired filter specifications, such as passband and stopband frequencies, transition width, and stopband attenuation.
2. Determine the number of coefficients needed to achieve these specifications.
3. Calculate the filter coefficients using the truncated Taylor series expansion.
4. Implement the filter in the digital domain using a suitable algorithm, such as convolution or fast convolution.

The key challenge in designing these filters is balancing the trade-offs between filter performance, computational complexity, and filter order (number of coefficients). The more terms used from the Taylor series, the better the filter performance; however, this also increases the filter order and computational complexity.
Versionshinweise:
Updated for new GKD backtests.
Versionshinweise:
Additions and Subtractions:

-All signal logic has been transferred to the new GKD-BT Backtests. You can access these backtests using the links provided below:

GKD-BT Giga Confirmation Stack Backtest:

GKD-BT Giga Stacks Backtest:

GKD-BT Full Giga Kaleidoscope Backtest:

GKD-BT Solo Confirmation Super Complex Backtest:

GKD-BT Solo Confirmation Complex Backtest:

GKD-BT Solo Confirmation Simple Backtest:

-Removed all Confirmation Type options except for "Confirmation" and "Continuation." The "Continuation" type is only used in GKD-BT Solo Confirmation Super Complex Backtest and GKD-BT Full Giga Kaleidoscope Backtest when selecting a Confirmation indicator.

-Added new signal plots based on the selected Confirmation Type. For the "Confirmation" type, only initial Longs and Shorts will be displayed on the indicator. For the "Continuation" type, both initial and continuation signals will be displayed. In both cases, if multiple signal types are present (e.g., middle cross, signal cross), these signals can be controlled using the "Signal Type" option.

-Implemented code optimizations to enhance the rendering speed of signals.

-Streamlined the export process by generating only a single value for export to other indicators or backtests. This exported value is named "Input into NEW GKD-BT Backtest."
Versionshinweise:
Updated for multi-ticker GKD.
Versionshinweise:
Added optimizer

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