**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

Added the ability to see dead zones where price didn't pass the clutter filter threshold, see image below. This is off by default.

Removed unused windowing loop. This indicator loads as fast as any other indicator now.

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