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

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

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