Computing FIR Filters Using Arrays [WMA Example]

Sep 28, 2020

Over the years, many FIR filters have been proposed by the Pine community, with the standard way of computing them being `for` loops. The arrival of arrays allows for a new, more efficient way to compute them.

This script provides a template showing how you can compute FIR filters using Pine arrays.

FIR Filters

FIR stands for "Finite Impulse Response", and is associated with types of filters whose impulse response reaches a steady state.

FIR filters are calculated using convolution, or more simply put, using a weighted sum between a set of filter coefficients and past input values over a finite window.

In Pine, FIR filters are generally computed inside a `for` loop executing three processes:

1- Computing the coefficients.
2- Summing all the computed coefficients.
3- Performing the weighted sum between the inputs values and the computed coefficients.

Then we divide the result of our weighted sum by the sum of the coefficients obtained in step 2.

Because the computations inside the `for` loop execute on each bar, execution time can be significant when the calculation of coefficients is complex. This is where arrays are handy, as we can compute the coefficients just once, store them into an array, and use them in a weighted sum without the need to recalculate them over and over. This drastically reduces the computation time required to calculate a FIR filter.

The new `array.sum()` function helps eliminate step 2, thus further decreasing computation time.

How to Use This Template

All you need to do is to put the code that computes your coefficients in the first `for` loop (variable `w`). If the code that computes your coefficients contains more than one line, just make sure your final coefficient is placed in variable `w` (or change the `value` argument in `array.push()`). Another option is to declare a function that computes the coefficients and use it instead of variable `w`.



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