# Finding Filter Coefficients

Algebra Level pending

A digital filter has an input $$x$$ and an output $$y$$. The filter is implemented as shown below:

$\large{y_k = a\,x_k + b \,x_{k-1} + c \,x_{k-2} + d \,x_{k-3}}$

Some input / output data from the filter is given below:

What is $$a^2 + b^2 + c^2 + d^2$$?

Note: $$x_k$$ denotes the most recent input to the filter, $$x_{k-1}$$ denotes the second-most recent input to the filter, etc.

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