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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