GATE ECE 2019 EC Q44: Discrete-time signals

Let

be a length-7 discrete-time finite impulse response filter, given by

, and

is zero for

. A length-3 finite impulse response approximation

has to be obtained such that

is minimized, where

and

are the discrete-time Fourier transforms of

and

, respectively. For the filter that minimizes

, the value of

, rounded off to 2 decimal places, is ______.

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