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The input $4\sin c(2t)$ is fed to a Hilbert transformer to obtain $y( t),$ as shown in the figure below:

Here $\sin c \left ( x\right )=\dfrac{\sin\left ( \pi x \right )}{\pi x}.$ The value (accurate to two decimal places) of $\int ^{\infty }_{-\infty } \mid y( t ) \mid ^{2}dt$ is ________.