Determine whether or not the filters with impulse responses given below are BIBO stable. and f

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Determine whether or not the filters with impulse responses given below are BIBO stable. α and f0 are positive constants.

(a) h1 (t) = exp(-α |t|) cos (2πf0t)

(b) h2 (t) = cos (2πf0t) u(t)

(c) h3 (t) = t-1 u(t - 1)

(d) h4 (t) = e-tu (t) – e-(t – 1) u (t - 1)

(e) h5 (t) = t-2u (t - 1)

(f) h6 (t) = sinc(2t)

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