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

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)