A continuous-time system is described by the differential equation, y?(t) + 6 y?(t) + 3y (t) = x (t) where x is the excitation and y is the response. Can the impulse response of this system contain
(a) An impulse?
(b) A discontinuity at t = 0?
(c) A discontinuous first derivative at t = 0?
Yes, No, No
(a) An impulse? No
Because then must be the second derivative of an impulse and the right side of the equation does not contain such a term.
(b) A discontinuity at ? No
Because then must be the first derivative of an impulse and the right side of the equation does not contain such a term.
(c) A discontinuous first derivative at ? Yes
Because then must be an impulse and the right side of the equation does contain such a term.
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