Consider a LTIC system with causal impulse response h(t). (a) Using the convolution property, show that the transfer function of an LTIC system is given by a transform-domain ratio of output to input,...

(a) Using the convolution property, show that the transfer function of an LTIC system is given by a transform-domain ratio of output to input, H(s) = Y (s)/X(s).

(b) Using Laplace transform properties, determine the transfer function of a system described by
 x(t).

(c) Using Table 1.5, determine the impulse response h(t) of a system described by

(d) Determine the output y(t) of a system described by
 to the everlasting sinusoidal input x(t) = cos(t).