Determine the impulse response hk of the ltid

Question

Question: When the DT sequence

x[k] = 4^-k u[k] + 3^-k u[k]

is applied at the input of an LTID system, the output response is given by

y[k] = 2(1/4)^k u[k] - 4(3/4)^k u[k]

(i) Determine the Fourier transfer function H(?) of the LTID system.

(ii) Determine the impulse response h[k] of the LTID system.

(iii) Determine the difference equation representing the LTID system.

(iv) Determine if the system is causal.