A digital filter with input x[n] and output y[n] is represented by the difference equation:

$$y[n]=1/2x[n]+1/3y[n-1]$$

The impulse response for this filter is most nearly:

A. $$h[n]=2delta[n]-2/3delta[n-1]$$

B. $$h[n]=1/2delta[n]-1/3delta[n-1]$$

C. $$h[n]=1/2(1/3)^n, n>=0$$

D. $$h[n]=1/2(-1/3)^n, n>=0$$

A digital filter with input x[k] and output y[k] is described by the difference equation:

$$y[k]=1/6(3x[k]+2x[k-1]+x[k-2])$$

The discrete-time transfer function of the filter H(z) is:

A. $$(6z^2)/(3z^2+2z+1)$$

B. $$(6z)/(3z^2+2z+1)$$

C. $$3z^2+2z+1$$

D. $$1/6[(3z^2+2z+1)/z^2]$$

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