The first difference filter has the impulse response h$[$n$]=\{1,-1\}.$

$($i$)$

By means of convolution, determine the filter output, yn$],$ given

the input xin$]=\{1,0,-1,2\}.$

$(4$ marks$)$

$($ii$)$

Determine the step response of the filter.

$(2$ marks$)$

$($lii$)$ Determine the discrete$-$time Fourier transform of the filter.

$(3$ marks$)$