Hw8

$\sum _{m=-M}^m{a}_{m}x[(r-m)T/2]=y(r)$

The number of add/multiply operations is half the limits of the sumation above. Half results from only needing to perform calculations on half the data.

$(2M+1)(1/2)$

Substitute

$r/2=n=m/2$

in y(r) to get the result of the interpolating filter

$y(t)=\sum _{r=-\mathrm{\infty }}^{\mathrm{\infty }}y(r)\delta (t-rT/2)$