Let Z$($t$)=$ X$($t$)+$ jY $($t$)$ be a complex$-$valued, zero$-$mean white Gaussian noise process

with autocorrelation function RZ $(\backslash$tau $)=$ N$0\backslash$delta $(\backslash$tau $).$ Let fm$($t$),$ m $=1,2,...,$ M$,$ be a set of

M orthogonal equivalent lowpass waveforms defined on the interval $0<=$ t $<=$ T $.$ Define

Nmr $=$ Re T

$0$

Z$($t$)$ f $$

m$($t$)$ dt

$,$ m $=1,2,...,$ M

$1.$ Determine the variance of Nmr$.$

$2.$ Show that E$[$Nmr Nkr$]=0$ for k $=$ m$.$