Problem $8\mathrm{.}93$ Suppose we sample a continuous$-$time signal at a sampling rate of $2$ kHz to obtain a discretetime signal $()$ for $0<800.$ We perform zero padding, such that $()=0$ for $800<1000.$ Next, we compute a DFT of length $1000$ to obtain $()$ for $0<1000.($a$)$ Determine the frequency spacing $($in Hz$)$ between the DFT points. $($b$)$ Calculate the frequency $($in Hz$)$ corresponding to $(900).$