A digital camera that uses a CCD image sensor has a $1024\backslash$times $768$ pixel matrix. The analog$-$to$-$digital converter takes $0\mathrm{.}02\backslash$mu $-$sec $(0\mathrm{.}02\backslash$times $10-6$sec$)$ to convert the analog charge signal for each pixel into the corresponding digital signal, including the time to switch between pixels. Determine $($a$)$ how much time is required to collect the image data for one frame, and $($b$)$ is this time compatible with the processing rate of $20$ frames per second?