$4.[15$pts$]$ a$)$ A waveform $()=10$ cos $1000++20$ cos $2000+$ is to be uniformly sampled for digital transmission. What is the maximum allowable time interval between samples that will ensure perfct signal reconstruction? If we want to reproduce $1$ hour of this waveform, how many samples need to be restored? b$)$ Determine the number of quantization levels if the number of bits per sample in a given PCM code is i$)5$; ii$)8$; iii$)$ x$.$