Figure P6.21 illustrates the basic idea for a lookup-table-based sinusoidal signal gen-e...

Figure P6.21 illustrates the basic idea for a lookup-table-based sinusoidal signal gen-erator. The samples of one period of the signal

are stored in memory. A digital sinusoidal signal is generated by stepping through the table and wrapping around at the end when the angle exceeds 2π. This can be done by using modulo addressing (i.e., using a "circular" buffer). Samples of x(n) are feeding the ideal D/A converter every T seconds.

(a) Show that by changing we can adjust the frequency of the resulting analog sinusoid.

(b) Suppose now that is fixed. How many distinct analog sinusoids can be generated using the given lookup table? Explain.