Question: Figure illustrates the basic idea for a lookup table based sinusoidal signal generator. The samples of the signal x ( n ) = cos(2?/N n)

Figure illustrates the basic idea for a lookup table based sinusoidal signal generator. The samples of the signal x(n) = cos(2?/N n) n = 0, 1 . . . N ? 1 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 2?. This can be done by using modulo-n 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 F_s we can adjust the frequency F₀ of the resulting analog sinusoid.

(b) Suppose now that F_s = 1/T is fixed. How many distinct analog sinusoids can be generated using the given lookup table? Explain

x(0) x(N x(1) 1) Idea! ) = cos 2nFgi DSP D'A

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