Consider this variant of the Fibonacci system y n = y...

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Consider this variant of the Fibonacci system:
y[n] = y[n - 1] - y[n - 2] + x[n], where x[n] represents the input and y[n] represents the output. The poles of the given system will be:

A. 1, 2

B. 0, 1, 2

C. $${e^{j\frac{\pi }{3}}},\,{e^{ - j\frac{\pi }{3}}}$$

D. $${e^{j\frac{\pi }{3}}},\,{e^{ - j\frac{\pi }{3}}},\,0$$

Answer: Option C

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