Question 2 (6 marks) a) Determine the even component of the signal $x[n] = e^{j3\frac{2\pi}{5}n} + e^{j\sqrt{2}\frac{2\pi}{5}n}$. Simplify your expression. b) Determine if signal $x[n] = e^{j3\frac{2\pi}{5}n} + e^{j\sqrt{2}\frac{2\pi}{5}n}$ is periodic or not. If it is periodic, find the period.
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To do this, we use the fact that the even function is given by f(x)=-x2. Show more…
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(a) For each of the following signals, determine whether the signal is periodic or nonperiodic. If it is periodic, find its fundamental period. i. x[n] = e^{jpi n/2} ii. x[n] = sin(pi n/4) + cos(pi n) iii. x(t) = cos(3pi t + pi/4) + 2cos(4pi t) (b) A signal x(t) is depicted in Figure 1. Sketch each of the following signals derived from x(t): i. x(-t + 2) ii. 2x(-t) iii. x(-2t + 1) (c) Sketch and label the following discrete time signal: 3h[-n - 1] where h[n] = delta[n + 2] + 2delta[n] - delta[n - 1] + delta[n - 2]
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