Test Academy | The discrete-time Fourier series representation of a signal x[n] with period N is written as x [ n ] = ∑ k = 0 N − 1 a k e j ( 2 k n π / N ) . A discrete-time periodic signal with period N = 3, has the non-zero Fourier series coefficients: a -3 = 2 and a 4 = 1. The signal is 2 + 2 e − ( j 2 π 6 n ) cos ⁡ ( 2 π 6 n ) , 1 + 2 e ( j 2 π 3 n ) cos ⁡ ( 2 π 6 n ) , 1 + 2 e ( j 2 π 6 n ) cos ⁡ ( 2 π 6 n ) , 2 + 2 e ( j 2 π 6 n ) cos ⁡ ( 2 π 6 n )

Question

The discrete-time Fourier series representation of a signal x[n] with period N is written as $x [n] = \sum_{k = 0}^{N - 1} a_{k} e^{j (2 k n π / N)}$ . A discrete-time periodic signal with period N = 3, has the non-zero Fourier series coefficients: a_-3 = 2 and a₄ = 1. The signal is

Options :

$2 + 2 e^{- (j \frac{2 π}{6} n)} \cos (\frac{2 π}{6} n)$
$1 + 2 e^{(j \frac{2 π}{3} n)} \cos (\frac{2 π}{6} n)$
$1 + 2 e^{(j \frac{2 π}{6} n)} \cos (\frac{2 π}{6} n)$
$2 + 2 e^{(j \frac{2 π}{6} n)} \cos (\frac{2 π}{6} n)$

Show Answer

Report

More Similar Tests

Related Tests