in - Σ x[n]e=jkown (N) Η - 1 -Ζ Σx[n]e=jk{2π/N) ζ του (1) (3.95) Example 3.12 In this example, we consider the discrete
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in - Σ x[n]e=jkown (N) Η - 1 -Ζ Σx[n]e=jk{2π/N) ζ του (1) (3.95)
Example 3.12 In this example, we consider the discrete-time periodic square wave shown in Fig- ure 3.16. We can evaluate the Fourier series for this signal using eq. (3.95). Because x[n] = 1 for -N₁sns N₁, it is particularly convenient to choose the length-N interval of summation in eq. (3.95) so that it includes the range -N₁ ≤ n ≤ N₁. In this case, we can express eq. (3.95) as ax -N -JA(Zw/N)n ··.IIIII.….…....IIIII….….....IIIII.. -N₁0 N₁ Figure 3.16 Discrete-time periodic square wave. N (3.102)