Using the results of Problem 4.13, verify the following properties of WN = exp(-j2m/N) appearing in...

 

 

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Using the results of Problem 4.13, verify the following properties of WN = exp(-j2m/N) appearing in Table 4.6. (a) w+N)* = w (b) w+N/2 = -Wi (c) W = WN/2 (d) W = Wy Solution (a) Using entry 4 of Table 4.6 wk+N = w (b) Using entry 2 of Table 4.6 wk+N/2 -w (c) Using (4.3.5) [exp(-27/N)2k exp(-4kr/N) expl-2kz/(N/2)] {exp[-27/(N/2)|}* (d) Using (4.3.5) [exp(-j27/N]* WN = exp(j2n/N) 1/ exp(-j2n/N) %3D I||| 4.13 Verify the following values of W = exp(-j2nk/N) appearing in Table 4.6. -j, k= N/4 -1, k = N/2 j, k= 3N/4 k = N W'N 1, TABLE 4.6: > Property Description Property Description Symmetry Properties of Ww wi+Nk = wi wNA = -j wN2 = -1 wNA = i WN 1 5 6. WNI2 = -W 3N/4 7 %3D Wi = W 4 1 8. %3D 2. 3. Using the results of Problem 4.13, verify the following properties of WN = exp(-j2m/N) appearing in Table 4.6. (a) w+N)* = w (b) w+N/2 = -Wi (c) W = WN/2 (d) W = Wy Solution (a) Using entry 4 of Table 4.6 wk+N = w (b) Using entry 2 of Table 4.6 wk+N/2 -w (c) Using (4.3.5) [exp(-27/N)2k exp(-4kr/N) expl-2kz/(N/2)] {exp[-27/(N/2)|}* (d) Using (4.3.5) [exp(-j27/N]* WN = exp(j2n/N) 1/ exp(-j2n/N) %3D I||| 4.13 Verify the following values of W = exp(-j2nk/N) appearing in Table 4.6. -j, k= N/4 -1, k = N/2 j, k= 3N/4 k = N W'N 1, TABLE 4.6: > Property Description Property Description Symmetry Properties of Ww wi+Nk = wi wNA = -j wN2 = -1 wNA = i WN 1 5 6. WNI2 = -W 3N/4 7 %3D Wi = W 4 1 8. %3D 2. 3.