Signals and Systems - Electrical Engineering

4.6 Fourier Coefficients from Laplace 259

0 0.2 0.4 0.6 0.8 1

0

0.5

1

1.5

2

Period

x(

t)

t

0 50 100

0

0.2

0.4

0.6

0.8

1

Magnitude line spectrum

|X

|k

|X

|k

Ω(rad/sec)

0 50 100

0

1

2

3

4

Phase line spectrum

Ω(rad/sec)

FIGURE 4.5
Period of train of rectangular pulses (top) and its magnitude and phase line spectra (bottom).

4. TheXkcoefficients and its squares, related to the power line spectrum, are obtained using the
   fourierseriesfunction (see Figure 4.5):

k Xk=X−k X^2 k

0 1 1

1 0.64 0.41

2 0 0

3 −0.21 0.041

4 0 0

5 0.13 0.016

6 0 0

7 −0.09 0.008