PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

328 Practical MATLAB® Applications for Engineers

b. If f(t) = −f(−t), indicating that f(t) is an odd function with respect to t, then

ft()
 bnsin(nwt 0 )

n

∑

where

b

T

n ft nwtdt n

T

4

0

0

2

()sin( )



∫ for 1, and all the coefficients an
^0

− 4 − 2 0 2 4

− 1

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

nw 0 (rad/s)

Line spectrum

− 4 − 2 0 2 4

− 3

− 2

− 1

0

1

2

3

4

5

6

nw 0 (rad/s)

Angle of

Fn

(rad)

Phase spectrum

Amplitude of

Fn

FIGURE 4.1
Plots of line spectrum.

− 4 − 2 0 2 4

− 1

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

nw 0 (rad/s)

Magnitude of

Fn

Magnitude spectrum

− 4 − 2 0 2 4

− 1

0

1

2

3

4

5

6

7

8

9

10

nw 0 (rad/s)

mag (

Fn

(^2) )
(w
)
Power spectrum (for T = 1)
FIGURE 4.2
Plots of magnitude and power spectrum.