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Sec. 2–8 Discrete Fourier Transform 103
1.5
Time Waveform
w(t)
1
0.5
0
0
1.5
1 2 3 4 5 6 7 8 9 10
t (sec)
Magnitude Spectrum Out to 4th Null
|W(f)|
1
0.5
¨(f) (degrees)
0
0
100
0
–100
–200
0
1.5
0.5 1 1.5 2 2.5 3 3.5 4
f (Hz)
Phase Spectrum Out to 4th Null
0.5 1 1.5 2 2.5 3 3.5 4
f (Hz)
Magnitude Spectrum over Whole FFT Frequency Range
|W(f)|
1
0.5
0
0
2 4 6 8 10 12 14
f (Hz)
Figure 2–21
Spectrum for a rectangular pulse, using the MATLAB FFT.
(See Example2_20.m for the MATLAB file.)
Using the DFT to Compute the Fourier Series
The DFT may be also used to evaluate the coefficients for the complex Fourier series. From
Eq. (2–89),
T
c n = 1 w(t)e -j2pnf0t dt
T L0