Signals and Systems - Electrical Engineering

10.4 Discrete Fourier Transform 623

FIGURE 10.15
Computation of the
FFT of a periodic
signal using (a) 4 and
(b) 12 periods to
improve the
frequency resolution
of the FFT. Notice
that both magnitude
and phase
responses look alike,
but when we use 12
periods these
spectra look sharper
due to the increase
in the number of
frequency
components added.

− 600 − 400 − 200 0 200 400 600

0

5

10

15

20

25

f(Hz)

|X

(f

)|

− 600 − 400 − 200 0 200 400 600

− 4

− 2

0

2

4

f(Hz)

<X

(f

)

0

5

10

15

20

25

|X

(f

)|

− 600 − 400 − 200 0 200 400 600

f(Hz)

− 600 −^400 − 200 0 200 400 600

f(Hz)

− 4

− 2

0

2

4

<X

(f

)

0 0.02 0.04 0.06 0.08 0.1 0.12

− 6

− 4

− 2

0

2

4

x(

nT

)s

nTs

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

− 6

− 4

− 2

0

2

4

x(

nT

)s

nTs

(a)

(b)