Signals and Systems - Electrical Engineering

586 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems

(a)

(b)

0 5 10 15

0 5 10 15

0 5 10 15

0

0.5

1

x[

n]

− 1 −0.5 0 0.5

− 1 −0.5 0 0.5

− 1 −0.5 0 0.5

0

5

10

|X

(e

jω

)|

|Y

(e

jω

)|

|Z

(e

jω

)|

0

0.5

1

y[

n]

0

5

10

0

0.5

1

z[

n]

n

0

5

10

ω/π

|X

(e

jω

)|

|Y

(e

jω

)|

|Z

(e

jω

)|

ω/π

0 5 10 15

0510 15

0 5 10 15

− 1

0

1

− 1 −0.5^0 0.5

− 1 −0.5 0 0.5

− 1 −0.5 0 0.5

0

50

100

− 1

0

1

0

50

100

− 1

0

1

n

0

50

100

x

[n

]

y[

n]

z[

n]

FIGURE 10.4

Downsampling of (a) non-band-limited and (b) band-limited discrete-time signals. The signalsx[n]correspond

to the original signals, whiley[n]andz[n]are their downsampled and decimated signals, respectively. The

corresponding magnitude spectra are shown. Notice the difference between the downsampled and the

decimated signals, they are identical when the signals are band-limited, slightly different otherwise.