Digital Signal Processing Reference
In-Depth Information
y
[
n
]
y
(
t
)
multirate
converter (TX)
s
[
n
]
48Khz D
/
A
l
g
r
,
y
i
d
.
,
©
,
L
s
multirate
converter (TX)
/
s
ˆ
[
n
]
48Khz A
D
Figure 11.24
Transmission scheme for high-quality audio over a phone line.
sampler as in Figure 11.25 where
L
TX
(
z
)
is a lowpass filter with cutoff fre-
quency
25. At the receiver the chain is inverted, with
an upsampler by four, followed by a lowpass filter with cutoff frequency
π/
25 and gain
L
0
=
4
/
π/
4
and gain
L
0
=
25
/
4 followed by a 25-times downsampler.
s
[
n
]
25
↑
L
TX
(
z
)
4
↓
y
[
n
]
Figure 11.25
A 6.25-times upsampler.
Because of the upsampling (which translates to a slowed-down signal) it will
take a little over three hours to send the audio (6.25
187.5 minutes).
The quality of the received signal is determined by the SNR of the telephone
line; the in-band noise is unaffected by the multirate processing and so the
final audio will have an overall SNR of 40 dBs.
Now let us compare the above solution to a fully digital communication
scheme. For a telephone line with the bandwidth and the SNR specified
above a commercially available digital modemcan reliably achieve a through-
put of 32 kbits per second. The 30-minute DVD-audio file contains
×
30
=
(
30
×
60
×
48, 000
bits. At 32 kbps, we will need approximately 18 hours to trans-
mit the signal! The upside, however, is that the received audio will indeed be
identical to the source, i.e. DVD-quality. Alternatively, we can sacrifice qual-
ity for time: if we quantize the original signal at 8 bits per sample, so that
the SRN is approximately 48 dB, the transmission time reduces to 6 hours.
Clearly, amodern audio transmission systemwould employ some advanced
data compression scheme to reduce the necessary throughput.
×
24
)
Example 11.2: Spectral cut and paste
By using a suitable combination of upsampling and downsampling we can
implement some nice tricks, such as swapping the upper and lower parts of
a signal's spectrum. Consider a discrete-time signal
x
[
n
]
with the spectrum
