Digital Signal Processing Reference
In-Depth Information
sample a speech signal that contains signal frequencies from 300 to 3,000 Hz at a
frequency of 8,000 Hz (which satisfies Nyquist's criteria). The waveform would
need a file size of 480,000 bytes (480 kilobytes) to store one minute's worth of
data using only 1 byte per sample. On the other hand, if we stored one minute of
stereo music using 2 bytes of data for each channel (left and right), the file size
would need to be over 10 million bytes (10 megabytes). This large file size is
necessary to accommodate a sampling rate of 44 kHz, which is the normal rate
used for high-fidelity audio signal with frequencies up to 20 kHz.
The second drawback is the speed of conversion from analog-to-digital form.
Although ADC chips are very fast these days, obtaining more accuracy requires
more time for conversion. Eventually, a limit on accuracy will be reached because
the conversion cannot be made in the allotted sample interval. This limitation is
more common when processing video signals that have bandwidths in the millions
of hertz (MHz).
It is important to note at this point that theoretically the sampling of an analog
waveform does not normally produce any error. (This assumes that the sample
clock does not introduce error because of timing jitter.) It is the quantization of the
sample that produces the error in a digital system. If the samples could be stored in
their original continuous-amplitude form, they could be used to regenerate the
original signal with no error (assuming the Nyquist criteria is met). The maximum
amount of error introduced into the system by this quantization is equal to one-
half of the difference between amplitude levels. As we can see, selecting a method
for the digitization of an analog signal is a compromise between conversion speed,
waveform accuracy, and storage or transmission size.
5.1.3 A Complete Analog-to-Digital-to-Analog System
Figure 5.3 shows a block diagram of a complete system that first converts an
analog signal to digital form for processing, transmission, or storage. Then the
conversion is undone by converting the digital signal back to analog form at
another time and/or place using a digital-to-analog converter (DAC). As shown in
Figure 5.2(b), the process of sampling a signal produces replicas of the original
analog spectrum at intervals of the sampling frequency. In order to recover the
original analog signal we simply have to eliminate the frequencies higher than
f
s
/2.
This filtering is accomplished by a high-order lowpass filter.
A good example of such a complete procedure is the processing of audio
signals for a music CD. The original sounds of the music are supplied by
instruments or voices and are then recorded on tape in analog form. At some later
time, these analog signals are digitized and encoded on the compact disc. We can
then buy this CD and take it home and play it on our stereo system where the
musical data is first converted from digital to analog form and then reproduced for
us. In this example, the data is processed, stored, and reproduced at a later time
and different place.
