Delay 811units. Digital shift registers are conceptually similar to
analog CTD devices with the important advantage that
only the presence or absence of a charge carries the sig-
nificant signal information. Now random access mem-
ory (RAM) provides flexibility and economic tradeoffs
for design. Until recently, the cost of memory was the
dominant factor in delay design considerations. Cur-
rently, with the trend for DSPs to include large amounts
of on-board memory, the systems have vastly reduced in
cost and now the dominant cost factor is in the A/D and
D/A converters.24.4 Sampling in timeBoth analog CTD delays and digital delays rely on
breaking the delayed signal up into discrete samples.
These samples are created by looking at a signal’s
amplitude at regular intervals and disregarding its ampli-
tude at all other times. The procedure is shown in Fig.
24-14. The sequence of pulses (B) controls a switch that
turns on the signal (A) for a brief instant, then discon-
nects it for the remainder of the sampling period. The
result is an amplitude-modulated pulse train (C) where
each pulse has amplitude equal to the instantaneous sig-
nal value. According to the sampling theorem, a contin-
uous bandwidth-limited signal that contains no
frequency components higher than a frequency fc can be
recreated if it is sampled at a rate greater than 2fc sam-
ples per second. This rate is called the Nyquist fre-
quency. Since the real world never completely satisfies
theoretical conditions, sampling frequencies are usually
chosen to be higher than 2fc. Thus, 20 kHz bandwidth
delays will typically be found with a sampling frequency
of 48 kHz rather than the bare minimum of 40 kHz.
24.4.1 AliasingSampling of the audio signal is a form of modulation.
Modulation of a bandwidth-limited signal with an upper
frequency of fc , by the sampling frequency fs produces
additional copies of the original spectrum centered on
frequencies fs, 2 fs, 3fs, etc. If the sampling frequency is
not high enough or the bandwidth is not adequately lim-
ited, part of the spectrum centered on fs will fold over
into the original signal spectrum as in Fig. 24-15. The
fold-over components become part of the signal in the
recovery process, producing unwanted frequencies that
cannot be filtered out.An example of the effect of aliasing can be seen on
moving wagon wheels in a movie that appear to reverse
direction. The sampling rate of the film is lower than the
rate at which individual spokes pass the top of the
wheel. When the image is reconstructed, the spoke fre-
quency has folded over and the wheel appears to move
at a different rate. This phenomenon is known as alias-
ing. Fig. 24-16 shows that aliasing where the sample
points lie have the same amplitude on two waveforms
of different frequencies.Aliasing must be eliminated or at least largely
reduced by selection of a high sampling rate and an ade-
quately sharp antialiasing filter. At the output side, a
similar low-pass antiimaging filter must be used to
reduce the number of high-frequency glitches due to the
Figure 24-14. The process of sampling a signal. switching at the sample rate.A. Analog signal. B. Sampling pulses.C. Modulated pulses. D. Held pulses.1.0
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Figure 24-15. Frequency spectrum folding over around the
sampling frequency.Figure 24-16. Aliasing.A Afs fc fc fs 2 fs
fc fs +fcFrequency
folding0 5 10 15 201.5
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