478 Chapter 15
background noise will average out, leaving a “ cleaner ” sequence of sample values that
describe the impulse response. This is the basis behind practical measurement systems.
Shift registers combined with feedback are also used in error detecting and correction
systems.
15.10 Sampling and Quantizing ......................................................................................
It is not possible to introduce each element of this broad topic without requiring the
reader to have some foreknowledge of future topics. The aforementioned text has tacitly
admitted that you will wish to match the description of the processes involved to a
digitized audio signal, although we have pointed out that handling audio signals in the
digital domain is only an example of some of the fl exibility of digital signal processing.
The process of converting an analogue audio signal into a sequence of sample values
requires two key operations. These are sampling and quantization. They are not the same
operation, for while sampling means that we only wish to consider the value of a signal
at a fi xed point in time, the act of quantizing collapses a group of amplitudes to one of a
set of unique values. Changes in the analogue signal between sample points are ignored.
For both of these processes the practical deviations from the ideal process are refl ected in
different ways in the errors of conversion.
Successful sampling depends on ensuring that the signal is sampled at a frequency at
least twice that of the highest frequency component. This is Nyquist’s sampling theorem.
Figure 15.20 shows the time domain view of the operation, whereas Figure 15.21 shows
the frequency domain view.
15.10.1 Sampling
Practical circuitry for sampling is complicated by the need to engineer ways around the
various practical diffi culties. The simple form of the circuit is shown in Figure 15.22.
The analogue switch is opened for a very short period, tac each 1/ Fs seconds. In this short
period the capacitor must charge (or discharge) to match the value of the instantaneous
input voltage. The buffer amplifi er presents this voltage to the input of the quantizer or
analogue-digital converter (ADC). There are several problems. The series resistance of
the switch sets a limit on how large the storage capacitor can be while the input current
requirements of the buffer amplifi er set a limit on how low the capacitance can be. The