Processing of Signals - Digital Signal Processing: A Practitioner's Approach - page 17

The switch is controlled by an extremely accurate timing device. When it is
switched on it facilitates the transfer of the input signal y ð t Þ at that instant to an
analogue memory; after transfer, it is switched off, holding the value, and
conversion is initiated. In specifying an A/D device there are four important
timings: on time t on of the switch is a non-zero quantity, because any switch
takes a finite time to close; hold time t hold is the period when the signal voltage is
transferred to analogue memory; off time t off is also non-zero, because a switch
takes a finite time to open; finally, there is the conversion time t c .
The sampling time T s is the sum of all these times, thus T s ¼ t on þ
t hold þ t off þ t c . As technology is progressing, the timings are shrinking, and with
good hardware architecture, sampling speeds are approaching 10 gigasamples per
second with excellent resolution (24-bit). Way back in 1977 all these units were
available as independent hardware blocks. Nowadays, manufacturers are also
including anti-aliasing filters in A/D converters, apart from providing as a single chip.
There are many conversion methods. The most popular ones are the successive
approximation method and a flash conversion method based on parallel conversion,
using high slew rate operational amplifiers. A wide range of these devices are
available in the commercial market.

1.6.3 The Need for Normalised Frequency
We enter the discrete domain once we pass through an A/D converter. We have only
numbers and nothing but numbers. In the discrete-time domain, only the normalised
frequency is used. This is because, once sampling is performed and the signal is
converted into numbers, the real frequencies are no longer of any importance. If
f actual is the actual frequency, f n is the normalised frequency, and f s is the sampling
frequency, then they are related by

f actual ¼ f n f s : ð 1 : 36 Þ

Due to the periodic and symmetric [2] nature of the spectrum, we need to consider
f n only in the range 0 5. This essentially follows from the Nyquist

theorem, where the minimum sampling rate is twice the maximum frequency
content in the signal.

< f n < 0 :

1.6.4 Care before Sampling
Once the conversion is over, damage is either done or not done; there are no
halfway houses. Information is preserved or not preserved. All the care must be
taken before conversion.

1.7 It Is Only Numbers
Once the signal is converted into a set of finite accurate numbers that can be
represented in a finite-state machine, it is only a matter of playing with numbers.