8.8. Digital Signal Processing 507
subsequent filtration are done digitally therefore the process totally eliminates the
need to shape the signal before its digitization.
ADC
Analog In Digital OutAnalog In Digital Out(a)AnalogFilter Fast ADCAmpliferAmplifer
(b)DSPDSPFigure 8.8.1: (a) Basic steps involved in digital signal processing.
(b) Fast ADCs and pre-filtration is required in most applications to
avoid aliasing of data.Fig.8.8.1(a) shows the basic steps needed to digitally process the signal. Before
the signal could be digitally processed, it must first be preamplified and converted to
digital form. The reader would recall that the pulse from a preamplifier generally has
a fast rise time. This implies that the ADC must be able to perform the conversion
so quickly that the reconstructed pulse does not get aliased. Aliasing is a term that
was introduced in the chapter on imaging detectors. There, we were concerned with
spatial aliasing and saw that its effect is to introduce additional data and/or miss
actual data points due to under-sampling of the image. The same is true for temporal
aliasing. If the signal has high frequency components (such as the ones embedded
in the fast rise time of the pulse) and the ADC sampling frequency is lower than
the Nyquist frequency then the data will be aliased. As described in the chapter on
imaging detectors, Nyquist frequency is twice the highest frequency component in
the signal. That is, if one Fourier transforms the analog pulse, the Nyquist frequency
would be twice the highest frequency in the Fourier spectrum. Fig.8.8.2 shows the
effect of sampling frequency on thereconstructedanalog pulse. It is apparent that
high frequency components are most affected by undersampling. In Fig.8.8.2(a)
the data is sampled at a frequency much lower than the Nyquist condition and is
therefore severely aliased. On the other hand, as shown in Fig.8.8.2(b), sampling at a
frequency higher than the Nyquist value leads to an almost perfect replication of the
analog pulse. Now, practical ADCs have sampling and conversion rate limitations
and therefore it is not always possible to satisfy the Nyquist condition for all types
of input analog signals. A way around this problems is to pre-filter the data before
digitization. This is actually what is done in most practical systems (see Fig.8.8.1).
After digitization by the analog to digital converter, the data are fed into the
digital signal processing unit. This is where the data are digitally shaped, filtered,
and further processed using complex mathematical algorithms. Here the processing
is done solely through software (exceptions are the digital processing units consisting
of hardware components designed to perform specific operations). This is where the