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3.3 Signals 61

tern will be limited by the analog parts that are necessary at interfaces to the out-
side world.
The flexibility of digital signal processing, which is indirectly due to the deter-
ministic nature of the component errors, makes a DSP system easy to change and
also makes it easy to dynamically adapt the processing to changing situations.
This feature can, for example, be exploited to allow hardware to be multiplexed to
perform several filtering functions. Another important application is adaptive fil-
tering. Expensive tuning procedures, which contribute significantly to the overall
cost of analog circuits, are completely eliminated in a digital implementation.
Further, sensitivity to coefficient errors in an algorithm determines a lower
bound on the round-off errors or signal quality [25, 40]. In practice, an arbitrarily
good signal quality can be maintained by using sufficiently high numerical accu-
racy in the computations. Note that the accuracy of floating-point numbers is
determined by the mantissa. Generally, a large dynamic range (large exponent) is
not required in good signal processing algorithms. Therefore, DSP algorithms are
normally implemented using fixed-point arithmetic.

3.2.2 Robustness
Latch-up and different types of oscillations resulting from abnormal disturbances
may appear in analog systems, but most often analog systems return to normal
operation when the disturbance disappears. Corresponding phenomena, so-called
parasitic oscillations, are also present in digital signal processing algorithms, but
additionally some unique phenomena occur due to finite word length effects [251.
In fact, a major design challenge is to maintain stability of the system and recover
to normal operation in the presence of external disturbances. Of special interest
therefore are algorithms that guarantee that the system will return to normal
operation when the disturbance has subsided. Disturbances that cause abnormal
behavior can originate from transients on the power supply lines, ionic radiation,
initial values in the memories at the start-up, or abnormal input signals. The most
important filter algorithms with guaranteed stability are wave digital filters and
non-recursive FIR filters (finite-length impulse response filters), which will be dis-
cussed in detail in Chapter 4.

3.2.3 Integrated Circuits

The development of VLSI technology is an important prerequisite for making
advanced and complex digital signal processing techniques not only viable, but
also economically competitive. The use of VLSI technology also contributes to
increased reliability of the system.

3.3 SIGNALS

A signal conveys information by using a signal carrier. Typically, information is
modulated onto a physical quantity, e.g., a speech signal can be represented by a
voltage variation. Voltages or currents are commonly used as signal carriers in
electronic signal processing systems. In practice, several types of modulations are