Page 67 - Understanding Automotive Electronics

2735 | CH 2 Page 54 Tuesday, March 10, 1998 10:55 AM

2 THE SYSTEMS APPROACH TO CONTROL AND INSTRUMENTATION

determined by the desired processing algorithm. Although there are a great
many algorithms used in automotive electronics, it is possible to illustrate an
important class of DSP algorithms with the following recursive digital filter
algorithm:

K J
kn k ∑
y = ∑ ax – – by –
jn j
n
k = 0 j = 1
In this algorithm, the coefficients a and b are constants. The variables x are
k j n–k
previous inputs, beginning with the most recent (x ) and ending with the oldest
n
input used to find y (that is, x ). Similarly y are previously computed
n n–k n–j
outputs, beginning with y (the most recent) and ending with y . The
n–1 n–j
microcomputer calculates each product (that is, a x and b y ) and sums the
k n–k j n–j
products for each k from 0 to K and for each j from 1 to J.
As an example of DSP application, consider a low pass filter. The digital
equivalent of such a filter has a very simple algorithm,
y = ax – by n 1
n
–
n
where a and b are constants that determine the dynamic response of the digital
filter.
Throughout the remainder of this book, there will be specific examples
given of DSP systems in which the signal processing operations are performed by
computation in a microcomputer. The trend for virtually the entire spectrum of
automotive electronics is for digital implementation of signal processing.

ANALOG SIGNAL PROCESSING
Although signal processing is mostly digital today, it is worthwhile to
explain certain aspects of analog signal processing, as it is still the preferred
method for low-cost signal processing involving simple functional operations.
The operational ampli- The primary building block of analog signal processing is the operational
fier is the predominant amplifier, which is depicted symbolically in Figure 2.18. An operational
analog signal processing amplifier is a very high gain differential amplifier; that is, it amplifies the
building block. difference between the two input voltages. These voltages (relative to ground)
are denoted v and v . The input labeled + in Figure 2.18 is known as the
2
1
noninverting input, and the one labeled – is called the inverting input. The
output voltage v , relative to ground, is given by the following equation:
o
v = A(v – v )
2
1
o
where A is the open-loop gain. For an ideal operational amplifier, the open-loop
gain should be infinite. In practice it is finite, though very large (e.g., more than
100,000, typically).

54 UNDERSTANDING AUTOMOTIVE ELECTRONICS