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APPLICATION EXAMPLES
Simple Pole Calculations
BOl
=
e-
aT = exp [-(5222)(0.0001)]
= 0.593214
B oI +
1070
= 0.10011001011 (in binary)
BOl = 0.10010111110.
BoI-I % = 0.10010110010.
A value in this range can be represented as
= 2-
1
+ 2-
4
+ 2-
5 -rID
dc gain = III -B
OI
= 2.4583
Complex Pole Calculation
B\l
=
2e
-aT
coswT
= 2exp [-(1955.8)(0.0001)]
cos [(6873.7)(0.0001)]
1.271229.
B\l+1 %
=
1.01001000101 (in binary)
B\l
=
1.01000101011
=
2
0
+2- 2 +2-
6 •
BII-I %
=
1.01000010001.
BI2
=
-e- 2aT =exp[-(2)(1955.8)(0.0001)]
=
-0.67627194.
B
12
+I%
=
0.10101110110.
B\2
=
0.10101101001.
B I2 -1%
=
0.10101011011.
=
-r
L
2-
L
2-
L
r
6 .
max gain
=
[(l+B 2
)V
l+(B I 2/4B 2 )] I
=
4.7949.
Complex-zero calculations
AID
=
I.
All
=
-(2) (A oI ) e- a2T cosw2T
=
-0.28798805
= 0.01001001101 (in binary)
=
-rLrL2-s.
AI2
=
AOle-2aH
=
(l)exp(O)
=
1.0
7.4 The 2920 as a Spectrum Analyzer
A scanning spectrum analyzer embodies many functions
usable in a broad class of analog applications. These
functions
include lowpass and band path filters,
multipliers (mixers), detectors, and oscillators. The
spectrum analyzer is a useful circuit which lends itself to
7-7
applications such as speech processing, industrial con-
trol, medical electronics, seismic and sonar signal detec-
tion and analysis.
The implementation of a spectrum analyzer using a
sampled data system requires an understanding of
sampling theory and digital signal processing, as well as
the ability to specify the system in analog terms. A basic
review of sampling theory was provided in Chapter 2.
Once the analog block diagram of the application is
complete, it is relatively straightforward to implement
each subsystem as a block of code in the 2920 signal pro-
cessor. The following section describes the block
diagram of the spectrum analyzer and discusses design
considerations.
Implementation
of
the
spectrum
analyzer is discussed in terms of the actual design pro-
cess using the signal processor.
7.4.1 Description of Spectrum Analyzer
The purpose of this spectrum analyzer is to determine
the long term spectral characteristics of a signal in the
200 Hz to 3.2 KHz frequency band. The approach is to
sweep the input signal through a high resolution (nar-
rowband) bandpass filter and observe the filter response
as a function of the frequency sweep. The spectrum
analyzer block diagram and parameters are determined
and sampled data considerations are taken into account.
The 2920 signal processor code is then straightforward
to develop for the multiplier, sweep generator, voltage-
controlled oscillator, full-wave rectifier, and output
lowpass filter sections of the analyzer. The specifica-
tions of the analyzer are given below:
Table 7-2. Spectrum Analyzer Specifications
• input bandwidth
: 3 KHz
• resolution bandwidth : 100 Hz
• sweep rate
: 6 KHz/sec or 0.5 sec/Band
• dynamic range
: 48 dB
• inputs - analog signal
-IV:li;SIG:li;IV
• outputs - frequency response amplitude (vertical
axis) sweep waveform (sawtooth)
(horizontal axis)
7.4.2 Block Diagram Description
Ideally, a scanning spectrum analyzer could be imple-
mented by simply scanning a tunable narrowband band-
pass filter across the input signal frequency to determine
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