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Informe técnico harta parte 3 desarrollo matemático
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About HART -- Part 3By Analog Services, Inc.Revised 8-9-99Revised 12-1-99Back to Table of ContentsBack to Part 1: PreliminariesBack to Part 2: Practical StuffBack to Papers Index
Part 3: Ponderous Stuff
Equation Describes CPFSK The HART signal is described mathematically as
where V = signal voltage, t = time, Vo = amplitude, Theta_sub_0 is an arbitrary starting phase, and Theta(t) is given by
where Bn(t) is a pulse that exists from 0 < t < T and has a value of 1 or -1, according to whether the nth bit is a 0 or 1. T is one bit time. If phase is plotted versus time it is a steadily increasing value that increases with two possible slopes.
Generating HART Signal With MATLAB The following "M" file listing is a program for generating HART modulation with MATLAB [3.1]. This is useful for testing or simulation. The program uses random input bits and generates square, trapezoidal, and sinusoidal outputs. The output ranges from -1 to +1. Figure 3.1 is an example of the output. The curves have been separated for clarity. The bottom curve is the modulating signal.
% hartgen.m
% Generates HART signals.
% Stephen D. Anderson --- November 29, 1999.
% Arrays are identified by a capital letter.
clear;
% comment out the following statement to get a different set of
% random bits each time program is run.
rand('seed',0);
% Generate a random bit stream.
numb_bits = 200;
Bits = round(rand(numb_bits,1));
% Convert bits to levels of +/- 1.
Xmit = 2*Bits - 1;
% Generate bit boundary times.
H_time = (0:(length(Xmit)-1))*(1/1200);
% Set sample rate to 50 kHz.
sample_time = 1/50e3;
% Sample the transmit bits.
i=1;
for j=1:length(H_time);
while ((i-1)*sample_time