The Procedure.
Signal we will name the data ordered concerning some argument (for example, time, frequency, spatial coordinate). If as argument time equivalent concepts will be time process, time realization is chosen.
For generation of signals Matlab environment functions, including function of package Signal Processing are used.
In package Signal Processing following functions of generation of signals are realized:
Function |
Action
|
chirp |
Generates cosinusoid with variable frequency |
diric |
Calculates function of Dirihle |
gauspuls |
Generates a sinusoid modulated by function of Gauss |
gmonopuls |
Generates a monoimpulse of Gauss |
pulstran |
Generates impulses |
rectpuls |
Generates aperiodic rectangular impulses |
sawtooth |
Generates sawtooth fluctuations |
sinc |
Function sinc |
square |
Generates rectangular impulses |
tripuls |
Generates a periodic triangular impulses |
vco |
Operated source of pressure |
The detailed description of functions and their parameters can be received from help system Matlab or using a command help <a function name>.
Let's consider examples of signals generation.
1. It is required to receive a signal a sinusoidal signal with the set frequency f=0,2 Hz and various frequencies of discretization fD=1 Hz, 3 Hz, 10 Hz. Length of a signal 20 sec.
Since Matlab environment work is focused on matrix representation of signals, we will set at first three vectors of time t which will correspond to various frequencies of removal given (to frequencies of discretization).
>> fs1=1; fs2=3; fs3=10;
>> T=20; f=0.2;
>> t1=0:1/fs1:T;
>> t2=0:1/fs2:T;
>> t3=0:1/fs3:T;
%fs1 – sampling frequency – frequency of discretization
% T – length of a signal; f - frequency of a signal
For generation of a sinusoidal signal (function evaluations sin in set the vector ti points uses function Matlab – sin. We will specify, demanded by the given function, arguments:
>> help sin
SIN Sine.
SIN (X) is the sine of the elements of X
Overloaded methods
help sym/sin.m
Further we will set a vector of signals:
>> y1=sin (f*t1);
>> y2=sin (f*t2);
>> y3=sin (f*t3);
For visualization of signals we will use function plot:
>> plot (t1, y1, ' - ro ', t2, y2, ' - g> ', t3, y3, ' - b ')
>> grid on
>> xlabel (' Time ');
>> ylabel (' Amplitude ');
>> title (' SIGNAL ');
% grid Display
% the Signature of an axis X
% the Signature of axis Y
% drawing Heading
The result of work is represented on Figure 1
Figure 1
All above operations can be decorated in the form of m - file in the editor of m - files (Figure 2).
Figure 2.
2. It is required to receive function MATLAB generating a signal duration 10 with, removed with step 1/f and representing
The parameter f is argument of function.
Function appears a reserved word function after which expression [output_value_function] = the name of function [( arguments - functions)] follows.
One possible variants of the decision of the given problem it is resulted more low
function A = example1_2 (f)
t=0:1/f:10;
t1=0:1/f:3;
A (1:length (t1)) =sin (7*pi*t1);
t2 = (3+1/f):1/f:6;
A (length (t1) +1:length (t1) +length (t2)) =2+sin (7*pi*t2);
t3 = (6+1/f):1/f:10;
A ((length (t1) +length (t2) +1) :( length (t1) +length (t2) +length (t3))) =sin (2*pi*t3);
plot (t, A);
grid on;
The given function can be caused from other functions or is started from Command Window:
>> example1_2 (128);
The result of performance of function is resulted more low
Figure 3 |
Convolution
Convolution plays the main role in COS theory (look the lectures ).
Discrete resultant of two signals g and h is discrete convolution of two signals g и h называют one - dimensional mass
In the environment of MATLAB convolution is realized by the following function conv (And, B).
As a result the vector in length LENGTH (A) +LENGTH (B) - 1 turns out