While doing convolutions, I wanted to convolve a function f() with a square wave. There are two Laplace transformations of a square wave that I tried, as shown below. The problem occurs when I do the inverse Laplace on the Laplace of the original square wave, or more precisely when I attempt to plot that result. (In the code below I only show the inverse laplace of the laplace transformed squarewave, not the convolution.)
% P1 = ilaplace( 1/s*(1-2/(exp(T/2*s)+1)) );
P2 = ilaplace( 1/s*tanh(s*T/4) );
% Unfortunately, both don’t work with the symbolic toolbox.
assume(P2,’real’)
Tsteps = 0.1:0.5:20;
num = vpa(subs(P2,t,Tsteps),6)’;
stairs(Tsteps(:),num(:,1))
When I inspect the contents of num, the (voluminous!) contents are largely symbolic:
[conj(subs(diff(floor(s), s), s, -400))*(35.334851093590259552001953125 + 0.00000000023283064365386962890625i) + conj(s …
My program works with ‘simpler’ functions, like sinewaves, and then plots OK.
The stairs function faults in the (undocumented) getRealData().
Do I have to assume() something on the arguments of laplace(), ilaplace(), subs() or vpa()?
% getRealData returns the real components of ARGS. If ARGS contains any
% complex data, a warning is displayed. If any of ARGS are not numeric
% and cannot be converted to a double, an error is thrown.While doing convolutions, I wanted to convolve a function f() with a square wave. There are two Laplace transformations of a square wave that I tried, as shown below. The problem occurs when I do the inverse Laplace on the Laplace of the original square wave, or more precisely when I attempt to plot that result. (In the code below I only show the inverse laplace of the laplace transformed squarewave, not the convolution.)
% P1 = ilaplace( 1/s*(1-2/(exp(T/2*s)+1)) );
P2 = ilaplace( 1/s*tanh(s*T/4) );
% Unfortunately, both don’t work with the symbolic toolbox.
assume(P2,’real’)
Tsteps = 0.1:0.5:20;
num = vpa(subs(P2,t,Tsteps),6)’;
stairs(Tsteps(:),num(:,1))
When I inspect the contents of num, the (voluminous!) contents are largely symbolic:
[conj(subs(diff(floor(s), s), s, -400))*(35.334851093590259552001953125 + 0.00000000023283064365386962890625i) + conj(s …
My program works with ‘simpler’ functions, like sinewaves, and then plots OK.
The stairs function faults in the (undocumented) getRealData().
Do I have to assume() something on the arguments of laplace(), ilaplace(), subs() or vpa()?
% getRealData returns the real components of ARGS. If ARGS contains any
% complex data, a warning is displayed. If any of ARGS are not numeric
% and cannot be converted to a double, an error is thrown. While doing convolutions, I wanted to convolve a function f() with a square wave. There are two Laplace transformations of a square wave that I tried, as shown below. The problem occurs when I do the inverse Laplace on the Laplace of the original square wave, or more precisely when I attempt to plot that result. (In the code below I only show the inverse laplace of the laplace transformed squarewave, not the convolution.)
% P1 = ilaplace( 1/s*(1-2/(exp(T/2*s)+1)) );
P2 = ilaplace( 1/s*tanh(s*T/4) );
% Unfortunately, both don’t work with the symbolic toolbox.
assume(P2,’real’)
Tsteps = 0.1:0.5:20;
num = vpa(subs(P2,t,Tsteps),6)’;
stairs(Tsteps(:),num(:,1))
When I inspect the contents of num, the (voluminous!) contents are largely symbolic:
[conj(subs(diff(floor(s), s), s, -400))*(35.334851093590259552001953125 + 0.00000000023283064365386962890625i) + conj(s …
My program works with ‘simpler’ functions, like sinewaves, and then plots OK.
The stairs function faults in the (undocumented) getRealData().
Do I have to assume() something on the arguments of laplace(), ilaplace(), subs() or vpa()?
% getRealData returns the real components of ARGS. If ARGS contains any
% complex data, a warning is displayed. If any of ARGS are not numeric
% and cannot be converted to a double, an error is thrown. laplace, inverse laplace, symbolic, plot MATLAB Answers — New Questions

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