Exponential decay in MATLAB time to frequency domain

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Ill ch
Ill ch 2019-9-6
评论： Ill ch 2019-9-26
Hello Everyone,
can anybody help how i can convert time domain to frequency domain following formula? i need it for signal parametrization. If i used fft for A=1,1,1 Delta 200,200,200 Omega 100,1001,1200 and phi 0. It is possible in time domain but if i want in frequency domain then fft dont work parameter vise optimization.
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Thank you so much

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Greg Wolff
Greg Wolff 2019-9-24
If I understood the question correctly, you can use a Laplace table to look for solutions:
See #20 here: http://tutorial.math.lamar.edu/Classes/DE/Laplace_Table.aspx
You can then translate to the frequency domain if need be:
https://math.stackexchange.com/questions/102627/how-do-the-laplace-s-domain-and-the-complex-frequency-domain-differ
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Greg Wolff
Greg Wolff 2019-9-26
Cool. Glad you found a solution.
Just to provide a bit of context for other readers:
Star Strider's response essentially uses same idea. But instead of looking up the Laplace transform in a table, the code in Star Strider's response performs the Laplace Transform symbolically for the specific equation.
See https://en.wikipedia.org/wiki/Laplace_transform#Formal_definition
for generalized information about transformation from the time-domain to the frequency-domain.
The MATLAB Code provided in that response does require the Symbolic Math Toolbox, so if you don't have access to that, you will need to use some other method to transform your equation to the frequency domain.
Either you can look up a table, solve it analytically yourself, or perhaps use another software that performs algebraic maths to solve for your equation.
Ill ch
Ill ch 2019-9-26
Thank you very much for kind informations. Its right here symbolic toolbox is necessary however in your code not.

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