Hello; I'm using the symbolic maths toolbox, specifically the fourier function. How do I access the positive and negative frequency components of the result separately ?

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Gordon Cooper 2016-11-30

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评论： Star Strider 2016-12-1

Hello; I'm using the symbolic maths toolbox, specifically the fourier function. How do I access the positive and negative frequency components of the result separately ? I need to multiply the positive frequency components by -i and the negative frequency components by i, to compute the Hilbert transform. Note that Matlab's Hilbert function does not work with the symbolic maths toolbox.

Thank you.

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Answer 1

Star Strider 2016-11-30

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The fourier function will give you the symbolic expression for the Fourier transform of your time- or spatial-domain function. You then are free to calculate and plot it for the frequency values you wish.

Also consider using simplify (with the 'Steps',10 name-value pair) and matlabFunction to create a function you can use in numerical computations.

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Gordon Cooper 2016-12-1

Thanks for all the effort, but I'm using Matlab's symbolic Fourier transform function 'fourier' and I'm battling to manipulate the results.

Star Strider 2016-12-1

This is my alternative approach. I don’t know what function you’re transforming, but in my experience, coding my own transform — as I did here — generally produceds the result I want.

The ‘problem’ with the fourier function is that it integrates from -Inf to +Inf. If your time-domain function has other than infinite support, this will cause problems. That’s the reason I generally code my transforms myself.

If I know the function has infinite support, fourier produces the appropriate result.

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Answer 2

Gordon Cooper 2016-11-30

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Hello, yes, the fourier function gives me the symbolic expression for the FT of my symbolic function. But how do I access the positive and negative frequency components separately ? I want to multiply the former by -i and the latter by i, to implement a Hilbert transform.

thank you

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Answer 3

Walter Roberson 2016-11-30

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Multiply the symbolic output by the Heaviside function on the frequency to get the positive components, and by Heaviside of negative of the frequency to get the negative components.