# Plot real and imaginary part, modulus, phase and imaginary plane for a CFT transform given by equation on f from -4Hz to 4Hz

I'm trying to understand the basics of signal processing and I encountered this kind of a problem:

A CFT transform is given by
$$Y(f)=X(f)\cdot H(f)$$
where
$$X(f) = \Pi (\dfrac{f+1}{4})-j\cdot \Pi(\dfrac{f-1}{4})$$
and
$$H(f) = \Pi (\dfrac{f}{4})-j\cdot \Pi(\dfrac{f}{4})$$

I'm trying to plot the real and imaginary part of the CFT transform, as well as the modulus, phase and imaginary plane. However, I'm not really getting anywhere and would really appreciate help here - how do I go about this kind of task?

• What is CFT?

• Continuous Fourier Transform

• What are \Pi and j here?

• I guess the Pi function is the "door" = 1 on (-1/2, 1/2) and zero elsewhere, and I will answer accordingly. Let us know if the assumption is not accurate.

• Yes, this is accurate

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• Some symbols and images are broken, I see question marks instead of them. Could you please correct this?

• Yes, I notice that, I'm fixing it progresssively . (When editing they appear correctly so it is slightly complicated, I need to save each time to see what's not yet OK ...)

• I hope all is fixed now. You can also see it at https://docs.google.com/document/d/e/2PACX-1vRfUL0BdVAplAZRoyEXPdrpe1ym2CmtnaTAvev_knVZ1e87EDyZKNygMv6v6jll4CXGXynKtFu6spLb/pub

• I fixed a few more bugs (pi vs Pi ...) the editor has introduced after subsequent edits, against my will....

• Thanks a lot!