SymPy Fourier Transform of Cosine and Sine Returns Zero

[ODARI KIBISI CHARLES]

Hi everyone,

I'm currently working on implementing Fourier Transform computations using SymPy to better understand the transforms of signals such as cos(2πf0​t) and sin(2πf0​t).

However, when I use fourier_transform() on these functions, SymPy returns 0 instead of the expected result involving Dirac delta functions, for example:

• F{cos(2πf0​t)}=21​[δ(f−f0​)+δ(f+f0​)]
• F{sin(2πf0​t)}=2j1​[δ(f−f0​)−δ(f+f0​)]

From my understanding, these transforms are distributions (generalized functions), so I'm wondering:

1. Does SymPy's fourier_transform() support Fourier transforms in the distributional sense?
2. Is there a specific way to define the assumptions on the variables (e.g., real, positive) or to invoke the transform so that the Dirac delta terms are returned?
3. If not, what is the recommended approach for symbolically computing or representing Fourier transforms of pure sinusoids in SymPy?

Any guidance, examples, or best practices would be greatly appreciated. Thank you!

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