Fourier Transforms

1.    If  and  , use the Fourier Transform properties to determine the following.

2. Use the Fourier Transform tables and properties to determine the following.

3.    Prove that the trigonometric, complex exponential and Cosine with phase form of Fourier series are equivalent and derivable from each other.



4.    Using trigonometric form Find the Fourier series of:



 And derived the same results using complex exponential form.



5.    Prove that the integral:

6.    Define the Fourier and inverse Fourier Transforms and Prove that the Fourier transforms are a special case of Laplace Transforms.




7.    Find the Fourier Transforms of the following signals:







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