Fourier Transforms from the Definition

 

 

Example 1: Fourier Transform of  Delta Dirac Function 

Example 2: Fourier Transform of a Constant 

Example 3: Fourier Transform of Exponent 1 

Example 4: Fourier Transform of Exponent 2 

Example 5: Fourier Transform of Cosine 

Example 6: Fourier Transform of Square Pulse 

 

 

 

Example 1: Fourier Transform of  Delta Dirac Function

 

 

Useful result 1:

 

Useful result 2:

 

 

Example 2: Fourier Transform of a Constant

 

 

Example 3: Fourier Transform of Exponent 1

 

 

Example 4: Fourier Transform of Exponent 2

 

 

Example 5: Fourier Transform of Cosine

 

Another way to calculate it, is:

 

 

Example 6: Fourier Transform of Square Pulse