The Fourier Transform can be found by noting the Fourier Transforms of the unit step and the cosine:
 
[Equation 2] 
 
[Equation 3] 
Using Equations [2] and [3] along with the
modulation property of Fourier Transforms, we obtain the result:
 
[Eq4] 
The plot of the magnitude of the Fourier Transform of Equation [1] is given in Figure 2. Note that the vertical
arrows represent diracdelta functions.
Figure 2. Plot of Absolute Value of Fourier Transform of RightSided Cosine Function.
The RightSided Sine Function
The rightsided Sine function can be obtained in the same way. This function is mathematically written in Equation [5]:
 
[Equation 5] 
The plot of the rightsided Sine Function is given in Figure 3 for A=2:
Figure 3. Plot of Step Function times the Sine Function for A=2.
Recall the Fourier Transform of the Sine Function:
 
[Equation 6] 
And we can procede exactly as before to obtain the final result:
 
[Eq7] 
Equation 7 gives the Fourier Transform of the rightsided sine function. The absolute value of this function
is plotted in Figure 4:
Figure 4. Plot of the Absolute Value of The RightSided Sine Function.
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