Module 2.5 – Fundamentals (Fourier Transform)

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  • Fourier Transform (continuous, sampled input, discrete)
  • Short Time Fourier Transform
  • Fourier Transform properties

1. What is the Fourier Transform of two delta impulses located symmetrically around 0?

 
 
 
 

2. Mark the true statements.

 
 
 
 

3. What happens to the Fourier Transform of a signal if it is multiplied (in the time-domain) with a cosine wave with non-zero frequency?

 
 
 
 

4. Mark the correct statements.

 
 
 
 
 
 
 
 

5. Given that the Fourier transform of x(t) is X(jomega), what is the Fourier transform of x(t-T0)?

 
 

6. Each of the following magnitude spectra has a corresponding time domain signal. Give the correct grouping (e.g., 1A, 2B, etc.).

 
 
 
 

7. The Fourier transform of a rectangular window is WR(jomega). Given basic operations like duplication, multiplication, addition, convolution, time-scaling, etc., how do you derive the shape Fourier transform of a triangular window? What is the result?

 
 
 

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