Module 2.5 – Fundamentals (Fourier Transform)


  • 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?