1. Chapter 4 Fourier transform Prepared by Dr. Taha MAhdy

2. Fourier transform FT extends the basic idea of the Fourier series to incorporate nonperiodic signals. Think of it as a kind of generalization of the Fourier series concept-because it will allow us to obtain a frequency representation of periodic and nonperiodic signals.

3. FT lets us convert the representation of a signal in time into a representation of the signal in frequency. The inverse Fourier transform does the opposite. It lets us convert the representation of a signal in frequency into a representation of the signal in time.

4. Fourier transform of continuous time signals

5. Fourier transform of the discrete time signals Note: The Fourier transform of a discrete signal is always periodic with a period = 2π

6. Examples

7. THE SINC FUNCTION

8. Example, find the Fourier transform of the following pulse

9. Solution

10. PROPERTIES OF THE FOURIER TRANSFORM Time shifting

11. Frequency shifting

13. Linearity

14. Convolution (very important) Convolution in time domain equals multiplication in the frequency domain and vice versa.

15. Spectrum Plots

21. Problems Schaums’s Book 5.19, 5.20, 5.21, 5.23 6.11, 6.12, 6.22, 6.25, 6.31, 6.32, 6.34