DSP Lecture 7: The Discrete-Time Fourier Transform

ECSE-4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 7: The Discrete-Time Fourier Transform (9/18/14)
0:00:02 The Discrete-Time Fourier Transform (DTFT)
0:00:16 How are the CTFT and DTFT different?
0:03:10 DTFTs are 2pi-periodic
0:07:25 Deriving the inverse DTFT
0:12:56 The DTFT and IDTFT formulas
0:13:39 Relationships between the FS, FT, and DTFT
0:18:39 The 4 kinds of Fourier Transforms
0:20:36 How does the DTFT converge?
0:24:00 Inverse DTFT of a pulse (i.e., an ideal low pass filter)
0:23:59 DTFT examples
0:27:24 Delta function
0:29:55 One-sided exponential
0:35:12 Time-domain pulse
0:42:06 DTFT convolution property
0:45:54 LTI systems and sinusoidal inputs: new frequencies can't be introduced
0:48:49 Response of a real LTI system to a real cosine
0:50:39 Example: system responses involving pure cosines
0:53:41 Magnitude and phase response
0:56:09 Ideal filters in the frequency domain
0:59:02 Why is linear phase response desirable?
1:02:24 Why can't we have zero delay in the real world?
Follows Sections 4.2.3 and 4.4 of the textbook (Proakis and Manolakis, 4th ed.).