DSP Lecture 10: The Discrete Fourier Transform

ECSE-4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 10: The Discrete Fourier Transform (9/29/14)
0:00:13 Review of the 4 Fourier transforms
0:00:54 The DFT's place
0:02:30 Recall the Fourier Series
0:06:32 Discrete-time exponentials are periodic
0:07:53 Definitions: the DFT and inverse DFT
0:09:42 The W_N notation
0:16:27 Thinking of the DFT as a change of coordinates
0:23:32 Writing the DFT as a matrix-vector product
0:26:23 The Fourier matrix F
0:32:44 How are the DTFT and DFT related?
0:34:58 The DFT samples the DTFT at equally spaced frequencies
0:38:45 Examples of computing the DFT
0:38:56 Delta function
0:40:56 A constant
0:44:19 The orthogonality principle
0:45:36 A pulse: the DTFT vs. the DFT
0:52:47 Matlab demonstration of how the DFT samples the DTFT
0:58:19 DFT properties
1:00:03 Cyclic convolution
1:05:19 Representing cyclic convolution as a matrix-vector product
1:10:55 Representing normal convolution as a matrix-vector product
1:13:50 Computing normal convolution as cyclic convolution with zero-padding
1:16:50 Block diagram for zero padding
Follows Sections 7.1-7.2 of the textbook (Proakis and Manolakis, 4th ed.).