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DSP Lecture 10 The Discrete Fourier Transform
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Video Source: www.youtube.com/watch?v=jnxTpxB7HR8
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.).
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