ECSE-4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 25: Perfect reconstruction filter banks and intro to wavelets (12/4/14)
0:00:20 What is a basis?
0:04:16 Bases for functions (e.g., Fourier series)
0:06:30 What are Fourier methods bad at?
0:08:54 Time-domain, frequency-domain and wavelet bases
0:14:01 Filter banks
0:18:06 Is perfect reconstruction with 1 channel possible?
0:23:01 Analyzing one channel of the filter bank
0:24:45 Summing up two channels
0:26:08 Conditions for perfect reconstruction
0:28:00 Choosing filters to remove aliasing
0:30:57 Simplifying the distortion equation
0:32:37 Satisfying the no-distortion condition
0:34:00 Halfband filters
0:34:45 The structure of halfband filters
0:36:57 An example halfband filter, and choices about its decomposition
0:41:48 Orthogonal filter banks
0:43:44 Quadrature mirror filters
0:44:42 Wavelet filter banks
0:50:45 Wavelet basis functions
0:53:56 The Discrete Wavelet Transform is O(N)
1:00:08 DWTs in image processing
1:04:03 Further discussion
1:08:14 DSP topics not discussed in this course
