Applied Algebra

Rutgers MATH 357 Spring 2020
Applied Algebra


Jpeg2000 2-level wavelet transform-lichtenstein
Lecture 1: These are the notes I prepared, but they contain more information than I ended up covering
Lecture 2: The complex exponential function
Lecture 3: The (complex) Fourier series for a periodic function
Lecture 4: The complex Fourier coefficients as dot products. Intro to the discrete Fourier transform.
Lecture 5: The discrete Fourier transform
Lecture 6: Filters
Lecture 8: Overview and the fast Fourier transform
Lecture 9: Waveforms vs wavelets. Intro to the Haar wavelet transform.
Lecture 10: The philosophy of wavelets, and more details on the Haar transform.
Lecture 11: The CDF(2,2) Wavelet transform.
Lecture 12: Haar Wavelet examples on epidemiological data. Overview of wavelet design considerations.
Lecture 13: What makes a good wavelet?
pre-Lecture 14: The CDF(2,2) Wavelet
Lecture 14: The CDF(2,2) Wavelet
Lecture 15: The linear algebra of wavelet transformations
pre-Lecture 16: The Daub4 Wavelet
Lecture 16: The Daub4 Wavelet
pre-Lecture 17: Scaling and wavelet vectors
Lecture 17: Scaling and wavelet vectors
Lecture 18: Review
Lecture 19: Intro to 2-D wavelet transforms, and overview of filter banks.
Lecture 20: 2-D wavelet transforms.
Lecture 21: 2-D wavelet transforms.
Lecture 22: Wavelet transforms for unbounded signals, part 1.
Lecture 23: Wavelet transforms for unbounded signals, part 2.