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Signal Analysis

This site provides links to a variety of topics related to signal analysis, image processing and the harmonic analysis of tides. It started as a set of links for teaching marine science students about the Fourier Analysis of Time Series. There are also links to an undergraduate mathematics course in Fourier and Complex Analysis. This has resulted in a draft of a text devoted to the mathematics behind these topics.

Fourier and Complex Analysis Course

• Course Site

• Class Notes (in textbook format)

• Course Links

• Class Project using Matlab

Fourier Analysis of Time Series 

Class notes

Fourier Analysis of Time Series MS Word, PDF,  HTML (HTML needs work and the overall set of notes need to be proofread.)  Last Revised - 9/18/02
Harmonic Analysis MS Word Last Revised - 10/16/02
Filters.doc - not proofread or ready for prime time.

• Introduction

  • Signal Processing for Everyone - G. Strang

  • Harmonic Analysis - Lepikult

  • Signal Processing - Michael McCumiskey's site with audio and tidal harmonics

  • Primary Tidal Components

  • Analog Signal Processing, Digital Signal Processing from Cuthbert Nyack

  • The Scientist and Engineer's Guide to Digital Signal Processing - Free book

• From Integral Transforms to Series

  • Fourier Transform, Fourier Series, Discrete Fourier Transform - Eric Weinstein's World of Math

• Fourier Series

  • Orthogonality of Trigonometric Basis

  • Special Trigonometric Bases - Harvey Mudd College

  • Products of Trigonometric Functions, also at ThinkQuest

  • Fourier Series - Eric Weinstein's World of Math

  • Fourier Trivia - Amara's Wavelet Page

• Discrete Fourier Transform

  • Discrete Orthogonality

  • Exponential Sum Formula - Math World

  • Discrete Fourier Transform - Eric Weinstein's World of Math

  • DFT and FFT - P. Bourke

  • Discrete Transform with BASIC code

  • Complex Numbers - World of Math, or SOSMATH

  • Mathematics of the Discrete Fourier Transform (DFT) - Text!

    • Derivation of DFT

  • Sums of Cosines

  • The Discrete Cosine Transform - G. Strang

• Matlab Implementations

  • Basic Matlab

  • DFT Implementations - Old, Loops, Compact

  • Harmonic Analysis - Example1, Example 2, Maple 8 Implementation

  • Functions - harm.m, plotharm.m

  • Using Matlab fft function - fanal.m

  • Matlab Educational Demos

  • Filter - filterdata.m

• Fast Fourier Transform

  • Fast Fourier Transforms in Different Computer Languages

  • FFT Tutorial

  • Basic FFT Butterfly

  • Eight point FFT Butterfly

• Harmonic Analysis

  • Tidal Analysis at Duck, NC

  • Marine Geophysical Data Analysis - Lectures by Dietmar Müller & Michael Hughes

  • Harmonic Analysis and the Prediction of Tides

  • Nonlinear Regression Sites

    • Visual Fit - A Teaching Tool on Nonlinear Regression
    • Visualizing Best Fit Line
    • Nonlinear Least Squares Curve Fitter
    • MathPad - CurveFitting
  • NOAA
    • NOAA Tides https://tidesandcurrents.noaa.gov/noaatidepredictions.html?id=8658120 
    • Harmonic constituents at Wilmington https://tidesandcurrents.noaa.gov/harcon.html?id=8658120 
    • What are they? https://tidesandcurrents.noaa.gov/about_harmonic_constituents.html  - good references/information at the bottom of the page.
  • New Links
    • Analyzing & Predicting Your Own Tides MATLAB Gui
    • LP-Tides
    • Pawlowicz's Matlab including t-tide, article
    • shorter description
    • attempts to convert to Python: https://github.com/moflaher/ttide_py
    • tide_pyqt5
    • ttide_py
    • OceanPython.org
    • pytides or https://github.com/sam-cox/pytides, discussion of tidal harmonics
  • History
    • https://hackaday.com/2015/10/08/how-analog-tide-predictors-changed-human-history/  Tide Predictors
    • More history - https://notendur.hi.is/~einar/HistoireMarees.pdf
    • Modern Theory And Practice Of Tide Analysis And Tidal Power https://uaf.edu/cfos/files/research-projects/people/kowalik/Book2019_tides.pdf

• Spectral Analysis

  • LabView Tutorials

• Rotary Component Method

• Effects of Sampling

  • Shannon Sampling Theorem and Nyquist Rate

• Windowing and Filtering

  • Windowing Applet from MIT Biomedical Signal and Image Processing 
    course. 

  • Digital Filters - and Java applets for windows and filters 

  • SPMLAB Filtering Applet 

  • FIR Applet

  • Windowing for Speech Analysis 

• Wavelets and Signal Processing
  • Spectral Analysis and Filtering with the Wavelet Transform
  • http://www.bearcave.com/misl/misl_tech/wavelets/index.html 
• Software
  • Spectrogram
  • Spectrum Lab 
  • Cool Edit
  • Gold Wave
  • Audacity

Marine Science/Bioacoustics Links

The Mathematical Foundation of Image Compression

This is student research into image compression using fractal compression techniques. 

• Lisa Soberano's Honors Research, May 2000.  PDF (2.2 MB) DOC (2.2 MB)

• Paper on Even Extensions in 2D DOC  (611 KB)