Stochastic Signal Processing 與 Least Squares Curve Fit 使用情況與統計
Speech, music, seismic vibrations, oil prices, and climate measurements are all examples of stochastic (random) signals. In this textbook—intended for individuals with prior training in introductory signal processing and introductory probability theory—we develop techniques to process such signals to extract useful information. We present case studies ranging from music to photographic images to oil prices to climate data to the motion of individual biomolecules. This textbook, as an interactive textbook ("iBook"), makes use of your device's ability to display dynamic information through films and animations and to hear the results of the techniques applied to music. At the end of every chapter there are homework problems ranging from easy to "olympic".
A new and exciting aspect is that we make use of your device's interactive capabilities to offer 59 laboratory experiments in signal processing. The experiments use the camera, the microphone, the speakers, and the graphical user interface. These experiments are not simulations; they are examples of real digital processing of signals in your device. In this time of at-home and online learning, this is the way to learn signal processing through study and experimentation.
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“Least Squares Curve Fit” is a user friendly, free of charge and free of ads app.
User inputs point sets and chooses function types.
Utilizing the Least Squares Linear Regression Method, the app calculates best fit curves, reports equations and draws graphs.
Point sets can be stored in a table and are available after app is closed.
Currently available function types are:
2D:
1. Line.
2. Parabola.
3. Polynomial up to 8th degree.
4. Circle.
5. Conic section (Ellipse or Hyperbola).
6. Trigonometric function as
C + A1*cos(ω*x) + B1*sin(ω*x) + … + An*cos(n*ω*x) + Bn*sin(n*ω*x),
where user can select n between 1 and 8 and enter any ω.
7. Exponential Function.
8. Bell Curve.
3D:
1. Plane.
2. Sphere.
Also, there is an option to choose the Best Fit:
the app goes through all the possible shapes and lists them in order from best to worst fit based on residuals.
In some cases, when the standard Least Squares method with orthogonal projection does not work, best fit for Line, Parabola, Polynomial and Trigonometric functions can be calculated with SVD.
Links to four other free apps by same developers are included in the app:
1. “Matrix Solver Step by Step” Linear Algebra Visual Guide.
2. “Polynomials and Linear Systems” Equation Solver.
3. “GraphMath” Graphing Calculator.
4. “Vectors and Planes” (and Spheres and Ellipsoids) 3D Geometry Guide.
Developers hope to get feedback from users at graphmath@aol.com.
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- 免費版
- 教育
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Stochastic Signal Processing VS. 
Least Squares Curve Fit12月 31, 2024