Matlab and Radial Basis Functions

This lens intends to provide a basic discussion on Matlab and Radial Basis Functions.  I'll first provide resources on Matlab and then on radial basis functions.  This lens will continue to evolve as I will provide future multimedia presentations here and when appropriate at my website at Freedom University.  Please check this lens often as I will update as best as I can as time permits.

Visit Freedom University Blog  for a applications and demonstrations of Matlab and Simulink.

If you would like to help me develop this large topic, please contact me at john@e-liteworks.com or visit Freedom University or elite WORKS, LLC.  For a list of courses that I attempted to use Matlab please visit. Freedom University Courses.  I will provide access to various matlab code used in these courses as well if there is interest.

For the newcomer to Matlab, below are some MATLAB resources and in this case, most for now deals with digital signal processing.  If anyone has MATLAB links for radial basis functions, please contact me.

FLASH Demos.  See Flash-animated demos from Purdue University of continuous-time convolution, sampling, discrete-time convolution, FIR & IIR filter, FFT, pole-zero plots and frequency response, and spectograms.  

Filter Solutions.   An external website, Filter Solutions contains many different types of filters to choose from. Passive, Transmission Line, Active, and Digital IIR and FIR are all supported. See our FIR page for information about our FIR filters that are supported. Analog and IIR filters may all be quickly and easily delay equalized with our real time updates to all pass pole/zero manipulation.

Passive and active filters may be quickly and easily modified and reanalysed with our real time analysis feature. Finite Q may be included in the analysis.

Digital filters may be modified and analysis in real time for finite precision analysis.

Table one below lists the type of analog filters that are supported along with the parameters that are available for you to define.

M-Files.  The section provides categories of m-files for the powerful MATLAB program.  These files are intended to help you reduce your debugging time and encourage you to experiment more by varying the parameters and doing "what-if" thinking.  For example see if you can get a square wave sequence based on sinusoidal sequences. You can use any of the files to suit your style or programming needs.

DSP/Matlab Resources.  DSP and Matlab references of other web sites, especially for those who are new to Matlab. The web page will evolve as the course progresses during the next five weeks to provide better teaching projects and educational material.

MIT List of References

HST.582J/6.555J/16.456J
Signal Processing Resources
[ Course Resources | Probability ]

Overview:

New Links: Gibbs Phenomenon, Linear Algebra

This page describes several applets and on-line tutorials that cover some of the material presented in the first few weeks of the course. They are organized below according to lecture topic. All of the applets come from four main sites, listed here along with a general note about each. If you are aware of other web-based resources for learning this material, please let us know so that we can include them on the course website.

1. JHU Signals, Systems & Control Demonstrations - Has many different tutorials and applets available. In general the applets on this site are the best of those listed. If you are limited on time, go to this site.
    
2. Mississippi State Applets - Has a handful of applets with three that relate to this course. The applets are good at demonstrating various concepts, but do not include explanations. Therefore they are good for reviewing the material, but not a good place to start.
    
3. J-DSP - A very broad application where the user defines what signal processing is done through the setting up of a block diagram. Takes a little time initially to become familiar with the application, but can be very useful. A detailed description follows in its own section below.
    
4. RPI Links - Has a lot of applets, but most are not related to the early part of this course. Look to this site later for help on probability, which we plan to cover in a later handout.

• JHU Sampling - An OK applet that shows the results of changing the sampling frequency on the sampled signal and also the frequency magnitude.
   
• JHU Discrete-Time Frequency - A quick overview of the differences between continuous and discrete time frequency components.

• JHU LTI Systems and Convolution - An interactive lecture that contains a very good overview of LTI system properties and convolution. Includes an applet that allows the user to view the flip and shift method of continuous time convolution.
   
• JHU Discrete-Time Convolution - Discrete Time convolution applet that is easy to use and shows the flip and shift method. Not a lot of explanation provided.
   
• J-DSP - See below.
   
• Miss St Filter Design Tool - Under "user defined" option, you can input the filter coefficients and view the resulting magnitude and phase of the filter. Can also specify the filter type and frequency parameters, the applet will then produce the filter coefficients.
   
• Miss St Convolution Tool - Not much explanation. The user defines two signals and the resulting flip and shift convolution is shown.

• JHU Discrete-Time Fourier Series - Discrete Time Fourier Series (DTFS): applet that shows the relationship of DTFS coefficients, which are closely related to the DFT.
   
• JHU Continuous Fourier Transform - Continuous Time Fourier Transform (CTFT): Gives some properties of the CTFT, and allows the user to view the changes to the magnitude and phase of the transform given a change in amplitude, time shift, or derivative of the original signal.
   
• J-DSP - See below.

• http://web.mit.edu/6.555/www/matweb/demo.html - Interactive demonstration of spectral analysis developed for this course and used in Week 2 of Lab 1.
   
• Miss St Spectrum Analysis Tool - Applet graphs magnitude and phase of CTFT after a signal and window are defined. Helps to see the differences between various types of windows, but not real easy to use.

Java Digital Signal Processing (J-DSP) is an on-line DSP simulator. The program is very broad and does not target a specific topic like the other tutorials. But it can be very useful for filter design, FFT evaluation, and even speech analysis. JDSP does take a little bit of time to get used to, however.

Filter Example:

For a quick example we can design an FIR or IIR filter. The figure below is the main screen of the JDSP editor, refer to it while reading the example below.

The first step is to skim over the General Information tutorial found under the exercises heading on the main page. This exercise goes through the same example as below and explains in more detail how to attach and manipulate blocks, etc.

1. At the main page click on "start J-DSP" under the "J-DSP Main" header to get started.
    
2. First we need an input signal. To do this, simply click on [Sig. Gen] on the left side of the page and then click on the white area to place a sig. gen. block. Clicking on this box will bring up another window where you can define a sequence or select a standard sequence such as a sine or exponential.
    
3. Next we place a filter block on the white area and connect our input signal to it with an arrow. Note that we have not defined any part of the filter, and for now it is just passing the input signal through. To adjust our filter we need to change coefficients.