NeXT Education Software Sampler 1992 Fall

home *** CD-ROM | disk | FTP | other *** search

/ NeXT Education Software Sampler 1992 Fall / NeXT Education Software Sampler 1992 Fall.iso / READMEFiles / SigProc2.0.README < prev next >

Wrap

Text File | 1992-08-29 | 24.5 KB | 517 lines

(Public Domain) Signal Processing Packages (SPP) and Notebooks 2.72 for Mathematica Version 1.2 and higher by Brian Evans, James McClellan, Kevin West, Wallace McClure, Lina Karam, and James Proctor Digital Signal Processing Laboratory School of Electrical Engineering Georgia Institute of Technology Atlanta, GA 30332-0250 evans@eedsp.gatech.edu ---> Introduction This is an unsupported release of Mathematica code for symbolic signal processing copyrighted by The Georgia Tech Research Foundation. Once installed (see below), this collection of Mathematica packages can be loaded by any user. Bundled with the packages are many Notebooks. Those that are tutorials are: AnalogFilters, DTFT, PiecewiseConvolution, and zTransform (in three parts). The other Notebooks serve as on-line help: EducationalTool, LaPlaceTest, README, SignalProcessingExamples, Signal- ProcessingIntroduction, and SignalProcessingUsage. They demonstrate the abilities of these packages. A complete set of references is given at the end of this file. ---> Index of Files The files that contain a complete set of the signal processing packages and Notebooks for Mathematica are: SigProc2.0.tar.Z compressed tar file for Unix systems SigProc2_IBM_PC.zip zip file for the IBM PC running MS-DOS SigProc2.0.mac.sea.hqx binhexed self-extracting archive for Mac Please transfer these files as binary files. In the case of the IBM PC version, the release was loaded on to a PC, zipped, and reloaded on the FTP site. All of the file names have been truncated so that they are unique. In the case of the Mac version, the release was loaded on to a Macintosh--- the files were then converted to Mathematica format and archived using Compact Pro 3.1 into one self-extracting archive. The self- extracting archive was then run through BinHex 4.0 and put on the FTP site. Other files of interest are: CHANGES text file documenting changes in code README this text file StanfordNotebooks.tar.Z Notebooks from CCRMA at Stanford (see "Related Archive Sites Below") VERSION-x.xx indicates the FTP site has version x.xx c-src.tar a tar file of useful C programs math.el configuration file for Emacs so that Emacs becomes a front-end to Mathematica usage.ps PostScript version of the reference guide usage.tex TeX version of the reference guide usersguide.ps PostScript version of the user's guide usersguide.tex TeX version of the user's guide --> Installation on an IBM PC After downloading "SigProc2.zip", move the zip file to a directory other than the one in which Mathematica is installed. Then, type ms-dos> unzip -d SigProc2.zip You can see all of the possible options for unzip by typing just "unzip". If your machine cannot find "unzip", try "pkunzip". If that fails, then acquire a copy of "unzip" (which is in the public domain) or "pkunzip" (which is shareware). The unzipped archive will produce a Packages and a Notebooks directory. You will need to edit Mathematica's "init.m" to add the new directory to Mathematica's $Path variable. The command to do this is "$Path = Append[$Path, <new_path>]" where <new_path> is the new direc- tory path surrounded by double quotes. ---> Installation on a NeXT Machine Move the file "SigProc2.0.tar.Z" into a temporary directory. Then evaluate the Unix commands "uncompress SigProc2.0.tar.Z" and then "tar xf SigProc2.0.tar". It will create a Packages and a Notebooks directory. To move them to a standard place, type the following Unix commands: NeXT-Unix> cp -r Packages /LocalLibrary/Mathematica NeXT-Unix> cp -r Notebooks /LocalLibrary/Mathematica The SPP will be in /LocalLibrary/Mathematica/Packages/SignalProcessing and the SP Notebooks will be /LocalLibrary/Mathematica/Notebooks in the sub- directories Handouts, Help, and Tutorials. --> Installation on a Unix Workstation Other Than a NeXT Move the file "SigProc2.0.tar.Z" into a temporary directory. Then evaluate the Unix commands "uncompress SigProc2.0.tar.Z" and then "tar xf SigProc2.0.tar". It will create a Packages and a Notebooks directory. To move them to a standard place, type the following Unix commands: Unix> cp -r Packages /usr/local/math If you cannot write to /usr/local/math, then put the packages in another directory and edit Mathematica's "init.m" file to add the new directory to Mathematica's $Path variable by saying "$Path = Append[$Path, <new_path>]" where <new_path> is the new directory. Once there is a Notebook reader under X Windows, then you can move the Notebooks to a "standard" place by evaluating Unix> cp -r Notebooks /usr/local/math Otherwise, you can discard the Notebooks (for documentation, refer to the TeX files "usage.tex" and "usersguide.tex". ---> Installation on a Macintosh Download "SigProc2.0.mac.sea.hqx" to your Macintosh in a temporary directory. Run BinHex 4.0 on it (with the Text Filter option disabled) to produce "SigProc2.0.mac.sea" which is a self-extracting archive. Now, double click on the .sea file, and it will produce a Packages and Notebooks folder. Move the SignalProcessing folder in the Packages folder to Mathe- matica's Packages folder. You can keep the Notebooks anywhere you want such as in one of the Mathematica folders. Also, please see the note below. ---> Macintosh Users Please let Mathematica allocate as much memory as possible. I give it 8000 kb. You can check the value by clicking once on the Mathematica icon and select the Get Info option from the Finder's File menu. It is the number that appears in the lower left-hand corner of the info window. If you are using Mathematica 1.2, please make sure that the start up procedure includes the loading of the Elliptic functions, symbolic inte- gration, and Series packages. ---> Warning A warning about opening some Notebooks under Mathematica 2.0. The signal processing Notebooks are appear in their ASCII form. The binary side information like graphic bit maps are not included so Mathematica will have to regenerate them from the ASCII Notebook. In Mathematica 2.0 and higher, the Notebook will generate all missing bit maps for graphics contained in a Notebook, and it will inform the user by saying "Rendering ..." in the header of the window containing the Notebook. Each bitmap roughly adds 20 kb to the memory required by the Notebook. Some Notebooks will double and triple in size. Under Mathematica 1.2, it only generates missing bit maps as needed (i.e., when you want to see the picture). ---> Related Archive Sites An additional set of related Notebooks is available in the same anonymous FTP site (gauss.eedsp.gatech.edu or IP # 130.207.226.24) in the compressed tar file "StanfordNotebooks.tar.Z" (which is also available for the PC in zip form as well). These three Notebooks investigate the use of windows in masking data and designing filters. Another set of Notebooks that describe cochlear signal processing and analog filter design, written by Malcolm Slaney, are available from Apple Inc. via anonymous FTP to ftp.apple.com. They are available free of charge by sending e-mail to corp.lib@applelink.apple.com which comes with a hard copy version. The Mathematica Special Interest Group runs a very large FTP site at yoda.physics.unc.edu (IP #128.109.180.137). It does contain the Note- books written by Malcolm Slaney as well as a version of the signal pro- cessing packages and Notebooks. A set of controls packages have been developed based on the signal processing packages. Accompanying the set of controls packages is a set of Notebooks that follow Ogata's 1991 textbook "Modern Control Theory". COSYPAK and COSYNOTES are available via anonymous FTP to veda.esys.cwru.edu (IP #129.22.40.9). ---> Getting started The Mathematica file "Master.m" loads in all the necessary files under Mathematica 1.2 but only tells Mathematica 2.0 where to find all of the new routines. Load it in by Needs["SignalProcessing`Master`"]. The one-dimensional/two-dimensional signal analyzing functions DSPAnalyze and ASPAnalyze are good examples of the code's ability to switch between symbolic, numeric, and graphical representations (the hooks being provided by Mathematica). The four symbolic transform objects ZTransform, InvZTransform, InvLaPlace, and LaPlace demonstrate their ability to handle multidimensional transforms and the region of conver- gence. (The other transform objects are CTFTransform, InvCTFTransform, DFTransform, InvDTFTransform, DTFTransform, and InvDTFTransform.) All of the transforms can completely justify their answers by displaying each step of the transformation process (use the option Dialogue -> True). Besides the examples in the ICASSP '90 paper, [1] try 1. ASPAnalyze[ t Exp [ - 4 t / 5 ] Cos [ 3 Pi t / 4 ] CStep[t], t ] 2. DSPAnalyze[ n (4/5)^n Step[n], n ] 3. DSPAnalyze[ (4/5)^n1 Impulse[n1 - n2] Step[n1,n2], {n1,n2} ] 4. ASPAnalyze[ Exp[- 4 t1 / 50] Delta[t1 - t2] CStep[t1,t2], {t1,t2} ] 5. DSPAnalyze[ (1/2)^n1 (2/5)^n2 Multinomial[n1,n2] Step[n1,n2], {n1,n2} ] Note that the analog analyzer (ASPAnalyze) only displays the interesting section of magnitude and phase plots (part encompassing the breakpoints). Also, note that two-dimensional pole-zero plots are actually root maps, unless the two-dimensional transform is separable (then two pole-zero plots will be displayed). Note that a. Delta is the Dirac delta function, b. Impulse is the unit Kronecker delta function, and c. Mathematica's Laplace transform is Laplace whereas mine is LaPlace. The paper entitled "Symbolic Transforms with Applications to Signal Processing"[2] gives Mathematica's output for four of the examples above. ----> Transform Capabilities Fourier, Laplace and z-transforms are useful for analyzing linear systems and signal processing operations. We have implemented packages for all the transforms commonly used in signal processing: (discrete signals) z-transform discrete-time Fourier transform discrete Fourier transform (continuous signals) Laplace transform Fourier transform This implementation of the transforms is very general in that multi- dimensional versions. The packages also track properties of the trans- forms, so it is also possible to deduce the stability or instability of a linear system. Using the transforms, the packages can solve linear constant-coefficient difference and differential equations for right-sided (defined for t > t0) and left-sided (defined for t < t0) functions. ---> Knowledge Representation for Signals and Systems We have added many functions (signal primitives) and operators (system primitives) that are common in signal processing and linear systems theory but missing in Mathematica: (basic signals) Kronecker impulse, Dirac delta, sinc, continuous and discrete step functions, continuous and discrete pulse functions, aliased sinc, filter representations (basic operators) aliasing, convolution, DFT, DTFT, backward difference, downsampling, Fourier transform, interleave samples, Laplace transform, periodic, reverse, scale axis, shift, summation, upsampling The transform packages support all of these new objects. ---> Other Abilities of These Packages (continuous signals) analog 1-D filter design 1-D piecewise convolution plots of 1-D and 2-D signals (discrete signals) 1-D convolution plots of 1-D and 2-D sequences (general plotting) pole-zero diagrams root loci frequency responses ---> Signal Processing Notebooks In order to extend the use of these extensions in the educational environment, we have written several Notebooks on subjects that are studied in transform theory and signal processing courses: (tutorial Notebooks) z-transform (in three parts) piecewise convolution analog filter design discrete-time Fourier transform (directed help/guide) signal processing examples introduction to Mathematica and SP packages Mathematica as an educational tool Laplace transform (reference guide) signal processing usage information In the tutorial Notebooks, we give numerous examples such as might be found in a standard textbook and solve problems that are at the level of elementary homework problems. We use the Notebook's animation ability whenever possible. In the analog filter design Notebook, for example, we illustrate the dependence of the filter's magnitude response on the filter order (and elsewhere on the ripple control parameter) as an animation sequence. --> Hierarchical Relationship Between Files The Mathematica packages are grouped OORBP into four categories: supporting routines, / \ digital signal processing packages (DSPRBP), DSPRBP ASPRBP analog signal processing packages (ASPRBP), \ / and object-oriented extensions (OORBP). SUPPORT The supporting routines are maintained in six files (as shown on the right). These are kept in the Mathematica package directory TransSupport.m S SignalProcessing/Support. "SupCode.m" defines Convolution.m | U general purpose Mathematica routines like | -----+----- P Second, SeriesQ, ToList, GenerateCode, and | | | P PrintIt (which sends Mathematica output to a | | ROC.m O a PostScript printer). The file "SigProc.m" | | | R establish the representation of common signal | FilterSupport.m | T processing operators (like Upsample, Shift, | / | and Convolve), as well as common signal pro- SigProc.m | cessing functions (like Step, CStep, Impulse, | | Delta, and Sinc). "ROC.m" defines routines to -----+---------- extract and combine regions of convergence | (ROC's), where an ROC is one open interval of SupCode.m points. The file "FilterSupport.m" defines filter objects like IIR, FIR, and IIRFunction, as well as filter types like Butterworth and Elliptic. The remaining file is "TransSupport.m" which provides a general set of routines to aid in the writing of transformation rule bases, extends Mathematica's graphics capa- bilities (to include magnitude/phase responses, pole-zero diagrams, root- loci), and defines tools for stability analysis LSI systems. The file "Convolution.m" defines one-dimensional piecewise discrete and continuous convolution. The digital signal processing routines are maintained in the hierarchy shown on the next page. These files are maintained in the Mathe- matica package directory under SignalProcessing/Digital. Most files in the DSPRBP rely on the forward and inverse z-transform capabilities in "ZTransform.m" and "InvZTransform.m", respectively, which in turn depend on the file "ZSupport.m". "ZSupport.m" defines the z-transform object, supporting routines for rule writing, and checking for valid transforms. The files "DTFT.m" and "DFT.m" contain the rules for the discrete-time Fourier transform and the discrete Fourier transform, respectively. The file "DSPAnalyze.m" provides a powerful analyzer of one- and two- dimensional signals generated by linear, shift-invariant systems. This routine graphs a signal in the time-domain, prints out its z-transform, indicates conditions for the sequence to be stable, displays its pole-zero diagram, gives its DTFT, and plots its magnitude and phase responses. The package "ZSolve.m" provides the ability to solve linear, constant coef- ficient difference equations. | ----------+-------+--------- | | | DSPAnalyze.m DFT.m | | D | | | | I -----------+ | | G | | | I DTFT.m ZSolve.m Correlation.m T | | | A -----------+ --+-----------------+------ L | | | | | ZTransform.m InvZTransform.m | | | | --------------------------- | | DSupport.m ZSupport.m | | ---------------------------------- | The analog signal processing packages are arranged in a similar manner, as shown below. "LaPlace.m" and "InvLaPlace.m" provide the forward and inverse Laplace transforms, which are able to transform expressions involving signal processing operators and functions. Note that the Laplace transform extensions released by Wolfram Research only do one-dimensional, one-sided transforms and are biased toward higher order mathematical functions (which are common in physics). Ours work for multidimensional, ASPAnalyze.m | | | Fourier.m LSolve.m A | | | N | ----+-------------+---- A | | | L LaPlace.m InvLaPlace.m O | | G --------+------------------ | FilterDesign.m LSupport.m | | multi-sided functions and, therefore, track the region of convergence. ASPAnalyze provides the same capabilities as does the DSPAnalyze. The top layer is not yet included with the signal processing packages. It implements properties of signals and systems, including routines that reason about them. Because this code implements some of the work of Gary Kopec, Cory Myers, and Michele Covell, we originally called it the object-oriented signal processing packages, which is a misnomer because Mathematica is object-oriented. Anyway, the files "Signal.m" and "System.m" provide signal and system definitions, respectively. Since Mathematica is formula-based, it can compute signal values in a point-by- point fashion. These new packages add array-based, stream-based, and state machine-based signals. This will eventually allow simulation of a wide variety of signals and systems. ---> Alteration of Standard Mathematica Routines 1. the first argument to ClearAttributes and SetAttributes is held, 2. the determinant Det of a number is that number, and 3. the dot product (Dot) of two numbers is their product. ---> Disclaimer and Future Releases This software is the property of the Georgia Tech Research Cor- poration. We have signed a licensing agreement with Wolfram Research Inc. (WRI) so that WRI can distribute the extensions. The Mathematica Journal also has the rights to distribute an earlier version of the packages. I would like to know if you find bugs in it. I have stopped mailing new releases since I post updated code in anonymous FTP locations. Brian L. Evans and James H. McClellan Georgia Tech, School of Electrical Engineering, Atlanta, GA 30332-0250 USENET: ...!{allegra,hplabs,ulysses}!gatech!eedsp!evans INTERNET: evans@eedsp.gatech.edu ---> Suggestion Please, please, use lower case one-letter symbols as variables and do not assign values to them. This includes variables like n, t, x, and y, as well as t1, t2, etc. Use one-letter upper case variables to represent constants (A, G,...), although Mathematica reserves I and N and we reserve L and Z. ---> Documentation Most of the documentation is in Notebook format. Since many users do not have access to the Notebook interface, I have also include two LaTeX files: "usage.tex" (reference guide) and "usersguide.tex". Another option is to find a Macintosh computer and acquire MathReader (from the anonymous FTP sub-directory) which is a public domain Notebook reader. MathReader will at least allow you to peruse Notebooks but you will not be able to evaluate any code fragments. ---> References on the Signal Processing Packages 1. Evans, Brian, James McClellan, and Wallace McClure. "Symbolic Trans- forms Using DSP Knowledge Bases", Proc. of the 1990 IEEE Inter. Conf. on Acoustics, Speech, and Signal Processing. pp. 1775-1778. 2. Evans, Brian, James McClellan, and Wallace McClure. "Symbolic Trans- forms with Applications to Signal Processing". Mathematica Journal. vol. 1, issue #2. Dec., 1990. pp 70-80. 3. Evans, Brian, and James McClellan. "Transforms for Signal Processing". 1991 Mathematica Conference. Jan., 1991. ---> References on the Signal Processing Packages and Notebooks 4. Evans, Brian, James McClellan, and Kevin West. "Mathematica as an Educational Tool for Signal Processing". Proc. IEEE Southeastern Conference (Southeastcon). April, 1991. pp. 1162-1166. 5. Evans, Brian, and James McClellan. "Symbolic Analysis of Signals and Systems", ch. 3 of Symbolic and Knowledge-Based Signal Processing ed. by Alan Oppenheim and Hamid Nawab. Prentice Hall, Englewood Cliffs (NJ), May, 1992. 6. Evans, Brian, Lina Karam, Kevin West, and James McClellan. "Learning Signals and Systems with Mathematica." IEEE Transactions on Education Feb. 1993 ---> References on Transforms 7. Clements, Mark, and Jerrold Pease. 1989. "On Causal Linear Phase IIR Digital Filters," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-37, issue #4, pp. 479-484. 8. Churchill, Ruel. 1958. Operational Mathematics. McGraw-Hill, New York. 9. Dudgeon, Dan, and Russel Mersereau. 1984. Multidimensional Digital Signal Processing. Prentice Hall, Englewood Cliffs (NJ). 10. Muth, Eginhard. 1978. Transform Methods. Prentice Hall, Englewood Cliffs (NJ). 11. Oberhettinger, Fritz, and Larry Badii. 1973. Tables of Laplace Trans- forms. Springer-Verlag, New York. 12. Oppenheim, Alan and Alan Willsky. 1983. Signals and Systems. Prentice Hall, Englewood Cliffs (NJ). 13. Oppenheim, Alan, and Ronald Schafer. 1989. Discrete-Time Signal Pro- cessing. Prentice Hall, Englewood Cliffs (NJ). ---> References on Symbolic Signal Processing 14. Covell, Michele. 1989. An Algorithm Design Environment for Signal Pro- cessing. Ph.D. Thesis and RLE Tech. Rep. #549. MIT, Cambridge (MA). 15. Kopec, Gary. 1980. "The Representation of Discrete-Time Signals and Systems in Programs." Ph.D. Thesis. MIT, Cambridge (MA). 16. Kopec, Gary. 1985. "The Signal Representation Language SRL." IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-33, issue #4, pp. 921-932. 17. Myers, Cory S. 1986. "Signal Representation for Symbolic and Numeric Processing" Ph.D. Thesis and RLE Tech. Rep. #521. MIT, Cambridge, MA. 18. Oppenheim, Alan, and Hamid Nawab, eds. {Symbolic and Knowledge-Based Signal Processing}. Prentice Hall: Englewood Cliffs, NJ. 1992.