DDS:background | numerical distortion | products

Simulations of DDS inMathcadworksheets

"Visual learning is not just for kids."

DDS:Direct Digital Synthesis =point(memory location)-skipping at constant update(clock)-rate[ vs.traditional PPC (point-per-clock) synthesis at variable clock-rate]Mathcad

combinesthe mathematical power of a spreadsheet with the WYSIWYG interface of a word processor and allows you to solve just about any math problem you can think of.

In this environment, you can placeequations,text, andgraphsanywhere on the screen and use real math notation throughout.

Remarks:

(1) The Mathcadexecution orderis just as you read: left-to-right, top-to-bottom.

(2)Changethe parameters andseethe consequences. ("Learning-by-doing.")

(3) MathcadExploreris afree viewerfor Mathcad files (.mcd,version 8or earlier ) ... Unfortunately, MathSoft is no longer offering the downloadable viewer (Sept/2001), but ...

see: http://www.ntu.edu.sg/CITS/SoftwareDirectory/Utilities/Viewers.htm -mcexp802.exeMirrors for

mcexp802.exe: http://www.filewatcher.com/m/mcexp802.exe.12715922.0.0.html

Downloadable *.

mcd(ver. 8) files :

aquant2.mcd Spectra of quantized sinusoidin highly oversampled case, and some properties of the quantization erroralias.mcd Two ways of computing the location of harmonic lines due to aliasing, and an example of "Nyquist voodoo"modieee.mcd Illustration of numerical distortions (spurious components) due to amplitude quantization (AQ):overlapped harmonic structure.

ModT plotis a reversible temporal permutation of samples. This shows samples plotted as a function of their true phase rather than as a function of original time index. (This illustrates also thepoint-skippingnature of DDS.)

see:

Comments on 'The Modulo Time Plot : A Useful Data Acquisition Diagnostic Tool' (Fig. 1)

IEEE Trans. on Instrumentation and Measurements, Vol. IM-45, No.6, (959)1996[ pdf ] and (error correction) Vol. IM-46, No. 3, (739)1997[ pdf ]inverse.mcd Multiplicative inverse( )function - finds J such that "m.J = 1 (modN)".

Simple, slow (linear) search: the equation is equivalent to finding J (and k) such that "m.J = N.k + 1" (k integer)aquant3.mcd Tuning-dependence of AQ-spurs

a version for creatinganimation: aquant3A.mcd

Movie Clip:AQspurs.avipwheel.mcd Vizualization of the phase wheel(and the phase approximation error)

a version for creatinganimation: pwheelA.mcd

Movie Clip:pACC.avi (790 KB)param.mcd Basic parameters of NCO and numerical periodicity of errorsptrunc.mcd Illustration of numerical distortions (spurious components) due to phase truncation (PT):overlapped modulation structure.ptrunc2.mcd Scrambled versions of PT-spurs

a version for creatinganimation: ptrunc2A.mcd

Movie Clip:PTperm.avi (1.5 MB)ptrunc3.mcd Tuning-dependence of PT-spurs

a version for creatinganimation: ptrunc3A.mcd

Movie Clip:PTspurs.avinco.mcd Numerical distortion in DDS

due toAQ(amplitude quantizing) andPT(phase truncation)xilinx2.mcd Xilinx LogiCore - DDS V2.0, anFPGA example

Product spec: c_dds_v2_0.pdf (Nov. 3, 2000);

V3.0(c_dds_v3_0.pdf, March 2, 2001),

V3.1(dds.pdf - May 11, 2001 ),

V4.0(dds.pdf - Oct. 4, 2001 ),

V4.1(dds.pdf - March 25, 2002)

V4.2(dds.pdf - March 28, 2003)

new:V5.0(dds.pdf - May 21, 2004; April 28, 2005) product link*

allMCD.zip Contains all .mcd of the above (120 KB) allAVI.zip Contains all .avi of the above (160 KB)

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Notes:

(1) If you are using a Web browser to access these files, links will take you to the ASCII readout of Mathcad files ( .mcd) unless you have configured your browser to use Mathcad as a viewer/helper application.

(2)Mathematica imports Mathcad worksheets (the converter will work for all versions of Mathematica3or later, it can be downloaded free of charge).Date:Feb/2001

questions or comments e-mail:papay@hit.bme.hu