Simulations of DDS in Mathcad worksheets
| 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 combines
the 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 place equations
, text, and graphs anywhere on the screen
and use real math notation throughout.
Remarks:
(1) The Mathcad execution order is just
as you read: left-to-right, top-to-bottom.
(2) Change the parameters and see
the consequences. ("Learning-by-doing.")
(3) 
Mathcad Explorer is a free
viewer for Mathcad
files ( .mcd , version 8 or earlier ) ... Unfortunately, MathSoft is no
longer offering the downloadable viewer (Sept/2001), but
...
see: https://linkiewicz.edu.pl/software/mathcad
- mcexp802.exe
Downloadable *.mcd (ver. 8)
files :
| aquant2.mcd | Spectra of quantized sinusoid in highly oversampled case, and some properties of the quantization error |
| alias.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 plot is 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 the point-skipping nature 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 creating animation: aquant3A.mcd Movie Clip: AQspurs.avi |
| pwheel.mcd | Vizualization of the phase
wheel (and the phase approximation error) a version for creating animation: pwheelA.mcd Movie Clip: pACC.avi (790 KB) |
| param.mcd | Basic parameters of NCO and numerical periodicity of errors |
| ptrunc.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 creating animation: ptrunc2A.mcd Movie Clip: PTperm.avi (1.5 MB) |
| ptrunc3.mcd | Tuning-dependence of
PT-spurs a version for creating animation: ptrunc3A.mcd Movie Clip: PTspurs.avi |
| nco.mcd | Numerical distortion in
DDS due to AQ (amplitude quantizing) and PT (phase truncation) |
| xilinx2.mcd | Xilinx LogiCore - DDS V2.0
, an FPGA 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) |
~~~~~
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
Mathematica 3 or later, it can be downloaded free of
charge).
