Test notebook for my Mathematica package
copyright Nasser M. Abbasi
Last updated Jan 10, 2017
This notebook tests each function on nma.m, which is package I maintain that contains some useful functions.
butterd
butterworth digital filter design
test1
test2
butterToBandPass
test1
make a normalized butter low pass analog filter of order 4
convert to band pass
Plot the magnitude spectrums
butterToBandStop
test1
make a normalized butter low pass analog filter of order 4
convert to band stop
Plot the magnitude spectrums
butterToHighPass
test1
make a normalized butter low pass analog filter of order 4
convert to high pass
Plot the magnitude spectrums
butterToLowPass
test1
make a normalized butter low pass analog filter of order 4
convert the cut off frequency to a new cutoff frequency
Plot the magnitude spectrums
centerImageData
convertToLCD
diagonalBlockMatrix
diagonalDominantMatrixQ
displayHurwitz
| Hurwitz Matrix |  |
root locations | Real part of roots | |||||||||||||||||
|
|
 |
|
fcPulseTrain
get nth fourier series complex coeff
| -4 | 0 |
| -3 |  |
| -2 | 0 |
| -1 |  |
| 0 |  |
| 1 |  |
| 2 | 0 |
| 3 |  |
| 4 | 0 |
formatBinary
generateLTVControllabilityMatrix
generateLTVObservabilityMatrix
getButterworthPolynomial
Generate butterworth H(s) given order and cuttoff
test1
test2
test3
test4 find normalized Butterworth
test 5, even
getControllableForm
getMagnitudeOfPulseTrainFourierCoeff
getMaxPadding
 |
 |
getPhaseOfPulseTrainFourierCoeff
getPositiveAndNegativeTerms
getStateGainVector
hurwitz
| 9 | 6 | 1 | 0 | 0 |
| 11 | 8 | 3 | 0 | 0 |
| 0 | 9 | 6 | 1 | 0 |
| 0 | 11 | 8 | 3 | 0 |
| 0 | 0 | 9 | 6 | 1 |
kharitonovPoly
 |
 |
 |
 |
leadingDet
linspace
makePulseTrain
matrix2DLexOrdering
matrix2DredBlackPositions
To apply the 2D Laplacian on a matrix using red-black
numIt
numItse
plotFourierTransform
poissonMatrixOnSquareDirichlet
polarForm
quantizationLevel
snip
 |
 |
str
stripGraphMouseAppearance
toOffsetBinary
toOnesComplement
| 0.9375 | 0111 |
| 0.875 | 0111 |
| 0.8125 | 0110 |
| 0.75 | 0110 |
| 0.6875 | 0110 |
| 0.625 | 0101 |
| 0.5625 | 0100 |
| 0.5 | 0100 |
| 0.4375 | 0100 |
| 0.375 | 0011 |
| 0.3125 | 0010 |
| 0.25 | 0010 |
| 0.1875 | 0010 |
| 0.125 | 0001 |
| 0.0625 | 0000 |
| 0. | 1111 |
| -0.0625 | 1111 |
| -0.125 | 1110 |
| -0.1875 | 1101 |
| -0.25 | 1101 |
| -0.3125 | 1101 |
| -0.375 | 1100 |
| -0.4375 | 1011 |
| -0.5 | 1011 |
| -0.5625 | 1011 |
| -0.625 | 1010 |
| -0.6875 | 1001 |
| -0.75 | 1001 |
| -0.8125 | 1001 |
| -0.875 | 1000 |
| -0.9375 | 1000 |
| -1. | 1000 |
toSignMagnitude
toTwoComplement
Function to obtain Fourier series approximation given fundamental period and complex fourier coefficients 0..N-1
test on a square pulse
Funtion to divide polynomial by powers of variable and keep powers in form 
test
 |
Function to convert low pass digital filter to high pass using frequency transformation
test
 |
 |
test2
 |
 |
Function to convert low pass digital filter to bandpass digital filter using frequency transformation
test
 |
 |
Function to convert low pass digital filter to bandstop digital filter by frequency transformation
test
 |
 |
checkForSingularity
| point | limit x p(x) | limit x^2 q(x) |
| 0 | c | 0 |
| 1 | 1+a+b-c | 0 |
| ∞ | 1-a-b | a b |
| point | limit x p(x) | limit x^2 q(x) |
| -1 | 1 |  |
| 1 | 1 |  |
| ∞ | 0 | ∞ |
