[BlindMath] Discrete Fourier Cosine Transform

[Neil Soiffer]

I'm not very experienced with JAWS, so I wasn't able to copy the math. With
NVDA and MathCAT, simply start to navigate the expression and use cntrl+C
to copy the current focused subexpression. You have your choice of copying
it as MathML, LaTeX, or ASCIIMath. I assume/hope that feature will be
coming to JAWS as they continue to integrate MathCAT into JAWS.

Note: if you try using NVDA, you need to use Firefox at the moment because
a change in Chrome broke NVDA's access to math. A fix is working its way
through the release pipeline.

The other alternative is that if you can simulate a right click, MathJaX
will bring up a context menu. The second item in the menu is "Copyto
Clipboard". You have your choice of MathML or TeX. Here is what that gives
for the basis vectors (defined just before Figure 3.3.9) as TeX:
\begin{equation*}
\begin{aligned}
\vvec_0 = \left[\begin{array}{c}
\cos\left(\frac{(2\cdot0+1)\cdot0\pi}{16}\right) \\
\cos\left(\frac{(2\cdot1+1)\cdot0\pi}{16}\right) \\
\cos\left(\frac{(2\cdot2+1)\cdot0\pi}{16}\right) \\
\vdots \\
\cos\left(\frac{(2\cdot7+1)\cdot0\pi}{16}\right) \\
\end{array}\right], \amp
\vvec_1 = \left[\begin{array}{c}
\cos\left(\frac{(2\cdot0+1)\cdot1\pi}{16}\right) \\
\cos\left(\frac{(2\cdot1+1)\cdot1\pi}{16}\right) \\
\cos\left(\frac{(2\cdot2+1)\cdot1\pi}{16}\right) \\
\vdots \\
\cos\left(\frac{(2\cdot7+1)\cdot1\pi}{16}\right) \\
\end{array}\right], \\ \\
\ldots,
\vvec_6 = \left[\begin{array}{c}
\cos\left(\frac{(2\cdot0+1)\cdot6\pi}{16}\right) \\
\cos\left(\frac{(2\cdot1+1)\cdot6\pi}{16}\right) \\
\cos\left(\frac{(2\cdot2+1)\cdot6\pi}{16}\right) \\
\vdots \\
\cos\left(\frac{(2\cdot7+1)\cdot6\pi}{16}\right) \\
\end{array}\right], \amp
\vvec_7 = \left[\begin{array}{c}
\cos\left(\frac{(2\cdot0+1)\cdot7\pi}{16}\right) \\
\cos\left(\frac{(2\cdot1+1)\cdot7\pi}{16}\right) \\
\cos\left(\frac{(2\cdot2+1)\cdot7\pi}{16}\right) \\
\vdots \\
\cos\left(\frac{(2\cdot7+1)\cdot7\pi}{16}\right) \\
\end{array}\right]\text{.} \\
\end{aligned}
\end{equation*}

If what you want is something with 64 irrational numbers, I don't see any
in the page. The column vector directly about Activity 3.3.3 is the not
particularly useful
\begin{equation*}
\coords{\xvec}{\bcal} = \left[\begin{array}{c}
F_0 \\ F_1 \\ F_2 \\ \vdots \\ F_7
\end{array}\right]\text{.}
\end{equation*}

Hopefully with the instructions given above, you can get the information
you are looking for since I don't think what I copied is what you want.

Good luck,

Neil Soiffer

On Sun, Dec 22, 2024 at 8:36 PM Ray McAllister via BlindMath <
blindmath at nfbnet.org> wrote:

> Hi, I'm totally blind, and am going through  linear algebra text online.
> They're discussing the Discrete Fourier Cosine Transform used in converting
> images to jpeg format.  It's fascinating, but I'm finding it hard to access
> the actual matrix so I can copy the numbers down and run them.  And,
> frankly, it's in r^8, so I'm not particularly in the mood to hand-copy 64
> irrational number expressions for use in a limited number of times.
>
>
>
> Does anyone out there have this matrix already written down and could send
> it to me by e-mail?  JAWS is really having a hard time breaking the thing
> down in the text.
>
>
>
>
>
> Here's the link to where I found the matrix, in case someone can make sense
> of it and make sure they're sending me the right thing:
>
> It's just before Activity 3.3.3.  Wow, 3 3's!
>
>
>
>
>
> https://understandinglinearalgebra.org/sec-jpeg.html
>
>
>
> Thanks,
>
> Ray.
>
>
>
>
>
> --
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