I'm trying to apply the DCT as described in [1], but it isn't working
well.* Please take a look at my Maple worksheet in [2] (it is an HTML
export). I would greatly appreciate a pointer as to what I could be
doing wrong. As far as I can tell I am implementing the FDCT correctly.

James Sumners wrote:
I'm trying to apply the DCT as described in [1], but it isn't working
well.* Please take a look at my Maple worksheet in [2] (it is an HTML
export). I would greatly appreciate a pointer as to what I could be
doing wrong. As far as I can tell I am implementing the FDCT correctly.

You need to make your term you're summing in the definition of the DCT
of course dependent on x and y. Otherwise, you of course only get the
constant term. That is, there should be an

A[x,y]

somewhere in your formula.

Hints:

a) This is a maple problem, and off-topic here.
b) I'm pretty sure maple offers a package containing the DCT readily
implemented. It's usually not a good idea to re-invent the wheel.
Specifically, the maple implementation might be faster and more general
than yours.

So long,
Thomas

On 2008-04-27 16:40:01 -0400, Thomas Richter <thor@math.tu-berlin.de> said:

James Sumners wrote:
I'm trying to apply the DCT as described in [1], but it isn't working
well.* Please take a look at my Maple worksheet in [2] (it is an HTML
export). I would greatly appreciate a pointer as to what I could be
doing wrong. As far as I can tell I am implementing the FDCT correctly.

You need to make your term you're summing in the definition of the DCT
of course dependent on x and y. Otherwise, you of course only get the
constant term. That is, there should be an

A[x,y]

somewhere in your formula.

Hints:

a) This is a maple problem, and off-topic here.
b) I'm pretty sure maple offers a package containing the DCT readily
implemented. It's usually not a good idea to re-invent the wheel.
Specifically, the maple implementation might be faster and more
general than yours.

So long,
Thomas

I asked here because I know there folks such as yourself who are quite
familiar with this specific transform, and I am using it in the context
of compressing an image with JPEG. So I felt it was at least
tangentially on topic. I'm not asking for Maple help; I'm asking for
help with the transform that is the basis of the JPEG compression scheme.

In regard to the A[x,y]. The 'z' in the inner sum is the 'f(x,y)' from
Wallace's paper. I copied the double summation directly from that paper.

As I understand it, if a grayscale image is represented by a 8x8 matrix
of integer color values, then f(x,y) is the integer at the [x,y]
position of the matrix. Is this not correct?

If Maple offers a DCT package then it isn't included in my student
installation. The closest thing I can find in the help file is a DFT.

James Sumners wrote:
On 2008-04-27 16:40:01 -0400, Thomas Richter <thor@math.tu-berlin.de> said:

James Sumners wrote:
I'm trying to apply the DCT as described in [1], but it isn't working
well.* Please take a look at my Maple worksheet in [2] (it is an HTML
export). I would greatly appreciate a pointer as to what I could be
doing wrong. As far as I can tell I am implementing the FDCT correctly.

You need to make your term you're summing in the definition of the DCT
of course dependent on x and y. Otherwise, you of course only get the
constant term. That is, there should be an

A[x,y]

somewhere in your formula.

Hints:

a) This is a maple problem, and off-topic here.
b) I'm pretty sure maple offers a package containing the DCT readily
implemented. It's usually not a good idea to re-invent the wheel.
Specifically, the maple implementation might be faster and more general
than yours.

So long,
Thomas

I asked here because I know there folks such as yourself who are quite
familiar with this specific transform, and I am using it in the context
of compressing an image with JPEG. So I felt it was at least
tangentially on topic. I'm not asking for Maple help; I'm asking for
help with the transform that is the basis of the JPEG compression
scheme.

The formula is correct, the implementation is not.

In regard to the A[x,y]. The 'z' in the inner sum is the 'f(x,y)' from
Wallace's paper. I copied the double summation directly from that paper.

Nope. You wrote "z", the paper wrote "f(x,y)". Z might be a number, or
a matrix, or anything else that can be multiplied or summed over, but
it's at least *not* the *component* (x,y) of a matrix Z, as z, as you
wrote it, does not depend on x and y, i.e. it's always the same number,
or matrix, independent of x and y, which is kind of pointless. For
that, you should write z[x,y]. Your code furthermore substitutes A[i,j]
for z, which is different from A[x,y] since i and j do not depend on
the summation indices x and y in the DCT transformation.

As I understand it, if a grayscale image is represented by a 8x8 matrix
of integer color values, then f(x,y) is the integer at the [x,y]
position of the matrix. Is this not correct?

This is correct, but that's not reflected in your code. (-:

As said, it's *not* a math problem. It's a problem with "how to program maple".