Using the SciPy DCT function to create a 2D DCT-II

Question

I am creating a 2D DCT-II in labview but want to be able to check my outputs are correct. SciPy has a nice DCT function which defaults to DCT-II but is 1D. I want to make it work for a 2D array. To do this the DCT must be applied to the columns and then the DCT must be again applied to the rows of this outcome. I'm not sure what function I want to use to do this. I have tried np.rot90 which rotates the numpy array 90 degrees counter clockwise as follows: ``` import numpy as np from scipy.fftpack import dct a = np.array([[1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0], [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0], [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0], [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0], [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0], [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0], [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0], [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0]]) b = dct(np.rot90(dct(a),3)) ``` However this outputs the following: ``` array([[ 1152. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [ -412.30867345, 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [ 0. , 0. , 0.…

Accepted Answer

I don't think that a rotation is what you want, since it converts rows into columns, but it also messes with the order of the data. Use `np.transpose` instead.

To apply dct first by columns, then by rows, you would do something like:

```
dct(dct(a.T).T)
```

The trailing `.T` is equivalent to `np.transpose`. Note how you need to undo the transposition after you operate on the columns, to get the return aligned by rows again.

I don't think that the order in which you apply the dct, i.e. columns then rows vs. rows then columns, makes any difference, but you could get rows then columns as:

```
dct(dct(a).T).T
```

Using the SciPy DCT function to create a 2D DCT-II

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