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High-pass filtering is often used in neuroimaging data analysis. Commonly, whenever a general linear model is fitted to the data (as for instance in statistic parametric mapping) a number of columns of the design matrix are assigned to discrete cosines (DC). See the figure below for a graphical example.

I am curious why this is preferred to taking the fourier transform (FT) of the data, and applying a filter or cutoff. Arguments I think would speak for the FT alternative are:

• You would not have to re-do the high-pass filtering upon every application of a GLM
• Since DCT is discrete I am guessing a FT would be more accurate in extracting all high frequeny components (looking at the figure above, I find it hard to believe that those few cosines cover all the low-frequency spectrum in between them)

Reasons I think DCT might be the preferred method:

• Maybe it is faster than FFT.
• Maybe there is a reason why it is desirable to perform the filtering concomitantly with your GLM fitting.

• Why is DCT preferred?
• Would FFT not be better?

High-pass filtering is often used in neuroimaging data analysis. Commonly, whenever a general linear model is fitted to the data (as for instance in statistic parametric mapping) a number of columns of the design matrix are assigned to discrete cosines (DC). See the figure below for a graphical example.

I am curious why this is preferred to taking the fourier transform (FT) of the data, and applying a filter or cutoff. Arguments I think would speak for the FT alternative are:

• You would not have to re-do the high-pass filtering upon every application of a GLM
• Since DCT is discrete I am guessing a FT would be more accurate in extracting all high frequeny components (looking at the figure above, I find it hard to believe that those few cosines cover all the low-frequency spectrum in between them)

Reasons I think DCT might be the preferred method:

• Maybe it is faster than FFT.
• Maybe there is a reason why it is desirable to perform the filtering concomitantly with your GLM fitting.

• Why is DCT preferred?
• Would FFT not be better?

High-pass filtering is often used in neuroimaging data analysis. Commonly, whenever a general linear model is fitted to the data (as for instance in statistic parametric mapping) a number of columns of the design matrix are assigned to discrete cosines (DC). See the figure below for a graphical example.

I am curious why this is preferred to taking the fourier transform (FT) of the data, and applying a filter or cutoff. Arguments I think would speak for the FT alternative are:

• You would not have to re-do the high-pass filtering upon every application of a GLM
• Since DCT is discrete I am guessing a FT would be more accurate in extracting all high frequeny components (looking at the figure above, I find it hard to believe that those few cosines cover all the low-frequency spectrum in between them)

Reasons I think DCT might be the preferred method:

• Maybe it is faster than FFT.
• Maybe there is a reason why it is desirable to perform the filtering concomitantly with your GLM fitting.

• Why is DCT preferred?
• Would FFT not be better?
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# Why is discrete cosine preferred to FFT in neuroimaging GLM

High-pass filtering is often used in neuroimaging data analysis. Commonly, whenever a general linear model is fitted to the data (as for instance in statistic parametric mapping) a number of columns of the design matrix are assigned to discrete cosines (DC). See the figure below for a graphical example.

I am curious why this is preferred to taking the fourier transform (FT) of the data, and applying a filter or cutoff. Arguments I think would speak for the FT alternative are:

• You would not have to re-do the high-pass filtering upon every application of a GLM
• Since DCT is discrete I am guessing a FT would be more accurate in extracting all high frequeny components (looking at the figure above, I find it hard to believe that those few cosines cover all the low-frequency spectrum in between them)

Reasons I think DCT might be the preferred method:

• Maybe it is faster than FFT.
• Maybe there is a reason why it is desirable to perform the filtering concomitantly with your GLM fitting.