# How do I use a Gaussian as a window function for a high-pass filter?

I'd like to apply a high-pass filter to some 2D data. Given the diagram on the documentation page for HighpassFilter, I assume the default window function is a Dirichlet window (i.e. a unit step, which amounts to no smoothing). I'd like to use a gaussian instead. I know I can do this by simply multiplying the FFT of the data by a gaussian, but I'd like to do it using the in-built HighpassFilter function if possible. However, I'm getting an error.

Here's a MWE:

data=RandomReal[{0,1},{40,40}];
cutoff=Pi/10;
HighpassFilter[data,cutoff,Automatic,NormalDistribution[]]]


The error I get is the following:

HighpassFilter::win: "Invalid window type NormalDistribution[0,1]. >>

Clicking on the link merely directs me to the HighpassFilter documentation, which contains a few example window functions and says I can define my own $f$ (which is what I tried to do above).

I tried reducing the data to 1D in case the problem was the gaussian being defined in 1D by default, but I got the same error, so it can't be that.

What am I doing wrong?

NormalDistribution[] is a distribution not a function. You want to use its probability density function:
HighpassFilter[data, cutoff, Automatic, PDF[NormalDistribution[]]]