[music-dsp] Moving average high-pass

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Hello guys, it's gone a bit quiet again on this list, so here goes!... I 
hope someone can help.

I've been looking at filters that I haven't tried out yet, and found Smith's 
enthusiasm for the Moving Average filter infectious.
Online book ref:- http://www.dspguide.com/ch15/4.htm
I found the shape and efficiency to be very nice indeed! - Just one multiply 
for any number of cascades for example.

I would really like the inverse, or high-pass equivalent to this filter, in 
such that they both add for perfect reconstruction, or near enough.
I've tried for a while and achieved something near, but it had a very large 
ripple in the top end.
Is this filter possible?

Thanks,
Dave