Applying Analytics

1-Dimensional Data Sets 115

data. Next apply the filter to the Y

k

to create the filtered

c

Y

k

, and then pass

c

Y

k

through the inverse DFT to construct the filtered

b

ψ

i

.

There are many types of filters that could be applied to your data . In fact,

you have great freedom to tune your filter to pass w hichever frequencies you

like, but there is no reason to filter ν outside the range of valid frequencies

from Equation 5.22. These fr e quencies don’t appear in your Y

k

anyway (exc ept

through aliasing to frequencies within the range of respo nse). It’s gener ally

better to build a filter based o n wavelength or frequency than wave number,

because λ and ν are quantities ...