Gri Commands
1: Introduction 2: Simple example 3: Fancy example 4: Running Gri 5: Programming Gri 6: General Issues 7: X-Y Plots 8: Contour Plots 9: Image Plots 10: Examples 11: Handling Data 12: Gri Commands 13: Gri Extras 14: Evolution of Gri 15: Installing Gri 16: Gri Bugs 17: System Tools 18: Acknowledgments 19: License 20: Newsgroup 21: Concept Index |
12.12: The `
|
x_new[i] = b[0] * x[i] \ + b[1] * x[i-1] \ + b[2] * x[i-2] \ + ... \ - a[1] * x_new[i-1] \ - a[2] * x_new[i-2] \ - ... |
a[i]
' = 0 results in a simple
backwards-looking moving-average filter applied in two passes. The real
power of this type of filter, however, comes when non-zero `a[i]
'
coefficients are given, thus adding recursion (i.e., `x_new[i]
'
depends on `x_new[i-...]
'). See any standard reference on digital
filters for an explanation. You might find that the Matlab command
`butter
' an easy way to design filter coefficients. Here are some
examples:
# Filter x column with simple 2-point moving # average. (This slurs into a 3-point moving # average, in effect, since the filter is run # forwards and then backwards.) filter column x recursively 0 0 0.5 0.5 # Use filter designed with the Matlab # command butter(2,0.1), which creates a # 2nd order lowpass butterworth filter # with a cutoff frequency of 0.1 # (in units which have a frequency # of 1 corresponding to one-half the # sampling rate). filter column x recursively \ 1 -1.561 0.6414 \ 0.0201 0.0402 0.0201 |
filter grid rows|columns recursively a[0] a[1] ... b[0] b[1] ...
'
Apply recursive filter (see `filter column ... recursively
' for
meaning of this filter operation) to the individual rows or columns of
the grid data. For example, `filter grid columns recursively 0 0 0.5 0.5
' applies a 2-point moving average filter across the columns,
smoothing the grid in the x-direction.
filter image highpass
'
Remove low-wavenumber components from image (ie, sharpen edges). Do
this by subtracting a Laplacian smoothed version of the image.
filter image lowpass
'
Remove high-wavenumber components from image (ie, smooth shapes). Do
this by Laplacian smoothing.