Circularly symmetric lowpass filters can be designed by assuming an idealized frequency response of the form
(7) |
Figure shows the desired and the fitted spectrum obtained using a 21 term zero-phase filter. The filter in the space domain is a symmetrical filter as shown in Figure . The filter coefficients correspond to h_{n} in Figure . The McClellan transformation filter is designed using the 5x5 filter shown in the Appendix. This filter corresponds to the G filter shown in Figure . Once the filter coefficients h_{n} are computed they are incorporated into the recursive structure shown in Figure . The implementation is done in both space and wavenumber domains. The wavenumber domain response of the filter is shown in Figure . A spike in x-y space was used to test the space-domain implementation. The output of the lowpass filter is a smoothed spike as shown in Figure
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Figure 4 Twenty-one coefficient symmetric 1-D filter in the space domain corresponding to Fig 3. These are the filter coefficients h_{n} used in the Chebyshev filter structure shown in Figure 2. |
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Figure 6 Output of Lowpass Filter in the x-y domain. The filter implementation is in the x-y domain. The modified McClellan filter in space-domain is used to do the transformation. |