126.

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where θ and r denote angle and radius, respectively. Both θ and r control the width of the filter’s effective area. Equation (5.38) results in a wedge filter with a vertical alignment. If one wants to generate a wedge filter with a horizontal alignment, the value tan⁻¹(v/u) in Equation (5.38) is altered to tan⁻¹(u/v). A spatial interpretation of Equations (5.38) and (5.39) is shown in Figure 5.13. Note that in the calculation of the wedge filter, the value of P(0, 0) is normally omitted because it is common to all wedges. One can therefore calculate the percentage of power in the area of the amplitude spectrum that is covered by the wedge filter by dividing the sum of the amplitudes in the area covered by the filter by the total power spectrum.

Figure 5.13 (a) Two wedge filters, one in the vertical and the other in the horizontal direction, defined by angles θ₁ and θ₂. (b) A ring filter specified by radii r₁ and r₂. See text for further explanation.

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