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### High pass Filtering:

An image can be blurred by attenuating the high-frequency components of its Fourier transform. Because edges and other abrupt changes in gray levels are associated with high-frequency components, image sharpening can be achieved in the frequency domain by a high pass filtering process, which attenuates the low-frequency components without disturbing high-frequency information in the Fourier transform.

### Ideal filter:

2-D ideal high pass filter (IHPF) is one whose transfer function satisfies the relation

where Do is the cutoff distance measured from the origin of the frequency plane. Figure 5.1 shows a perspective plot and cross section of the IHPF function. This filter is the opposite of the ideal lowpass filter, because it completely attenuates all frequencies inside a circle of radius Do while passing, without attenuation, all frequencies outside the circle. As in the case of the ideal lowpass filler, the IHPF is not physically realizable.

### Fig.5.1 Perspective plot and radial cross section of ideal high pass filter

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**Butterworth filter:**

The transfer function of the Butterworth high pass filter (BHPF) of order n and with cutoff frequency locus at a distance Do from the origin is defined by the relation

Figure 5.2 shows a perspective plot and cross section of the BHPF function. Note that when D (u, v) = Do, H (u, v) is down to ½ of its maximum value. As in the case of the Butterworth lowpass filter, common practice is to select the cutoff frequency locus at points for which H (u, v) is down to 1/√2 of its maximum value.

**Fig.5.2 Perspective plot and radial cross section for Butterworth High Pass Filter with n = 1**