Question

Using the feature of reciprocal relationship of filter in spatial domain and corresponding filter in frequency domain along with convolution, which of the following fact is true?

(a) The narrower the frequency domain filter more severe is the ringing

(b) The wider the frequency domain filter more severe is the ringing

(c) The narrower the frequency domain filter less severe is the ringing

(d) None of the mentioned

I have been asked this question in an online interview.

My question comes from Smoothing Frequency-Domain Filters topic in chapter Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

The correct choice is (a) The narrower the frequency domain filter more severe is the ringing

To elaborate: The characteristics feature of reciprocal relationship says that the narrower the frequency domain filter becomes it attenuates more low frequency component and so increases blurring and more severe becomes the ringing.