# Digital Image Processing Questions and Answers – Smoothing Frequency-Domain Filters

This set of Digital Image Processing Multiple Choice Questions & Answers (MCQs) focuses on “Smoothing Frequency-Domain Filters”.

1. Smoothing in frequency domain is achieved by attenuating which of the following component in the transform of a given image?
a) Attenuating a range of high-frequency components
b) Attenuating a range of low-frequency components
c) All of the mentioned
d) None of the mentioned

Explanation: Since, edges and sharp transitions contribute significantly to high-frequency contents in the gray level of an image. So, smoothing is done by attenuating a range of high-frequency components.

2. Which of the following is/are considered as type(s) of lowpass filters?
a) Ideal
b) Butterworth
c) Gaussian
d) All of the mentioned

Explanation: Lowpass filters are considered of three types: Ideal, Butterworth, and Gaussian.

3. Which of the following lowpass filters is/are covers the range of very sharp filter function?
a) Ideal lowpass filters
b) Butterworth lowpass filter
c) Gaussian lowpass filter
d) All of the mentioned

Explanation: Ideal lowpass filter covers the range of very sharp filter functioning of lowpass filters.

4. Which of the following lowpass filters is/are covers the range of very smooth filter function?
a) Ideal lowpass filters
b) Butterworth lowpass filter
c) Gaussian lowpass filter
d) All of the mentioned

Explanation: Gaussian lowpass filter covers the range of very smooth filter functioning of lowpass filters.

5. Butterworth lowpass filter has a parameter, filter order, determining its functionality as very sharp or very smooth filter function or an intermediate filter function. If the parameter value is very high, the filter approaches to which of the following filter(s)?
a) Ideal lowpass filter
b) Gaussian lowpass filter
c) All of the mentioned
d) None of the mentioned

Explanation: For high value of filter order Butterworth lowpass filter behaves as Ideal lowpass filter, while for lower order value it has a smoother form behaving like Gaussian lowpass filter.
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6. Butterworth lowpass filter has a parameter, filter order, determining its functionality as very sharp or very smooth filter function or an intermediate filter function. If the parameter value is of lower order, the filter approaches to which of the following filter(s)?
a) Ideal lowpass filter
b) Gaussian lowpass filter
c) All of the mentioned
d) None of the mentioned

Explanation: For high value of filter order Butterworth lowpass filter behaves as Ideal lowpass filter, while for lower order value it has a smoother form behaving like Gaussian lowpass filter.

7. In a filter, all the frequencies inside a circle of radius D0 are not attenuated while all frequencies outside circle are completely attenuated. The D0 is the specified nonnegative distance from origin of the Fourier transform. Which of the following filter(s) characterizes the same?
a) Ideal filter
b) Butterworth filter
c) Gaussian filter
d) All of the mentioned

Explanation: In ideal filter all the frequencies inside a circle of radius D0 are not attenuated while all frequencies outside the circle are completely attenuated.

8. In an ideal lowpass filter case, what is the relation between the filter radius and the blurring effect caused because of the filter?
a) Filter size is directly proportional to blurring caused because of filter
b) Filter size is inversely proportional to blurring caused because of filter
c) There is no relation between filter size and blurring caused because of it
d) None of the mentioned

Explanation: Increase in filter size, removes less power from the image and so less severe blurring occurs.

9. The characteristics of the lowpass filter h(x, y) is/are_________
a) Has a dominant component at origin
b) Has a concentric, circular components about the center component
c) All of the mentioned
d) None of the mentioned

Explanation: the lowpass filter has two different characteristics: one is a dominant component at origin and other one is a concentric, circular components about the center component.

10. What is the relation for the components of ideal lowpass filter and the image enhancement?
a) The concentric component is primarily responsible for blurring
b) The center component is primarily for the ringing characteristic of ideal filter
c) All of the mentioned
d) None of the mentioned

Explanation: The center component of ideal lowpass filter is primarily responsible for blurring while, concentric component is primarily for the ringing characteristic of ideal filter.

11. 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

Explanation: 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.

12. Which of the following defines the expression for BLPF H(u, v) of order n, where D(u, v) is the distance from point (u, v), D0 is the distance defining cutoff frequency?
a)
b)
c) All of the mentioned
d) None of the mentioned

Explanation: BLPF is the Butterworth lowpass filter and is defined as:
.

13. Which of the following defines the expression for ILPF H(u, v) of order n, where D(u, v) is the distance from point (u, v), D0 is the distance defining cutoff frequency?
a)
b)
c) All of the mentioned
d) None of the mentioned

Explanation: ILPF is the Ideal lowpass filter and is defined as:
.

14. State the statement true or false: “BLPF has sharp discontinuity and ILPF doesn’t, and so ILPF establishes a clear cutoff b/w passed and filtered frequencies”.
a) True
b) False

Explanation: ILPF has sharp discontinuity and BLPF doesn’t, so BLPF establishes a clear cutoff b/w passed and filtered frequencies.

15. A Butterworth filter of what order has no ringing?
a) 1
b) 2
c) 3
d) 4

Explanation: A Butterworth filter of order 1 has no ringing and ringing exist for order 2 although is imperceptible. A Butterworth filter of higher order shows significant factor of ringing.

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