# Digital Image Processing Questions and Answers – Filtering in Frequency Domain

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

1. Which of the following fact(s) is/are true for the relationship between low frequency component of Fourier transform and the rate of change of gray levels?
a) Moving away from the origin of transform the low frequency corresponds to smooth gray level variation
b) Moving away from the origin of transform the low frequencies corresponds to abrupt change in gray level
c) All of the mentioned
d) None of the mentioned

Explanation: Moving away from the origin of transform the low frequency corresponds to the slowly varying components in an image. Moving further away from origin the higher frequencies corresponds to faster gray level changes.

2. Which of the following fact(s) is/are true for the relationship between high frequency component of Fourier transform and the rate of change of gray levels?
a) Moving away from the origin of transform the high frequency corresponds to smooth gray level variation
b) Moving away from the origin of transform the higher frequencies corresponds to abrupt change in gray level
c) All of the mentioned
d) None of the mentioned

Explanation: Moving away from the origin of transform the low frequency corresponds to the slowly varying components in an image. Moving further away from origin the higher frequencies corresponds to faster gray level changes.

3. What is the name of the filter that multiplies two functions F(u, v) and H(u, v), where F has complex components too since is Fourier transformed function of f(x, y), in an order that each component of H multiplies both real and complex part of corresponding component in F?
b) High-boost filter
c) Zero-phase-shift-filter
d) None of the mentioned

Explanation: Zero-phase-shift-filter multiplies two functions F(u, v) and H(u, v), where F has complex components too since is Fourier transformed function of f(x, y), in an order that each component of H multiplies both real and complex part of corresponding component in F.
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4. To set the average value of an image zero, which of the following term would be set 0 in the frequency domain and the inverse transformation is done, where F(u, v) is Fourier transformed function of f(x, y)?
a) F(0, 0)
b) F(0, 1)
c) F(1, 0)
d) None of the mentioned

Explanation: For an image f(x, y), the Fourier transform at origin of an image, F(0, 0), is equal to the average value of the image.

5. What is the name of the filter that is used to turn the average value of a processed image zero?
b) Notch filter
c) Zero-phase-shift-filter
d) None of the mentioned

Explanation: Notch filter sets F (0, 0), to zero, hence setting up the average value of image zero. The filter is named so, because it is a constant function with a notch at origin and so is able to set F (0, 0) to zero leaving out other values.

6. Which of the following filter(s) attenuates high frequency while passing low frequencies of an image?
b) Lowpass filter
c) Zero-phase-shift filter
d) All of the mentioned

Explanation: A lowpass filter attenuates high frequency while passing low frequencies.

7. Which of the following filter(s) attenuates low frequency while passing high frequencies of an image?
b) Highpass filter
c) Zero-phase-shift filter
d) All of the mentioned

Explanation: A highpass filter attenuates low frequency while passing high frequencies.

8. Which of the following filter have a less sharp detail than the original image because of attenuation of high frequencies?
a) Highpass filter
b) Lowpass filter
c) Zero-phase-shift filter
d) None of the mentioned

Explanation: A lowpass filter attenuates high so the image has less sharp details.

9. The feature(s) of a highpass filtered image is/are ___________
a) Have less gray-level variation in smooth areas
b) Emphasized transitional gray-level details
c) An overall sharper image
d) All of the mentioned

Explanation: A highpass filter attenuates low frequency so have less gray-level variation in smooth areas, and allows high frequencies so have emphasized transitional gray-level details, resulting in a sharper image.

10. A spatial domain filter of the corresponding filter in frequency domain can be obtained by applying which of the following operation(s) on filter in frequency domain?
a) Fourier transform
b) Inverse Fourier transform
c) None of the mentioned
d) All of the mentioned

Explanation: Filters in spatial domain and frequency domain has a Fourier transform pair relation. A spatial domain filter of the corresponding filter in frequency domain can be obtained by applying inverse Fourier transform on frequency domain filter.

11. A frequency domain filter of the corresponding filter in spatial domain can be obtained by applying which of the following operation(s) on filter in spatial domain?
a) Fourier transform
b) Inverse Fourier transform
c) None of the mentioned
d) All of the mentioned

Explanation: Filters in spatial domain and frequency domain has a Fourier transform pair relation. A frequency domain filter of the corresponding filter in spatial domain can be obtained by applying inverse Fourier transform on spatial domain filter.

12. Which of the following filtering is done in frequency domain in correspondence to lowpass filtering in spatial domain?
a) Gaussian filtering
c) High-boost filtering
d) None of the mentioned

Explanation: A plot of Gaussian filter in frequency domain can be recognized similar to lowpass filter in spatial domain.

13. Using the feature of reciprocal relationship of filter in spatial domain and corresponding filter in frequency domain, which of the following fact is true?
a) The narrower the frequency domain filter results in increased blurring
b) The wider the frequency domain filter results in increased blurring
c) The narrower the frequency domain filter results in decreased blurring
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.

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