In the following set of questions, there are, possibly, multiple correct answers

Question

In the following set of questions, there are, possibly, multiple correct answers (1, 2, 3 or 4). Mark the answers you consider correct. What is the effect of sampling an image at sampling frequencies smaller than the Nyquist rates? the partial superposition of spectral replicas in the sampled image spectrum; a low pass filtering effect of the reconstructed image, as compared to the original; the reduction of the mean square error between the original image and the image reconstructed from its samples; the distortion of the high frequency content in the reconstructed image, due to the alias effect What is the condition for the optimal sampling? to use a rectangular sampling grid, with the Nyquist sampling intervals given by dx=dy=l the sampling frequencies must be greater than the Nyquist rates the finite sequence obtained as the result of the sampling should ensure that the mean square error between the original and the reconstructed image is minimal to represent the image as a Karhunen-Loeve series (expansion) of its samples. The role of image quantization is to: constrain the brightness of each spatial location to take values in a finite set only; produce a binary image; digitally filter the sampled image; take samples from the spatially continous brightness function A quantizer has the role of: converting a continuous variable into a discrete one; reading signal samples discretly, at evenly spaced spatial positions improving the signal-to-noise ratio of an image converting a continuous valued variable into a discrete (numerical) variable

Explanation / Answer

1. d. If we don't sample the signal as satisfying the nyquist theorem of sampling, then aliasing occurs.

2. c. is the condition for optical sampling.

3. a. Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. That means, it will constrain the brightness of each spacial location.

4. d . A quantizer converts discrete time continuous valued signal to continuous time discrete valued signal.

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