# ds4 - ECE 178 Digital Image Processing Discussion Session...

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ECE 178 Digital Image Processing Discussion Session #4 { anindya,msargin } @ece.ucsb.edu February 2, 2007 2D Sampling Example-I: Suggest a sampling scheme for the signal f ( x,y ) = 2cos(2 π (3 x - 2 y )) so as to be able to reconstruct the signal from its samples without any error. Clearly specify what the spacings in x and y should be. Sketch the region of support for the low pass ﬁlter, in the frequency domain, that you would use to reconstruct the signal from its samples. Answer: The highest frequency components are 3(unit frequency/ unit space) and 2(unit frequency/ unit space) along the x -axis and y -axis. According to the Nyquist sampling theorem, we have to sample at twice the highest frequency component in each direction. In this case, we have a component at frequencies u = 3 and v = 2. Hence, our sampling frequency must be strictly greater than twice either frequency or else we cannot recover the same exact signal by simply low-pass ﬁltering. Hence, Δ

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## This note was uploaded on 06/12/2009 for the course ECE 178 taught by Professor Manjunath during the Winter '08 term at UCSB.

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ds4 - ECE 178 Digital Image Processing Discussion Session...

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