1. Suppose the basis vectors of two sampling lattices are: A) v = [3,1], v2 =...

 

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1. Suppose the basis vectors of two sampling lattices are: A) v = [3,1], v2 = [0,2] B) v =[22,0], v = [2, 2]T For each of the sampling lattices defined above: (a) Sketch the basis vectors and the sample points. Illustrate the Voronoi cell. Illustrate how the entire spatial domain is tiled up by the shifted versions of the unit cell. Determine the sampling density. (b) Determine the basis vectors of the reciprocal lattice. Repeat part (a) for this lattice. (c) For a signal with a circular spectrum which lattice is better? Construct a spectrum (sketch its support region) that will cause aliasing by one lattice but not the other. (d) The basis vectors for a given lattice are not unique. Can you find another set of basis vectors for the lattices A and B? 1. Suppose the basis vectors of two sampling lattices are: A) v = [3,1], v2 = [0,2] B) v =[22,0], v = [2, 2]T For each of the sampling lattices defined above: (a) Sketch the basis vectors and the sample points. Illustrate the Voronoi cell. Illustrate how the entire spatial domain is tiled up by the shifted versions of the unit cell. Determine the sampling density. (b) Determine the basis vectors of the reciprocal lattice. Repeat part (a) for this lattice. (c) For a signal with a circular spectrum which lattice is better? Construct a spectrum (sketch its support region) that will cause aliasing by one lattice but not the other. (d) The basis vectors for a given lattice are not unique. Can you find another set of basis vectors for the lattices A and B?