Pt. 3 Working Backwards: Finding a Vector Given Magnitude and Direction Angle


In the third part of this lecture, we will be culminating our new-found knowledge to  derive a 2d Vector given only the magnitude and direction in word problem form. To be able to answer these style of questions there will be some instruction provided that goes “in detail” about the component make up of a Vector. I will explain the component parts (x,y) and their associated meanings. This will give a clear and intuitive understanding of how to provide a logical answer when faced with a similar question (usually in a Physics setting).




  1. The central result from this paper is that a sparse vector can be recovered exactly from a small number of Fourier domain observations. More precisely, let f be a length-N discrete signal which has B nonzero components (we stress that the number and locations of the components are unknown a priori). We collect samples at K different frequencies which are randomly selected. Then for K on the order of B log N, we can recover f perfectly (with very high probability) through l1 minimization.

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