α α B C N We observe samples M samples of f t at locations t 1 t 2 t M which

# Α α b c n we observe samples m samples of f t at

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. . α 0 . . . α B C N . We observe samples M samples of f ( t ) at locations t 1 , t 2 , . . . , t M which are not necessarily uniformly spaced, y [ m ] = f ( t m ) , m = 1 , . . . , M. (6) (a) Write a MATLAB function sampmat.m that takes a vector smptimes of length M con- taining the sample locations and a dimension N = 2 B + 1 (which you can assume is odd), and returns a M × N matrix A such that when A is applied to a vector of Fourier series coefficients (as in ( 5 )), it returns the sample values in ( 6 ). (b) The file hw8problem5.mat contains vectors samptimes and y of length M = 259, which contain sample times t m and sample values f ( t m ). Find the signal of bandwidth N = 51 (so B = 25) that best explains these samples in the least-squares sense. Plot your synthesized estimate ˆ f ( t ) as a function of time. 3 Last updated 11:21, October 31, 2019
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