Overview
10pts)Showthegraphicalrepresentationofthesignaly(n)=x(2n+5),wherex(n)isthesignal illustrated in the following figure.
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2. (5 pts) Convert the following binary numbers to decimal numbers. 11101010
1100001001101
3. (15pts)Calculatetheconvolutionofthetwotimesequences.Givetheprocedureindetail.
at = {−6,5,1,0,−1,3} and bt = {0.5,0.5}
4. (20pts)Atimeseriesissampledat200Hz.WhatarethesamplingintervalandNyquist frequency? The original signal, before digitizing, was contaminated with noise of about 350 Hz. At what frequency would this noise appear in the spectrum of the digitized sequence? Repeat the calculation for noise contamination at 475 Hz.
5. (20 pts) Find the Discrete Fourier transform of the sequence [0, 0, 1, -1]. Plot the amplitude spectrum.
6. (10pts)Isthesequence[2,32,5]minimumphase?Ifnot,findtheminimumphasesequence with the same amplitude spectrum.
7. (10pts)AwaveletandareflectivityaregivenbyXt=[3,2],Yt=[4,1,5].Calculatethecross- correlation γ xy (τ ) and autocorrelation γ yy (τ ) .
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8. (10pts)SketchtheFouriertransformsofthefollowingtimeseriesandexplainyourresults.