HW01_Team03

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University of Houston, Downtown *

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5307

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Mechanical Engineering

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Dec 6, 2023

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pdf

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Homework 01 Team 03 2022-09-07 Problem 1.2 Consider a signal-plus-noise model of the general form xt = st + wt , where wt is Gaussian white noise with SD =1. Simulate and plot n=200 observations from each of the following two models. Ans a. s = c(rep( 0 , 100 ), 10 *exp(-( 1 : 100 )/ 20 )*cos( 2 *pi* 1 : 100 / 4 )) ax = s + rnorm( 200 ) plot.ts(ax, main = "Plot A" ) Plot A Time ax 0 50 100 150 200 -5 0 5 Ans b. 1
s = c(rep( 0 , 100 ), 10 *exp(-( 1 : 100 )/ 200 )* cos( 2 *pi* 1 : 100 / 4 )) bx = s+ rnorm( 200 ) plot.ts(bx, main = "Plot B" ) Plot B Time bx 0 50 100 150 200 -10 -5 0 5 10 Ans c. Plot A looks similar to Explosion plot and Plot B looks similar to Earthquake Plot Upon plotting the data, Signal Modulator has a curve structure for the first condition and linear structure for the second. par( mfrow = c( 3 , 2 )) #Comparison of all the plots plot.ts(ax, main = "Plot A" ) plot.ts(bx, main = "Plot B" ) library(astsa) plot(EXP6, main= "Explosion" ) plot(EQ5, main= "Earthquake" ) signal_modulator = c(exp(-( 1 : 100 )/ 20 )) plot.ts(signal_modulator, main = "Signal Modulator A" ) signal_modulator = c(exp(-( 1 : 100 )/ 200 )) plot.ts(signal_modulator, main = "Signal Modulator B" ) 2
Plot A Time ax 0 50 100 150 200 -5 Plot B Time bx 0 50 100 150 200 -10 10 Explosion Time EXP6 0 500 1000 1500 2000 -0.4 Earthquake Time EQ5 0 500 1000 1500 2000 -0.4 Signal Modulator A Time signal_modulator 0 20 40 60 80 100 0.0 Signal Modulator B Time signal_modulator 0 20 40 60 80 100 0.6 1.0 3
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