1.2 Consider a signal-plus-noise model of the general form I = $t + wi, where wi is Gaussian white noise with o = 1. Simulate and plot n = 200 observations from each of the following two models (Save the data or your code for use in Problem 1.22 ): %3D (a) It = St + Wi, for t = 1, .., 200, where S0, ( 10 exp{- t = 1,..., 100 (t=100) } cos(2nt/4), t= 101,...,200. St = Hint: 1s = c(rep(0,100), 10+exp(-(1:100)/20)*cos(2+pi*1:100/4)) 21 = ts(s + rnorm(200, 0, 1)) s plot (z) (b) I = st + wi, for t = 1,..., 200, where t=1,..., 100 St | 10 exp{- } cos(2xt/4), t= 101,., 200.
1.2 Consider a signal-plus-noise model of the general form I = $t + wi, where wi is Gaussian white noise with o = 1. Simulate and plot n = 200 observations from each of the following two models (Save the data or your code for use in Problem 1.22 ): %3D (a) It = St + Wi, for t = 1, .., 200, where S0, ( 10 exp{- t = 1,..., 100 (t=100) } cos(2nt/4), t= 101,...,200. St = Hint: 1s = c(rep(0,100), 10+exp(-(1:100)/20)*cos(2+pi*1:100/4)) 21 = ts(s + rnorm(200, 0, 1)) s plot (z) (b) I = st + wi, for t = 1,..., 200, where t=1,..., 100 St | 10 exp{- } cos(2xt/4), t= 101,., 200.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
Shumway and stoffer 1.5
Transcribed Image Text:1.5 For the two series, r1, in Problem 1.2 (a) and (b):
(a) Compute and plot the mean functions 4(t), for t = 1,...,200.
(b) Calculate the autocovariance functions, 7(s, t), for s, t = 1,..., 200.
Transcribed Image Text:1.2 Consider a signal-plus-noise model of the general form r = st + we,
where wi is Gaussian white noise with o = 1. Simulate and plot n = 200
observations from each of the following two models (Save the data or your
code for use in Problem 1.22 ):
(a) r = st + w, for t = 1, .., 200, where
0,
St =
t = 1,..., 100
10 exp{-100) } cos(2nt/4), t= 101,.., 200.
Hint:
1s = c(rep(0,100), 10+exp(-(1:100)/20) *cos (2+pi+1:100/4))
2x = ts(s + rnorm(200, 0, 1))
3 plot (x)
(b) r = st + wt, for t = 1, ..., 200, where
S0,
( 10 exp{-100 } cos(2nt/4), t= 101,..., 200.
t = 1,..., 100
S =
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