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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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