An experiment produces the following data sample pairs: i. t₁: 0 Y₁: 4.9 ii. 0.1 3.9 0.2 3.1 For each measurement, the y; value is recorded along the time, t₁, at which it occurs. It is proposed to model the data as a decaying exponential as follows: Estimate the values of a₁ and the least mean squared error. 0.3 2.5 0.4 2.4 y(t) = a₁ + a₂e-5t Show how the problem of estimating a₁ and a₂ can be expressed in matrix form as a system of over-determined equations. | a₂ that will result in the optimum solution with respect to

MATLAB: An Introduction with Applications
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An experiment produces the following data sample pairs:
i.
t₁: 0
Y₁: 4.9
ii.
0.1
3.9
0.2
3.1
Estimate the values of a₁ and
the least mean squared error.
0.3
For each measurement, the y; value is recorded along the time, t₁, at which it occurs. It is proposed
to model the data as a decaying exponential as follows:
2.5
0.4
2.4
y(t) = a₁ + a₂e-5t
Show how the problem of estimating a₁ and a₂ can be expressed in matrix form as a
system of over-determined equations.
a₂ that will result in the optimum solution with respect to
Transcribed Image Text:An experiment produces the following data sample pairs: i. t₁: 0 Y₁: 4.9 ii. 0.1 3.9 0.2 3.1 Estimate the values of a₁ and the least mean squared error. 0.3 For each measurement, the y; value is recorded along the time, t₁, at which it occurs. It is proposed to model the data as a decaying exponential as follows: 2.5 0.4 2.4 y(t) = a₁ + a₂e-5t Show how the problem of estimating a₁ and a₂ can be expressed in matrix form as a system of over-determined equations. a₂ that will result in the optimum solution with respect to
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