2.2) Reducing the undesired effects of noise when a given signal is corrupted by noise with known (partially) statistics. Let x, be the original and x be the measured signal which is affected by additive white Gaussian noise. x[n] = xo[n] + N(n) where N(n) is the noise. Our task is to use moving average filter to extract xo[n] from the observed signal x[n]. Define the original signal as xo[n] = cos (n) + 2cos (n). Define the domain as – 1000 < n< 1000 Generate the noise signal by using randn command i) ii) iii) iv) Add noise signal to the original signal and obtain observed signal x[n]. v) Apply the moving average filter to x[n] and obtain the output y[n]. vi) Implement filter for different M, and M2, i.e M, = M2 = 4,10,20 ... and observe the output. Plot xo[n], x[n] and y[n] for every step. Comment on your %3D vii) results.

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Author:Robert L. Boylestad
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DSP - Electrical Engineering
2.2) Reducing the undesired effects of noise when a given signal is corrupted
by noise with known (partially) statistics.
Let x, be the original and x be the measured signal which is affected by
additive white Gaussian noise.
x[n] = x,[n] + N(n)
%3D
where N(n) is the noise. Our task is to use moving average filter to extract
xo[n] from the observed signal x[n].
Define the original signal as xo[n] = cos (n) + 2cos (
Define the domain as – 1000 <n < 1000
i)
ii)
iii)
Generate the noise signal by using randn command
iv)
Add noise signal to the original signal and obtain observed signal
x[n].
v)
Apply the moving average filter to x[n] and obtain the output
y[n].
vi)
Implement filter for different M, and M2, i.e M, = M2 =
4,10,20 ... and observe the output.
vii)
Plot xo[n], x[n] and y[n] for every step. Comment on your
results.
Transcribed Image Text:2.2) Reducing the undesired effects of noise when a given signal is corrupted by noise with known (partially) statistics. Let x, be the original and x be the measured signal which is affected by additive white Gaussian noise. x[n] = x,[n] + N(n) %3D where N(n) is the noise. Our task is to use moving average filter to extract xo[n] from the observed signal x[n]. Define the original signal as xo[n] = cos (n) + 2cos ( Define the domain as – 1000 <n < 1000 i) ii) iii) Generate the noise signal by using randn command iv) Add noise signal to the original signal and obtain observed signal x[n]. v) Apply the moving average filter to x[n] and obtain the output y[n]. vi) Implement filter for different M, and M2, i.e M, = M2 = 4,10,20 ... and observe the output. vii) Plot xo[n], x[n] and y[n] for every step. Comment on your results.
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