Question

A signal with power spectral density $$ |X(k)|^2=\{0,0,16,0,0,0,16,0\} $$ has been blurred by a process with finite impulse response $$ \left\{h_d(0)=0.5, h_d(1)=0.5\right\} $$ and corrupted by an additive Gaussian noise with power spectral density $$ \{0.1584,0.0055,0.0030,0.1719,0.0047,0.1719,0.0030,0.0055\} $$ The samples of the degraded signal are $$ y(n)=\{-0.3581,0.5292,0.5198,-0.3412,-0.5804,0.5697,0.5835,-0.5244\} $$ Restore the true signal using the Wiener filter.

   A signal with power spectral density
$$
|X(k)|^2=\{0,0,16,0,0,0,16,0\}
$$
has been blurred by a process with finite impulse response
$$
\left\{h_d(0)=0.5, h_d(1)=0.5\right\}
$$
and corrupted by an additive Gaussian noise with power spectral density
$$
\{0.1584,0.0055,0.0030,0.1719,0.0047,0.1719,0.0030,0.0055\}
$$
The samples of the degraded signal are
$$
y(n)=\{-0.3581,0.5292,0.5198,-0.3412,-0.5804,0.5697,0.5835,-0.5244\}
$$
Restore the true signal using the Wiener filter.

Digital Image Processing

D. Sundararajan 1st Edition

Chapter 5, Problem 5

Instant Answer

Step 1

The autocorrelation function is the inverse Fourier transform of the power spectral density. Show more…

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A signal with power spectral density $$ |X(k)|^2=\{0,0,16,0,0,0,16,0\} $$ has been blurred by a process with finite impulse response $$ \left\{h_d(0)=0.5, h_d(1)=0.5\right\} $$ and corrupted by an additive Gaussian noise with power spectral density $$ \{0.1584,0.0055,0.0030,0.1719,0.0047,0.1719,0.0030,0.0055\} $$ The samples of the degraded signal are $$ y(n)=\{-0.3581,0.5292,0.5198,-0.3412,-0.5804,0.5697,0.5835,-0.5244\} $$ Restore the true signal using the Wiener filter.

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