123
Other Signal and Image Processing Methods
6.4 For the symbols of Problem 6.3,
a. Design a Hoffman code.
b. Calculate the code rate for this code.
c. Using code rate as the criterion, compare this code with a fixed-length code
for these symbols.
6.5 T he EEG signal captured under a fixed condition, i.e., having no stimulation at
all or the same type of stimulation during the entire period of measurement, is
often considered as an ergodic signal. A typical recording of EEG over a relatively long period of time is given in the file “p_6_5.mat”.*
a. Calculate the mean of the stochastic process.
b. Calculate the variance of the stochastic process.
c. Assuming Gaussian distribution, find the PDF of the stochastic process.
d. Using the MATLAB command “xcorr”, calculate an estimation of the
autocorrelation function.
e. Using the correlation function estimated in part “c,” estimate the power
spectrum of the process.
f. Do y ou see any visible frequency(ies) in the power spectrum? Interpret your
observations.
6.6 Load images in “p_6_6.mat.” This file contains two images of the head that
have been captured using different MRI machines. The first image is the same
image used in Example 6.1. Another image has undergone a significant amount
of distortion due to poor machine calibration. We are to register these images
using a set of given tie points.
a. Show the images I and I′.
b. Use the following tie points to register the two images:
I
↔
I ′
( ,
5 1 )
( 4 , 3 )
( ,
10 3 )
( 7 , 2 )
( ,
3 2 )
( 5 2
, )
c. Show the resulting mapped image.
* Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.Ch., Mark, R.G., Mietus, J.E.,
Moody, G.B., Peng, C.K., and Stanley, H.E. (2000, June 13). PhysioBank, PhysioToolkit, and
PhysioNet: Components of a new research resource for complex physiologic signals. Circulation
101(23):e215–e220.
Other Signal and Image Processing Methods
6.4 For the symbols of Problem 6.3,
a. Design a Hoffman code.
b. Calculate the code rate for this code.
c. Using code rate as the criterion, compare this code with a fixed-length code
for these symbols.
6.5 T he EEG signal captured under a fixed condition, i.e., having no stimulation at
all or the same type of stimulation during the entire period of measurement, is
often considered as an ergodic signal. A typical recording of EEG over a relatively long period of time is given in the file “p_6_5.mat”.*
a. Calculate the mean of the stochastic process.
b. Calculate the variance of the stochastic process.
c. Assuming Gaussian distribution, find the PDF of the stochastic process.
d. Using the MATLAB command “xcorr”, calculate an estimation of the
autocorrelation function.
e. Using the correlation function estimated in part “c,” estimate the power
spectrum of the process.
f. Do y ou see any visible frequency(ies) in the power spectrum? Interpret your
observations.
6.6 Load images in “p_6_6.mat.” This file contains two images of the head that
have been captured using different MRI machines. The first image is the same
image used in Example 6.1. Another image has undergone a significant amount
of distortion due to poor machine calibration. We are to register these images
using a set of given tie points.
a. Show the images I and I′.
b. Use the following tie points to register the two images:
I
↔
I ′
( ,
5 1 )
( 4 , 3 )
( ,
10 3 )
( 7 , 2 )
( ,
3 2 )
( 5 2
, )
c. Show the resulting mapped image.
* Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.Ch., Mark, R.G., Mietus, J.E.,
Moody, G.B., Peng, C.K., and Stanley, H.E. (2000, June 13). PhysioBank, PhysioToolkit, and
PhysioNet: Components of a new research resource for complex physiologic signals. Circulation
101(23):e215–e220.