Digital Signal Processing Reference
In-Depth Information
G
n
is the additive noise vector, and
where
"
#
T
01
sin
ð
2
Þ
sin
sin
ðð
L
1
ÞÞ
sin
AðÞ¼
:
sin
ðð
L
2
ÞÞ
sin
10
1
The least squares estimate (LSE) of
X
n
ðÞ
in (3.64) is
ðÞAðÞ
1
T
T
X
n
ðÞ¼½A
A
ðÞY
n
ðÞ:
ðÞAðÞ
1
T
T
Each row of the weighting matrix
½A
A
ðÞ
represents an FIR filter of L
coefficients.
Consider a measurement vector
Y
n
ð!Þ
for an oscillation at
!
.If
X
n
ð!Þ
is
T
ðÞAðÞ
1
computed using
FðÞ
,
then its LSE is given by
X
n
ð; !Þ¼½A
T
A
ðÞY
n
ð!Þ
. The estimate of
Y
n
ð!Þ
is then
Y
n
ð; !Þ¼AðÞ
X
n
ð; !Þ¼P
A
ðÞY
n
ð!Þ:
3.13 Summary
This chapter described ways to specify a given filter. We presented a variety of
popular filters and their characteristics. We looked at IIR filters with real coeffi-
cients and truncated IIR filters for use in FIR designs. We also described a bank of
filters with complex coefficients pointing to discrete Fourier transforms. We gave a
simple presentation of adaptive filters and inverse problems having practical
significance. We demonstrated an application of BFSK demodulation and adaptive
phase shifting. And we looked at a practical inverse problem from target tracking.
We added an important dimension by giving Kalman filter applications. Then we
concluded this big topic with an application from array processing.
References
1. R. W. Hamming, Digital Filters, pp. 4-5. Englewood Cliffs, NJ: Prentice Hall, 1980.
2. R. D. Strum and D. E. Kirk, First Principles of Discrete Systems and Digital Signal Processing. Reading
MA: Addison-Wesley, 1989.
3. K. V. Rangarao, Adaptive digital notch filtering. Master's thesis, Naval Postgraduate School, Monterey
CA, September 1991.
4. G. C. Goodwin and K. S. Sun, Adaptive Filtering, Prediction and Control. Englewood Cliffs NJ:
Prentice Hall, 1984.
5. D. M. Himmelblau Applied Non-linear Programming. New York: McGraw-Hill, 1972.
6. K. Kadambari, K. V. Rangarao and R. K. Mallik, Demodulation of BFSK signals by adaptive digital
notch filtering. In proceedings of the IEEE International Conference on Personal Wireless Commu-
nications, Hyderabad, India, December 2000, pp. 217-19.
Search WWH ::
Custom Search