Case Studies - Digital Signal Processing: A Practitioner's Approach - page 128

¼k y y k

, where y ¼ A

p

Then the sum of squares of errors is given as SSE .So

¼ky A

SSE p k

¼ky AðA AÞ 1

t t

A y k : ð 6 : 24 Þ

Again, to find the sum of squares of errors, a closed-form solution for (6.24) is used
[4] to reduce the computational complexity:

X

N

y i :

¼

S yy p 2 S y p 1 S xy where S yy ¼

ð : Þ

SSE 6 25

i ¼ 1

We have illustrated various DSP techniques to improve or extract the hidden data by
ingeniously combining ideas from systems engineering. The numbers of interest are
^ p 1 , ^ p 2 (Figure 6.4) and SSE (6.25).

6.4 Summary
In this chapter we gave a detailed treatment of a specific problem in direction
finding, showing the need to understand systems engineering in order to implement
DSP algorithms. It is very difficult to isolate DSP problems from other areas of
engineering. Practical problems tend to cover many areas but centre on one area
that demands the principal focus.

References

1. A. Albert, Regression and the Moore-Penrose Pseudoinverse. New York: Academic Press, 1972.
2. D. M. Himmelblau, Applied Non-linear Programming, p. 75. New York: McGraw-Hill, 1972.
3. D. C. Montgomery et al., Introduction to Linear Regression, Ch. 8. New York: John Wiley & Sons, Inc.,
1982.
4. J. L. Devore, Probability and Statistics for Engineers and the Sciences. Monterey CA: Brooks Cole,
1987.
5. D. Curtis Scheler, Introduction to Electronic Warfare, pp. 326-30. Norwood MA: Artech House, 1990.
6. H. H. Jenkins, Small-Aperture Radio Direction Finding, pp. 139-48. Norwood MA: Artech House,
1991.
7. G. Multedo, 'Direction finding.' Revue Technique Thomson-CSF, 19 (2), 1987.