1. Advisor : 高永安 Student : 陳志煒
A Weighted Least Squares Algorithm for Quasi-Equiripple FIR and IIR Digital Filter Design
Advisor : 高永安
Student : 陳志煒

2. outline Introduction The Weighted Least Squares Method
The Least Squares Weighting Function
The New Algorithm
Termination of Algorithm
Conclusion

3. Introduction
In this paper, a novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi-equiripple design is presented
The algorithm converges very rapidly
Form experience, about 1dB away form the minimax optimum solution in two iterations and converges to within 0.1dB in six iterations

4. The Weighted Least Squares Method
actual frequency response
desired frequency response
appropriate trigonometrical function
impulse response of the filter

5. The Weighted Least Squares Method

6. The Weighted Least Squares Method
Minimized
Optimum solution

7. The Least Squares Weighting Function
The weighting function used in the (k+1) iteration
Lawson’s Algorithm

8. The New Algorithm
Define the i th extremal point of the k th iteration as
The envelope function

9. The New Algorithm Minimax weighting function
The constant affect convergent speed
= average of

10. The Constant The algorithm is said to have converged if
There is no know analytical method for obtaining that will make the algorithm converge at the maximum speed
The algorithm is said to have converged if
Peak weighted ripple of optimum minimax design
Peak weighted ripple of the weighted least squares design

11. The Constant
Averaging the results of 200 examples

12. Initial May be set equal to unity for all n
Using the method of rectangular windowing of the Fourier series of

13. Termination of Algorithm
It can be terminated after a prespecified number of iterations have been completed
Another criterion for termination of the algorithm is to check for quasi-equiripple condition
: average weighted ripple magnitude

14. Conclusion
We have present a novel fast convergent weighted least squares algorithm for quasi-equiripple FIR and IIR filter designs
N=151
=1.5

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