OPTIMAL DESIGN OF DIGITAL EQUIVALENTS TO ANALOG FILTERS
The proposed optimal algorithm for the digitizing of analog filters is based on two existing filter design methods: the extended window design (EWD) and the matched–pole (MP) frequency sampling design. The latter is closely related to the filter design with iterative weighted least squares (WLS). The optimization is performed with an original MP design that yields an equiripple digitizing error. Then, a drastic reduction of the digitizing error is achieved through the introduction of a fractional time shift that minimizes the magnitude of the equiripple error within a given frequency interval. The optimal parameters thus obtained can be used to generate the EWD equations, together with a variable fractional delay output, as described in an earlier paper. Finally, in contrast to the WLS procedure, which relies on a “good guess” of the weighting function, the MP optimization is straightforward.
Summary
This paper presents an algorithm that produces optimal digital equivalents of analog filters by combining extended-window design (EWD) and a matched–pole (MP) frequency-sampling approach. It shows how an MP-based equiripple digitizing error can be drastically reduced by selecting an optimal fractional time shift and how the resulting parameters generate EWD equations with a variable fractional-delay output.
Key Takeaways
- Apply the matched–pole frequency-sampling method to generate an equiripple digitizing error profile for analog-to-digital filter conversion.
- Compute and optimize a fractional time shift to minimize the magnitude of the equiripple error within a specified frequency interval.
- Derive extended-window design (EWD) equations from the optimal MP parameters and implement a variable fractional-delay output.
- Use the iterative weighted least-squares (WLS) interpretation to refine filter coefficients for improved digitization fidelity.
Who Should Read This
DSP engineers and researchers (intermediate to advanced) working on digital filter design and accurate analog-to-digital filter conversions for communications, audio, or radar systems.
Still RelevantAdvanced
Related Documents
- A New Approach to Linear Filtering and Prediction Problems TimelessAdvanced
- A Quadrature Signals Tutorial: Complex, But Not Complicated TimelessIntermediate
- An Introduction To Compressive Sampling TimelessIntermediate
- Lecture Notes on Elliptic Filter Design TimelessAdvanced
- Computing FFT Twiddle Factors TimelessAdvanced
