Digital Filter Design Using MATLAB

 

This three-day intensive course spans the ground from basic to advanced digital filters. Although several techniques require no tools more sophisticated than a calculator, most design methods showcased heavily exploit the rich support features incorporated in MATLAB’s Signal Processing and Filter Design Toolboxes. Design targets range from simple averagers, notch filters and resonators to tightly-specced high performance multiband and special-application filtering objectives. 

 

 The course style is to present a wide range of attack options for the easier of two categories of filters FIR (Finite-duration Impulse Response) filters. In some methods basic m-code must be written; in most, however, a semi-standard specification syntax must be mastered and critically assessed. All these are used and contrasted in the context of design specifications of varying difficulty. The more limited range of IIR (Infinite-duration Impulse Response) filter design approaches is also considered. Fortunately, the recently-released Filter Design Toolbox greatly expands designers’ options in the IIR arena, leading to a flurry of optimization-intense methodology starting on the second day of the course.

 

Participants are faced with design and equalization tasks in which they must choose from among the many FIR and IIR methods presented to achieve satisfactory filtering. Audioband signals (such as speech/music, ECG and instrumentation signals) are liberally used as exemplars of real-world jobs digital filters must perform. Most of this course assumes error-free ideal processing; some familiarity with the imposition of finite wordlength effects is furnished as an introduction to the very extensive treatment that the Filter Design Toolbox now facilitates.

 

 

Who Should Attend?

 

          The course is aimed at participants with some DSP familiarity. Experience with the MATLAB environment would be an advantage, but is not required.

 

Course Content

 

Day 1:  Elementary FIR and IIR Design

 

·        Summary of spectral measurements in the digital world, along with the crucial concepts of transfer functions and convolution. The DTFT, the DFT, the FFT, zooming by Chirp-z transformation, and spot frequency measures by scalar products.

·        Simple FIR filters such as differencers; distortionless transmission and desirability of linear phase.

 

·       The Smagnitude concept and links to Fourier Series notions. Pole-Zero Patterns and popular characteristic zero patterns; handcrafting zero movements for lightweight designs.

 

·        The Impulse-Invariant design method. Windowing and the Frequency-Sampling design method. Non-equispaced frequency specifications and required Vandermonde solutions.

 

·        FIR N-Point Moving Averagers contrasted with IIR Leaky Integrators. A first-order IIR filter for d.c. abatement; second-order IIR notches and resonators.

·        Traditional trio of IIR standard filters. Expert assistance shells in MATLAB.

 

Day 2: Optimal Digital Filters

 

• Optimizing parameters for point behaviour. Weighted Least Integral-Squared design of FIR filters. Why it’s so much more difficult for IIR.

 

• Minimax design, Remez Exchange and Hofstetter’s algorithms.

 

• Yule-Walk and iirlpnorm for good quality IIR designs.

 

• Variable-norm designs. Evaluation in a demanding Design Laboratory.

 

• Allpass filters and relations to notches and allpass filters. Group delay issues and measurement in MATLAB. Equalization and the use of iirgrpdelay.

 

• Simulink demonstration of filters, including variable and adaptive filters.

 

Day 3: Special Filter Features and Wordlength Effects

 

• Halfband filters, Nyquist filters and a square-root filter for special Doppler instrumentation. Advantages and failures of some methods we have met.

 

• Constrained designs: trying fircls and iirlpnormc. The power and utility of gremez.

 

• Minimum-phase and maximum-phase designs using Filter Design Toolbox facilities.

 

• Quantizing filter coefficients. Stability and accuracy risks. Sensitivity and filter structure interactions.

 

• Survey of various Finite Arithmetic issues, supported by Filter Design Toolbox.

 

• Consolidation Exercise on Filterbanks.