DIGITAL FILTER DESIGN
A Three-Day Intensive Course
Digital filters are widely used in data analysis and digital equipment for processing audio signals, data records, images and signals from biomedical instrumentation, radar/sonar and other sensing systems. The study of digital filters entails a mixture of analytical concepts, simple hand calculations and employment of powerful computer tools. This course gives a comprehensive experience of all these elements, providing participants with in-depth understanding of a wide cross-section of design issues and an ability to undertake serious design work, particularly in connection with the frequently-encountered problem of filter equalization.
2. Structure of the Three Days of Study
Each day of study is built around three core lecture sessions which are peppered with frequent hands-on computer-based confirmation and extension activities. These are followed by small design tasks aimed at consolidation of each session’s material. At least one Laboratory Investigation is undertaken daily to promote both individual reflection and small-group discussion of design issues. In total there is structured study time of about 8 hours per day.
(a) DAY 1: Spectra, Transfer Functions and Elementary FIR Digital Filters
The Discrete-Time Fourier Transform’s uses for signals and filters; impulse response and Fourier gain/phase matters illustrated for the Two-Point Moving Averager and the Differencer; z-plane and linear-phase concepts; interconnections to form larger filters; review of convolution, the DFT and the FFT; illustrations of the usefulness of the Chirp Transform Algorithm for finegrain examination of spectral features.
Impulse-invariant FIR design; introduction to filter quality measures and tradeoffs; the windowing approach to FIR design modifications and effects on quality metrics; using Kaiser and Chebyshev windows for precise sidelobe control; incorporation of fractional-sample delay in filter designs; qualitative effects of filters on audio signals and pulse waveforms.
Frequency-Sampling FIR design; where Type 1 or Type 2 can be preferable; inescapable obligations of even-length and odd-length linear-phase filters; employing and discovering optimal transition samples; utility of complex FIR filters and some design examples; non-equispaced Frequency-Sampling; manipulating frequency samples to steer approximation errors; precision hand-crafting tips; group delay in filters; aspirations for distortionless transmission.
(b) DAY 2: Optimal FIR Digital Filters and Classic IIR Filters
Minimax design criterion; equiripple-bandedge design by the Parks-McClellan Algorithm; guidelines for predicting minimax performance and rules of thumb for filter sizing; equiripple-corridor design; Selesnick lowpass and bandpass designs; Weighted Least-Summed-Square FIR design; Lawson’s Algorithm; balancing rms and peak approximation errors.
Quick design insight using Pole-Zero Patterns; stability requirements and IIR dangers; the leaky integrator; first- and second-order resonators; IIR versus FIR notch and allpass filters; automating tuning behaviour for narrowband interference removal by an adaptive notch filter; zero-insertion interpolation for creation of comb and multi-notch filters; minimum-phase filters and two avenues for their FIR design.
Butterworth, Chebyshev and Elliptic IIR filters and truncated FIR approximants; perils of classical error measurement definitions; gain flattening by inverse and quasi-inverse filters; contrasts with whitening filters for noise spectrum flattening.
(c) DAY 3: IIR Design and Equalization
Arbitrary group delay achievement in allpass design; phase-only equalization of filters and transducers by allpass sections; guidelines for attainment of near-distortionless transmission; practice with equalization of fixed filter characteristics; introductory LMS adaptive filtering for equalization of time-varying filters and transmission channels.
IIR Frequency-Sampling and Yule-Walker design of complex IIR filters with arbitrary gain targets; all-pole ARMA design; obtaining small IIR filters from large FIR prototypes using the Brandenstein-Unbehauen IIR design method; IIR filters with near-linear passband phase; dimensionality savings for equalization filters.
Finite wordlength effects in digital filters and the signals that pass through them; degradation of filter quality with coefficient quantization; cushioning against IIR instability; sensitivity and filter structure considerations; halfband filters and simple multirate filtering considerations; filterbank matters; Nyquist and Root-Nyquist filters and their use in data communication.
3. Makeup of Course Notes
Course notes are PowerPoint slide images, with consistent notation and careful referencing of the relevant DSP literature. These bound notes are self-contained; however, students wishing to gain an alternative perspective will be encouraged to access the course reference texts: Mitra, S.K., Digital Signal Processing- A Computer-Based Approach, Third Edition, New York: McGraw-Hill, 2005, and Ambardar, A., Digital Signal Processing: A Modern Introduction, Nelson, 2007. Students receive a DVD containing all course exercises and videoclips of indicative solution approaches.
4. Computation Support
This course has an exceptionally strong hands-on flavour. All student work is reliant on the ready availability of the DSP Creations’ toolset (Slifer, Sketch-a-Filt and DSP_Speedster) which are built around the MATLAB/Simulink environment from The MathWorks Ltd. Learning motivation is sharpened by a rich blend of user-friendly graphics display and interactive instrument control features and numerous audio illustrations of the issues in digital filter design. Students leave the course with their own personal copies of Slifer Lite and Sketch-a-Filt Lite for fuller absorption of, and later reflection upon, their course experience.
5. Course Pre-requisites
Engineers, mathematicians, physicists and other technical personnel with a ready grasp of mathematical analysis (including integral calculus and fundamentals of complex variables) are the intended participants. Familiarity with filtering terminology, DSP concepts, or basics of MATLAB - while not required - would be an added advantage.