What the syllabus asks you to cover
Structures for FIR and IIR, Conversion between direct form and lattice and vice versa, Lattice and lattice -ladder for IIR. Digital filters, finite precision implementations of discrete filters, Representation of Numbers; fixed point and floating binary point, Effect of Rounding and truncation, Quantization of filter coefficients and effects on location of poles, and zeros.
Start here for the core ideas. A dedicated GitBook topic page was not available; this original guide is introductory. Use the syllabus checklist and references below to study the remaining details.
Turn a difference equation into a structure
Delay elements, multipliers and adders implement discrete-time systems. Direct-form structures come from the difference equation; cascaded second-order sections factor a higher-order transfer function into smaller blocks. Lattice structures use a different parameterization and are useful in selected filtering and modelling tasks.
Account for finite precision
Fixed-point and floating-point arithmetic approximate real values. Coefficient quantization can move poles and zeros; rounding and truncation can introduce noise or limit cycles. Algebraically equivalent filter structures can therefore behave differently in an implementation.
Try it
For , one state stores the previous output. The ideal pole is at 0.5 and the causal ideal system is stable. Changing that coefficient changes its decay rate and may change stability if quantization moves it beyond the unit circle.
Check your understanding
Compare direct form I with direct form II. Why might second-order sections be preferable for a high-order IIR filter? Study overflow, scaling and lattice conversions next.
Pause and recall
Without looking back, explain the main idea, recall a key definition or formula, and describe when it applies. Include assumptions and units where relevant. Revisit any step you could not explain.