IIRstrukturer

IIRstrukturer refers to realizations of Infinite Impulse Response (IIR) digital filters. An IIR filter is described by a rational transfer function H(z) = B(z)/A(z), where A(z) and B(z) are polynomials in z^-1. The corresponding difference equation y[n] = -∑_{k=1}^M a_k y[n-k] + ∑_{k=0}^N b_k x[n-k] shows how the current output depends on past outputs and current and past inputs. This feedback gives the impulse response an infinite duration in general.

Common realizations include direct forms, canonical forms, and cascaded or lattice structures. Direct Form I implements the filter using separate delay lines for inputs and outputs, yielding straightforward coefficient mapping but with relatively high memory usage. Direct Form II reduces memory by combining the state into fewer delay elements, at the cost of more algebraic complexity. Transposed Direct Form II reorders the signal flow, often offering advantages in fixed-point hardware by improving numerical properties and reducing routing complexity.

To improve numerical stability and scalability, IIRstrukturer are frequently decomposed into cascades of second-order sections (SOS) or biquads. This approach limits pole proximity issues and allows better control over quantization effects. Cascaded or parallel SOS realizations are widely used in software and hardware due to improved conditioning and easier tuning.

Other realizations include lattice and lattice-ladder structures, which provide inherent numerical robustness and are convenient for adaptive filtering, reflection coefficient control, and straightforward coefficient updates.

Numerical considerations are central to choosing a structure. Finite word length effects, round-off noise, and coefficient quantization can alter pole locations and affect stability. Proper scaling, overflow protection, and, when possible, using SOS forms help maintain reliable performance in practical implementations.