FIR vs. IIR Filters: Advantages, Disadvantages, & Structures

FIR Filters

A Finite Impulse Response (FIR) filter is characterized by its finite-duration impulse response, settling to zero in a finite time. Unlike Infinite Impulse Response (IIR) filters, which can have internal feedback and respond indefinitely, an Nth-order discrete-time FIR filter's impulse response lasts precisely N+1 samples. FIR filters are predominantly implemented in software and can be continuous-time analog or digital and discrete-time.

Transfer Function of FIR Filter

Frequency Response

IIR Filters

An Infinite Impulse Response (IIR) filter is a recursive filter where the output is calculated using current and previous inputs and outputs. This feedback mechanism within the filter structure is a defining characteristic. IIR filter design involves determining the pulse transfer function G(z) that meets the filter specifications. This can be achieved by developing an analog prototype and transforming it or by designing directly in the digital domain.

Advantages of IIR Filters over FIR Filters

IIR filters achieve a specific filtering characteristic with less memory and fewer calculations compared to similar FIR filters.

Advantages of FIR Filters over IIR Filters

• Linear Phase Filtering: FIR filters can implement linear-phase filtering, eliminating phase shift across the frequency band.
• Stability: FIR filters are inherently stable.
• Ease of Design: Linear-phase FIR filters are straightforward to design.
• Implementation Flexibility: FIR filters can be realized in both recursive and non-recursive structures, avoiding limit cycle oscillations in finite word length digital systems.
• Precise Frequency Response Correction: FIR filters allow for finer precision in correcting frequency-response errors in loudspeakers compared to IIR filters.

Disadvantages of IIR Filters over FIR Filters

• Sensitivity to Finite-Length Arithmetic: IIR filters are more susceptible to issues like noise from calculations and limit cycles due to feedback.
• Implementation Complexity: Fixed-point arithmetic implementation is more complex for IIR filters.
• Limitations in Multirate Applications: IIR filters lack the computational advantages of FIR filters for decimation and interpolation.

Disadvantage of FIR Filters

The main drawback of FIR filters is their higher order requirement compared to IIR filters for achieving similar performance, resulting in potentially longer delays.

Signal Flow Graph

A signal flow graph visually represents the relationships between variables in a set of linear differential equations. It consists of directed branches connecting nodes. Nodes represent system variables, equal to the sum of incoming signals. Source nodes have no incoming branches, while sink nodes have only incoming branches. Signals travel along branches, multiplied by the branch gain. Arrowheads indicate direction, and branch gain is shown next to the arrowhead. Delay is represented by z^-1, often omitted if unitary.

Transposed Structures

Transposing a structure involves the following operations:

1. Reverse all branch directions in the signal flow diagram.
2. Interchange input and output.
3. Reverse the roles of all nodes.
4. Summing points become branching points.
5. Branching points become summing points.