Introduction

Filtering is a crucial aspect of signal processing, with finite impulse response (FIR) and infinite impulse response (IIR) filters being two of the most commonly used types. This article delves into the differences between FIR and IIR filters and explains why FIR filters are generally more stable, especially in environments where noise is prevalent.

Differences Between FIR and IIR Filters

Impulse Response

FIR Filters: Have a finite duration impulse response, meaning the output depends solely on a finite number of past input values. This makes them straightforward to design and implement. IIR Filters: Have an infinite duration impulse response, indicating that the output depends on both past input values and past output values through feedback loops.

Structure

FIR Filters: Are typically implemented through convolution with a finite number of coefficients taps. IIR Filters: Use feedback loops, making them more computationally efficient for achieving specific filter responses due to their recursive nature.

Stability

FIR Filters: Are always stable because they lack feedback. Any bounded input will result in a bounded output, making them ideal for applications with noisy signals. IIR Filters: Can become unstable when feedback coefficients are not chosen carefully. If the poles of the transfer function are outside the unit circle in the z-plane, the filter can produce unbounded outputs for bounded input.

Phase Response

FIR Filters: Can be designed to have a linear phase response, preserving the integrity of the waveform. IIR Filters: Typically have a non-linear phase response, potentially distorting the output signal.

Computational Efficiency

FIR Filters: Require more computational resources due to their non-recursive nature, meaning they have more coefficients for a given level of performance. IIR Filters: Are more computationally efficient because they use feedback to reduce the number of coefficients needed.

Stability of FIR Filters in Noisy Environments

No Feedback Loop

Since FIR filters do not use feedback, they are inherently stable. This characteristic makes them ideal for environments with noise, where output remains controlled and does not amplify errors or noise.

Bounded Output

FIR filters produce a bounded output for any bounded input. This is particularly crucial in noisy environments. Unlike IIR filters, FIR filters do not allow noise to accumulate over time, a feature especially valuable in applications with critical signal integrity requirements.

Design Flexibility

FIR filters can be designed with specific characteristics to minimize noise effects. Techniques such as windowing can be used to reduce side lobes in the frequency response, helping to maintain signal integrity even in noisy conditions.

Conclusion

In summary, FIR filters are generally more stable than IIR filters because they lack feedback, ensuring a bounded output for any bounded input. This stability is particularly advantageous in environments with noise, making FIR filters the preferred choice for applications where signal integrity and noise control are critical.