# FIR vs IIR Digital Filter

Introduction

In the realm of signal processing and filter design, understanding the difference between Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters is crucial. The impulse response of a filter refers to its output response when subjected to an impulse input. FIR filters have a finite impulse response duration, while IIR filters exhibit an infinite impulse response duration. Additionally, the operation of convolution plays a significant role in filtering operations, applying weighted local averaging to input signals based on the filter's impulse response. Let's delve deeper into the characteristics and implementations of FIR and IIR filters.

Overview:

FIR Filters

As one can see, the FIR filter output response y[n] only depends on input signal x[n].

FIR filters have a finite duration output response.

They rely solely on the input signal and do not incorporate previous output values.

The output response of an FIR filter eventually subsides when the input impulse reaches zero.

FIR filters can be implemented using convolution, which involves the weighted local averaging of the input signal.

The output response of an FIR filter depends only on the input signal and is not influenced by previous outputs.

IIR Filters

As one can see, the IIR filter output response y[n] depends on both input signal x[n] and y[n].

IIR filters exhibit an infinite duration output response.

They depend on both the input signal and previous output values (output feedback).

Even when the input impulse goes away, the IIR filter's output response persists due to the presence of alternate input signals and feedback from previous outputs.

IIR filters can be realized using a difference equation, where the input and output signals are multiplied by feedforward and feedback coefficients.

The output response of an IIR filter is influenced by both the input signal and the feedback from previous outputs.

Applications:

FIR and IIR filters find numerous real-world applications in various domains due to their distinct characteristics. Here are some examples:

Finite Impulse Response (FIR) Filters:

Audio Processing: FIR filters are commonly used in audio equalizers, noise cancellation systems, and audio effects processing to achieve precise frequency response shaping and signal enhancement.

Image Processing: FIR filters play a vital role in image enhancement, edge detection, and image smoothing applications, where they help in noise reduction and improving image quality.

Communication Systems: FIR filters are used in wireless communication systems, such as digital modulation and demodulation processes, to eliminate interference, enhance signal quality, and achieve reliable data transmission.

Infinite Impulse Response (IIR) Filters:

Biomedical Signal Processing: IIR filters are widely utilized in processing biomedical signals, such as electrocardiograms (ECG) and electroencephalograms (EEG), for noise removal, artifact suppression, and feature extraction, enabling accurate diagnostic analysis.

Control Systems: IIR filters are applied in control systems to shape the frequency response of feedback loops, stabilize systems, and improve transient response for achieving desired system performance.

Speech and Audio Compression: IIR filters are employed in speech and audio compression algorithms, such as speech codecs and audio codecs, to achieve efficient data compression while maintaining acceptable audio quality.

These examples highlight how FIR and IIR filters are integral to a wide range of applications, addressing diverse signal processing requirements across industries. The choice between FIR and IIR filters depends on factors such as desired frequency response, computational complexity, stability considerations, and specific application constraints. The main difference is time delay for the digital filter, for fast realtime output, typically IIR filters are used such as low pass or high pass filters due to lower number of coefficients.

Summary

FIR filters have a finite impulse response duration, while IIR filters have an infinite impulse response duration.

Convolution is the operation used in filtering to apply weighted local averaging based on the filter's impulse response.

FIR filters rely solely on the input signal, while IIR filters incorporate both the input signal and previous output values.

The output response of an FIR filter eventually subsides, while the output response of an IIR filter persists.

IIR requires lower number of coefficients which reduce delay.