Filters are used in digital signal processing to remove undesirable parts of the signal, such as random noise, or to extract useful parts of the signal, such as the parts of the signal belonging to a particular range.
For instance, audio recorded with poor equipment can be filtered to remove the undesired elements from the signal, making it sound as close to the original audio (without disturbances) as possible.
Digital filters can be classified into FIR (finite-duration impulse response) and IIR (infinite-duration impulse response) filters. When a system is provided with some input, the outcome or response achieved is known as its impulse response.
- IIR filters have feedback in their structure, allowing them to have an infinite impulse response, while FIR filters do not have feedback and have a finite impulse response.
- IIR filters are recursive and can create unstable responses, while FIR filters are non-recursive and always stable.
- IIR filters require less computational power than FIR filters, but FIR filters can have a better frequency response and a linear phase.
IIR vs FIR Filters
FIR and IIR filters differ because the former’s impulse response is nonzero for only a few samples. IIR filters have an infinite number of nonzero samples.
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|Parameter of Comparison||FIR Filter||IIR Filter|
|Nature||Non-recursive in nature because it does not reuse its outputs as inputs.||Recursive in nature because it re-uses one or more of its outputs as inputs.|
|Efficiency||Less computationally efficient.||More computationally efficient.|
|Ease of implementation in a circuit||Due to the absence of a feedback mechanism, it is easier to implement in a circuit.||Due to a feedback mechanism, it is more difficult to implement in a circuit.|
|Feedback mechanism||Do not use feedback circuitry.||Uses a feedback mechanism in which the previous output, in conjunction with the present and past input, is given as the present input.|
|Stability||More stable as the present output does not hold any relationship with the previous output.||Less stable as it uses previous output samples as well.|
|Input required to generate current output||Present and past samples of input||Present and past samples of input along with past output.|
|Delay offered||Offers more delay in providing a response||Offers lesser delay in providing a response|
|Memory requirement||Requires more memory||Requires less memory|
|Sensitivity||Less sensitive||More sensitive|
|Ease of controllability||Easy to control||Quite difficult to control|
What is an FIR filter?
Digital filters that generate a finite impulse response of a dynamic system are known as FIR filters. The impulse response provided by FIR filters is of finite duration.
FIR filters do not have a feedback mechanism. Their present input consists of only the present and past input values.
What is an IIR filter?
Digital filters that generate an infinite impulse response of a dynamic system are known as IIR filters. The present and past inputs are taken as the present input in conjunction with the past outputs.
IIR filter operates in a way that the present and past inputs and the past output sample are also considered. This feedback circuitry is what differentiates them from FIR filters.
The internal feedback mechanism makes these filters recursive. They never allow their response to settle at 0 for an applied impulse.
IR filters are best used for applications that require no phase information, for example, for monitoring signal amplitudes.
Main Differences Between FIR Filters and IIR Filters
- FIR filters are non-recursive. IIR filters are recursive as they have a feedback mechanism. The latter uses a feedback mechanism in which the previous output, in conjunction with the present and past input, is given as the present input.
- FIR filters are easier to implement but are less computationally efficient than IIR filters. Due to a feedback loop, IIR filters are difficult to implement in a circuit.
- FIR filters offer a higher delay in their response. IIR filters offer lesser delay in responding.
- FIR filters require more memory as compared to IIR filters. FIR filters are also more stable due to their non-recursive nature. IIR filters, being recursive, are unstable.
- FIR filters are less sensitive and are easier to control than IIR filters.
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Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.