FIR vs IIR Filters: Key Differences Explained
Digital filters are essential tools in signal processing. They are widely used to remove noise, extract useful frequency components, and analyze signals in various engineering applications. Among the most commonly used digital filters are FIR (Finite Impulse Response) filters and IIR (Infinite Impulse Response) filters. Although both filters are designed to modify signals in the frequency domain, they behave differently in terms of stability, computational complexity, and phase response.
In this article, we will explain the key differences between FIR and IIR filters, when to use each type, and how they are applied in practical signal analysis.
Digital filter system (= Difference equation)
What Is an FIR Filter?
An FIR (Finite Impulse Response) filter is a digital filter whose impulse response settles to zero in a finite amount of time.
In simple terms, the output of the filter depends only on the current input and a limited number of previous inputs.
The general form of an FIR filter is
x [n] is the input signal
y[n] is the filtered output signal
bk are filter coefficients (feedforward)
Key Characteristics of FIR Filters
Always stable
Can achieve linear phase response
Typically require higher computational cost
Often used in high-precision signal processing
Because of their predictable phase behavior, FIR filters are commonly used in applications such as:
Why finite?
A clear FIR example is the 3-point moving average
To obtain the impulse response, set the input to an impulse
Then the output becomes the impulse response
Substituting
Direct expansion
Final result
This shows explicitly that the impulse response is nonzero only for a finite number of samples, which is why the system is classified as an FIR filter.
What Is an IIR Filter?
An IIR (Infinite Impulse Response) filter is a digital filter whose impulse response theoretically continues indefinitely.
Unlike FIR filters, IIR filters use both previous inputs and previous outputs.
The general form of an IIR filter is
This recursive structure makes IIR filters computationally efficient.
Key Characteristics of IIR Filters
Requires fewer coefficients
More computationally efficient
Can approximate analog filters
May become unstable if not designed properly
IIR filters are widely used when computational efficiency is important.
Typical applications include
Why infinite?
A clear IIR example is the Exponential Moving Average (EMA)
To obtain the impulse response, set the input to an impulse:
Then the output becomes the impulse response
Substituting
Direct expansion
Final result
This shows explicitly that the impulse response extends over an infinite number of samples, which is why the system is classified as an IIR filter. The impulse response never becomes exactly zero.
FIR vs IIR Filters: Key Differences
The main differences between FIR and IIR filters can be summarized in the following table.
| Feature | FIR filter | IIR filter |
|---|
| Impulse Response | Finite | Infinite |
| Stability | Always stable | May become unstable |
| Phase Response | Linear phase possible | Usually non-linear |
| Computation | Higher computational cost | Lower computational cost |
| Implementation | Non-recursive | Recursive |
| Typical low-pass | MA (Moving Average) | EMA (Exponential MA): 1st order IIR |
When Should You Use FIR(Finite Impulse Response) Filters?
FIR filters are typically preferred when phase accuracy is important.
For example, in applications such as audio processing or biomedical signals, preserving waveform shape is critical.
Use FIR filters when
Linear phase response is required
Stability must be guaranteed
High precision filtering is needed
When Should You Use IIR Filters?
IIR filters are preferred when computational efficiency is more important.
Because they require fewer coefficients, IIR filters are well suited for real-time systems and hardware implementations.
Use IIR filters when
Low computational cost is required
Real-time processing is needed
Hardware limitations exist
Example: FIR and IIR Filtering in Signal Analysis
To better understand the difference between FIR and IIR filters, we can apply both filters to the same signal.
In this example, we analyze a measured signal and apply digital filtering to remove unwanted noise.
Using a signal processing tool like MALMIJAL, the filtering workflow can be built visually without writing code.
The typical steps include
Import signal data
Apply spectral analysis
Select filter type (FIR or IIR)
Adjust filter parameters
Analyze the filtered result
After applying the filters, the difference in frequency response can be observed in the resulting spectrum.
The phase of the FIR filter is linear with frequency. This type of workflow allows engineers and researchers to quickly experiment with different filtering methods and evaluate signal quality.
Conclusions
Both FIR and IIR filters play an important role in digital signal processing.
While FIR filters provide guaranteed stability and linear phase response, IIR filters offer higher efficiency and lower computational cost.
Choosing the right filter depends on the requirements of the application, including performance constraints, phase accuracy, and processing speed.
Understanding the differences between FIR and IIR filters helps engineers select the appropriate filtering method for their signal analysis tasks.
Suggested Further Reading
##You may also find the following topics useful:
FIR vs IIR Filters: Key Differences Explained
In this article, we will explain the key differences between FIR and IIR filters, when to use each type, and how they are applied in practical signal analysis.
Digital filter system (= Difference equation)
What Is an FIR Filter?
An FIR (Finite Impulse Response) filter is a digital filter whose impulse response settles to zero in a finite amount of time.
In simple terms, the output of the filter depends only on the current input and a limited number of previous inputs.
The general form of an FIR filter is
x [n] is the input signal
y[n] is the filtered output signal
bk are filter coefficients (feedforward)
Key Characteristics of FIR Filters
Always stable
Can achieve linear phase response
Typically require higher computational cost
Often used in high-precision signal processing
Because of their predictable phase behavior, FIR filters are commonly used in applications such as:
audio processing
communication systems
vibration analysis
biomedical signal processing
Why finite?
A clear FIR example is the 3-point moving average
To obtain the impulse response, set the input to an impulse
Then the output becomes the impulse response
Substituting
Direct expansion
Final result
This shows explicitly that the impulse response is nonzero only for a finite number of samples, which is why the system is classified as an FIR filter.
What Is an IIR Filter?
An IIR (Infinite Impulse Response) filter is a digital filter whose impulse response theoretically continues indefinitely.
Unlike FIR filters, IIR filters use both previous inputs and previous outputs.
The general form of an IIR filter is
This recursive structure makes IIR filters computationally efficient.
Key Characteristics of IIR Filters
Requires fewer coefficients
More computationally efficient
Can approximate analog filters
May become unstable if not designed properly
IIR filters are widely used when computational efficiency is important.
Typical applications include
real-time signal processing
embedded systems
control systems
audio filtering
Why infinite?
A clear IIR example is the Exponential Moving Average (EMA)
To obtain the impulse response, set the input to an impulse:
Then the output becomes the impulse response
Substituting
Direct expansion
Final result
This shows explicitly that the impulse response extends over an infinite number of samples, which is why the system is classified as an IIR filter. The impulse response never becomes exactly zero.
FIR vs IIR Filters: Key Differences
The main differences between FIR and IIR filters can be summarized in the following table.
When Should You Use FIR(Finite Impulse Response) Filters?
FIR filters are typically preferred when phase accuracy is important.
For example, in applications such as audio processing or biomedical signals, preserving waveform shape is critical.
Use FIR filters when
Linear phase response is required
Stability must be guaranteed
High precision filtering is needed
When Should You Use IIR Filters?
IIR filters are preferred when computational efficiency is more important.
Because they require fewer coefficients, IIR filters are well suited for real-time systems and hardware implementations.
Use IIR filters when
Low computational cost is required
Real-time processing is needed
Hardware limitations exist
Example: FIR and IIR Filtering in Signal Analysis
To better understand the difference between FIR and IIR filters, we can apply both filters to the same signal.
In this example, we analyze a measured signal and apply digital filtering to remove unwanted noise.
Using a signal processing tool like MALMIJAL, the filtering workflow can be built visually without writing code.
The typical steps include
Import signal data
Apply spectral analysis
Select filter type (FIR or IIR)
Adjust filter parameters
Analyze the filtered result
After applying the filters, the difference in frequency response can be observed in the resulting spectrum.
The phase of the FIR filter is linear with frequency. This type of workflow allows engineers and researchers to quickly experiment with different filtering methods and evaluate signal quality.
Conclusions
Both FIR and IIR filters play an important role in digital signal processing.
While FIR filters provide guaranteed stability and linear phase response, IIR filters offer higher efficiency and lower computational cost.
Choosing the right filter depends on the requirements of the application, including performance constraints, phase accuracy, and processing speed.
Understanding the differences between FIR and IIR filters helps engineers select the appropriate filtering method for their signal analysis tasks.
Suggested Further Reading
##You may also find the following topics useful: