Comparison between FIR digital filter and IIR filter

A major difference between the FIR and the IIR filter is that the FIR is a linear phase, while the IIR is a non-linear phase (bilinear transformation method). The impact on the non-linear phase can be considered as follows: for different frequency components of the input, the phase difference is not proportional to the frequency. The overlay phase of different frequency components in the output is changed from the input to produce distortion of the channel signal.

 

The IIR filter has the following features:

1. The system functions of the IIR digital filter can be written as closed functions.

2. The IIR Digital Filter adopts a recursive structure with a feedback loop. The calculation structure of the IIR filter is usually composed of basic operations such as delay, multiplication coefficient, and addition. It can be combined into four types: direct, positive, cascade, and parallel, all have feedback loops. Due to the rounding processing in the operation, the error accumulates constantly, and sometimes produces a weak parasitic oscillation.

3 in terms of the design, the mature analog filters, such as the barworth, chbievev, and elliptical filters, can be used as ready-made design data or charts for query, the design workload is relatively small, and the requirements for computing tools are not high. When designing an IIR digital filter, we first write the formula of the simulated Filter Based on the index, and then convert the formula of the simulated filter into the formula of the digital filter through certain transformations.

4 The phase characteristics of the IIR digital filter are difficult to control. When the phase requirement is high, a phase calibration network is required.

In the MATLAB design of the IIR filter, the buttterworth function can be used to design the butworth filter, the cheby1 function is used to design the cheby1 filter, and the cheby2 filter is used to design the chbixuefu II filter, use the ellipord function to design an elliptical filter.

Different from the design of FIR filters, the order of the design of the IIR filter is not specified by the designer, but based on the parameters of each filter input by the designer (cut-off frequency, strip filter, impedance band attenuation, etc ), the software designs the minimum order of filters that satisfy these parameters. Different types of IIR filters are designed in MATLAB to have corresponding functions for order selection.

The Unit response of IIR is an infinite pulse sequence. The unit response of FIR is limited.

Large Precision of amplitude-frequency characteristics of IIR, rather than linear phase, can be applied to audio signals that are not sensitive to phase information;

The accuracy of FIR amplitude-frequency characteristics is lower than that of IIR, but the linear phase is that the time difference of the signals of different frequency components after passing through the FIR Filter remains unchanged. This is a good property.

In addition, the limited unit response is also conducive to the processing of digital signals, easy to program, and low latency for computing, which is very important for real-time signal processing.

Comparison between FIR digital filter and IIR filter

Fir
IIR
 
Design Method
Generally, there is no parsing design formula, which must be completed by a computer program.
The AF design chart can be used for simple and effective design.
 
Design Results
The amplitude-frequency characteristics (multi-band) and linear phase (advantage) can be obtained ).
Only amplitude-frequency characteristics can be obtained, and the phase-frequency characteristics are unknown (disadvantages). If a linear phase is required, full-pass network calibration is required, but the order and complexity of the filter are increased.
 
Stability
All vertices are at the origin (always stable) and there is no stability problem.
Stability issues.
 
Causal
Always satisfied. Any non-causal Finite Long sequence can always be transformed into a causal sequence through a certain delay.

Structure
Non-recursion
Recursive System
 
Operation Error
Generally, there is no feedback, and the operation error is small.
With feedback, as rounding in an operation produces a limit cycle.
 
Fast Algorithm
FFT can be used to reduce the computational workload.
No quick calculation method
 

 

Comparison between fir and IIR (limited impact response and unlimited impact response)

Performance Comparison"

In terms of performance, the pole of the IIR filter transmission function can be located anywhere in the unit circle. Therefore, it can obtain high selectivity with a lower order, with fewer storage units, therefore, it is highly economic and efficient. However, this efficiency is at the cost of non-linear phase. The better the selectivity, the more serious the phase nonlinear. On the contrary, the FIR filter can obtain a strict linear phase. However, because the pole of the FIR Filter transmission function is fixed at the origin (the output is only related to the finite input, the denominator of the transfer function is 1, so we can only use a higher order to achieve a higher selectivity. For the same filter design index, the Order required by the FIR filter can be 5 to 5 higher than that of the IIR filter ~ 10 times. As a result, the cost is high, and the signal delay is also large. If the same selectivity and linear requirements are applied, the IIR filter must be added to the All-pass network for phase comparison, the number and complexity of filters must also be greatly increased.

In terms of structure"

The IIR filter must adopt a recursive structure, and the pole position must be within the Unit Circle. Otherwise, the system will be unstable. In addition, in this structure, due to the rounding processing of the sequence during the operation, this finite-character length effect sometimes introduces parasitic oscillation. On the contrary, the FIR Filter mainly uses non-recursive structures, and there is no stability problem in both theoretically and practically limited precision operations, and the operation error is also small. In addition, the FIR filter can adopt the fast Fourier transform algorithm, and the operation speed can be much faster under the same order.

 

This article from csdn blog: http://blog.csdn.net/henhen2002/archive/2010/09/03/5860432.aspx