阿啵呲嘚 -
Signal processing filter design is the core issue. As the finite impulse response (FIR) digital filter with infinite impulse response (IIR) digital filter is difficult to achieve linear phase characteristics, the signal transmission does not occur when significant phase distortion, thus FIR filter in engineering practice has been widely used. FIR filter is the core of the design of finite impulse response calculated to approximate the given frequency response, common design method is a window method and frequency sampling. In this paper, design of frequency sampling FIR filter, frequency sampling method can be directly in the frequency domain of the FIR filter design, for those who only a few selected non-zero value of the sampling frequency narrowband filter particularly effective. 】 【Body
A linear phase FIR digital filter characteristics:
1, the introduction of the linear phase
Set for the FIR filter frequency response function. Can be expressed as
Called the rate function for the real function. It should be noted and the amplitude frequency characteristics of different functions for the positive real function, while the desirable negative.
Known as the phase characteristic function, then known as the first class (A class) linear phase characteristics; At the time, called the second class (B class) linear phase characteristics.
2, FIR filters with linear phase characteristics (length)
1) The time-domain characteristics
A Class: (1)
B: (2)
Group delay: a constant, so the A class and B class of linear phase characteristic referred to as constant group delay characteristics.
2) frequency-domain characteristics
A Class: N is odd (case 1): About three dual symmetry.
N is even (case 2): on the odd symmetry ().
Class B: N is odd (case 3): About three odd symmetry.
N is even (case 4): On the odd symmetry, on the even symmetry.
3 points
(1) Case 1: You can achieve all filtering (low pass, high pass, band pass, band stop and point resistance, etc.).
(2) Case 2: impossible to have high-pass, band pass and point-stop filter.
(3) Scenario 3: You can only achieve band-pass filter.
(4) case 4: not achieve low-pass, band stop and point stop filter.
Second, the frequency sampling design method of design principles:
FIR digital filter is designed to meet the design requirements to find a filter or system unit impulse response function.
According to frequency of sampling theory, if the length, in the upper unit circle on the sampling interval be
(3)
As long as, there
, (4)
(5)
Thus, as long as that FIR digital filter frequency response function in the interval point sampling, we can determine the unit impulse response filter or system function, which is the frequency sampling design of the theory.
Frequency sampling frequency sampling is based on the above theory index constructed by the filtering characteristics of filter frequency response function approximation hope its in the sampled
, (6)
Then, obtain the unit impulse response, or obtain the system function. In this way, or is the result of FIR digital filter design.
Third, with the frequency sampling design of FIR filter design steps:
(1) According to the stop-band attenuation α minimum number of sampling points chosen transition zone m.
(2) to determine the width of transition zone B, estimate the frequency domain sampling points (filter length) N. If the increase in m were transitional zone samples, the transition zone width approximation into (m +1) 2π / N. When the N to determine when, m the greater the wider the transition zone. If the width of a given transition zone B, the requirement (m +1) 2π/NB, filter length N must satisfy the following estimation formula:
(3) to construct a wish to approximate the frequency response function:
=
Questions added: (4) According to (6) Type in the frequency domain sampling
(5) H (k) for N point IDFT, be the first class of linear phase FIR digital filter unit pulse response
6) test design results. If the minimum stopband attenuation does not meet the target, will have to change the value of transition zone sampling, up until the meet the requirements. If the filter does not meet the target frequency boundary requirement. If the filter does not meet the target frequency boundary requirements, will have to fine-tuning of the boundary frequency
4, frequency sampling design of FIR filters:
(1) The general frequency response function of the actual design of the ideal frequency response characteristics of the corresponding approximation as hoped, it will give the design simplified.
(2) linear phase FIR design constraints on and if, as the rate of sampling, said sampling phase
(3) the approximation error and the improvement measures, the estimated value
5, frequency sampling method and design characteristics of test results:
Features of this method are: the frequency domain directly involved in any frequency response of FIR digital filters, the concept clearly and directly. But difficult to control the border frequency. Therefore, the design, should be tested, can increase the frequency of sampling points to improve the accuracy of the boundary, but this will increase the cost of filters and calculation.
For narrow-band filter, even if the large passband and fewer non-zero sample, so that the interpolation of equation (5) items less effective, so that the slip road parallel to achieve low frequency sampling structure, so that filter cost reduction, reduced operations. Therefore, the design method for narrow-band filter design
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CarieVinne -
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