Filtering evaluation method of filter

Abstract

The invention provides a filtering evaluation method of a filter, which relates to the technical field of filter detection and comprises the following steps: acquiring a standard frequency response of a to-be-detected filter; the method comprises the following steps: inputting a test signal into a filter to be tested, and processing a filtering signal output by the filter to be tested through a network analyzer to obtain a test frequency response, which comprises the following steps: determining a plurality of groups of initial frequency point sets and initial scanning time; optimizing the initial scanning time to obtain a plurality of initial optimized scanning times; determining a plurality of groups of initial frequency responses through a network analyzer; obtaining a test frequency point set through a genetic algorithm; determining test scanning time; determining a test frequency response through a network analyzer; comparing the standard frequency response with the test frequency response, and determining the filtering performance of the to-be-tested filter; selection of frequency points is optimized, the precision of frequency sweep testing is improved, and the testing time is shortened.

Description

Technical Field

[0001] The present invention relates to the technical field of filter detection, and in particular to a filter testing and evaluation method for a filter. Background Art

[0002] A filter is a device or system that can selectively allow certain frequency components to pass through while attenuating or suppressing other frequency components. Existing filter evaluation methods include frequency sweep analysis and time domain testing. Frequency sweep analysis refers to the use of a network analyzer or spectrum analyzer to perform a frequency sweep test on the filter to obtain its amplitude-frequency response, phase-frequency response, group delay and other parameters. Time domain testing refers to the use of an oscilloscope and other instruments to observe the time domain response of the filter to a specific input signal, such as step response, pulse response, etc., to evaluate the transient characteristics of the filter. However, for frequency sweep testing, since frequency sweep analysis mainly focuses on the frequency response characteristics of the filter under steady-state sinusoidal signal excitation, it is impossible to directly evaluate its transient indicators such as response speed, overshoot, and settling time to rapidly changing signals; and frequency sweep analysis requires scanning the entire frequency range point by point. If the frequency range is wide or a higher frequency resolution is required, the test time will be longer, and the accuracy of frequency sweep analysis is closely related to the selection of frequency points. If the frequency points are not selected properly, it may cause large evaluation errors.

[0003] In view of this, the present invention proposes a filter evaluation method for a filter to optimize the selection of frequency points, improve the accuracy of frequency sweep testing and reduce testing time. Summary of the invention

[0004] The object of the present invention is to provide a filter evaluation method for a filter, comprising: obtaining a standard frequency response of the filter to be tested; the standard frequency response refers to an ideal frequency response of the filter to be tested, including a standard passband characteristic, a standard stopband attenuation, a standard transition band slope, a standard insertion loss and a standard bandwidth; inputting a test signal into the filter to be tested, and processing the filter signal output by the filter to be tested through a network analyzer to obtain a test frequency response; the test frequency response refers to the actual frequency response of the filter to be tested; obtaining the test frequency response comprises: determining a plurality of groups of initial frequency point sets and an initial scanning time based on the standard frequency response; optimizing the plurality of initial frequency point sets respectively through the plurality of initial frequency point sets. The invention discloses a method for preparing a filter to be tested by using a network analyzer. The method comprises the steps of: determining an initial scanning time, obtaining a plurality of initial optimized scanning times; determining a plurality of groups of initial frequency responses through the network analyzer based on an initial frequency point set and its corresponding initial optimized scanning time; constructing a fitness function based on an actual frequency response and the standard frequency response, optimizing the initial frequency point set through a genetic algorithm, and obtaining a test frequency point set; determining a test scanning time based on the test frequency point set; determining the test frequency response through the network analyzer based on the test frequency point set and the test scanning time; comparing the standard frequency response with the test frequency response to determine the filtering performance of the filter to be tested; the filtering performance is used to reflect the quality of the filter to be tested.

[0005] Furthermore, the genetic algorithm includes: using frequency points as genes and frequency point sets as chromosomes to construct an initial population; determining the fitness values ​​of multiple chromosomes in the initial population respectively; extracting multiple parent chromosomes from the multiple chromosomes based on the fitness values; performing crossover and mutation operations on the parent chromosomes to obtain a new population; calculating the fitness values ​​of multiple offspring chromosomes in the new population, repeating the population update operation until a loop stop condition is reached, and using the chromosome that reaches the loop stop condition as the test frequency point set.

[0006] Further, the mutation operation includes: obtaining the parent frequency response of the parent chromosome; processing the parent frequency response to obtain a first parent frequency response and a second parent frequency response; the first parent frequency response is related to the first-order derivative of the parent frequency response; the second parent frequency response is related to the second-order derivative of the parent frequency response; identifying the first parent frequency response to obtain a first point set and a second point set; the first point set is related to the corner point of the parent frequency response; the second point set is related to the maximum point of the parent frequency response; identifying the second parent frequency response The third point set is obtained; the third point set is related to the inflection point of the parent frequency response; the parent frequency points in the parent chromosome that are closest to the frequency points in the first point set, the second point set and the third point set are determined respectively, and the point distance is determined; when the point distance is greater than or equal to the resolution of the network analyzer, a new frequency point is added between the closest parent frequency point and the corresponding set point; the set point refers to the point in the first point set, the second point set and the third point set; when the point distance is less than the resolution of the network analyzer, the set point is used to replace the corresponding nearest parent frequency point. By guiding the variation direction, the frequency points can be effectively concentrated in the key area of ​​the filter response, improving the accuracy and efficiency of the measurement.

[0007] Furthermore, the fitness function is: ;in, represents the fitness function; N represents the total number of frequency points of the actual frequency response; i represents the frequency point variable; Indicates the value of frequency point i in the actual frequency response; Represents the value of frequency point i in the standard frequency response; A set of key frequency point features representing a standard frequency response; A set of key frequency point features representing the actual frequency response; represents the feature position accuracy function; represents the rate of change function; M represents the population size; j represents the population variable; Indicates the selected chromosome Not the current chromosome ; Represents the feature position accuracy function. By constructing a fitness function based on the difference and variation characteristics between the standard frequency response and multiple actual frequency responses in the population, the frequency sweep strategy can be optimized more effectively, while ensuring measurement accuracy, improving the ability to capture key features, and maintaining sufficient diversity in the population.

[0008] Furthermore, the change rate function is: ;in, Indicates the value of the frequency point i+1 in the actual frequency response; It represents the average value of the rate of change; represents the standard deviation of the rate of change; Represents an indicator function that returns 1 if the condition inside the parentheses is true, otherwise it returns 0.

[0009] Furthermore, the feature position accuracy function is: ;in, A set of key frequency point features representing the standard frequency response Elements in A set of key frequency point features representing the actual frequency response Elements in Indicates taking the maximum value; represents the exponential function; Indicates an adjustable parameter.

[0010] Furthermore, multiple groups of initial frequency point sets are determined, including: obtaining a design circuit diagram of the filter to be tested, and extracting multiple components of the design circuit diagram; determining the frequency response characteristics of the filter to be tested based on design parameters of the multiple components respectively; determining key frequency points based on the frequency response characteristics; the key frequency points include passband edge points, stopband starting points and high sensitivity area starting points; based on the key frequency points, generating the multiple groups of initial frequency point sets.

[0011] Furthermore, it also includes optimizing key frequency points, including: based on the frequency response characteristics, obtaining the theoretical frequency response curve of the filter to be tested, and based on the key frequency points, dividing the theoretical frequency response curve into multiple sub-theoretical frequency response curves; based on the key frequency points, generating multiple sub-reconstruction frequency response curves; respectively calculating the mean square error between the sub-theoretical frequency response curves and the corresponding sub-reconstruction frequency response curves; when the mean square error is greater than the error threshold, performing interpolation on the key frequency points within the range to obtain new key frequency points, and generating new sub-reconstruction frequency response curves, and repeating the calculation and judgment operations of the mean square error; when the mean square error is less than or equal to the error threshold, stopping the loop, and using the obtained new key frequency point as the final key frequency point.

[0012] Further, the frequency response characteristics of the filter to be tested are determined based on the design parameters of the multiple components, including: based on the design parameters, respectively determining the nominal values ​​and tolerance ranges of the multiple components; based on the nominal values ​​and the tolerance ranges, performing Monte Carlo analysis to generate multiple groups of randomly distributed component values, and simulating the changes of component values ​​through normal distribution or uniform distribution; for each group of component values, calculating the response of the filter at different frequency points; based on the response of the filter at different frequency points, determining the frequency response characteristics. The filter model is constructed by the Monte Carlo method to determine multiple optimal detection frequency points, further reducing the test time and cost.

[0013] Furthermore, the filtering performance is: ;in, Indicates the score of filtering performance. The higher the score, the better the filtering performance of the tested filter. represents the cut-off frequency error; represents the passband ripple error; represents the stopband attenuation error; represents the slope factor; represents the linearity factor; , , , and They respectively represent the first weight coefficient, the second weight coefficient, the third weight coefficient, the fourth weight coefficient and the fifth weight coefficient.

[0014] The technical solution of the embodiment of the present invention has at least the following advantages and beneficial effects: The present invention improves the accuracy of frequency sweep testing and reduces testing time by optimizing the selection of frequency points. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 An exemplary flow chart of a filter evaluation method for a filter provided by the present invention; Figure 2 An exemplary flow chart for obtaining a test frequency response is provided for the present invention. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0017] Figure 1The following is an exemplary flow chart of a filter evaluation method provided by the present invention. Figure 1 As shown, the filter evaluation method of the filter includes the following contents: Step S1: Obtain the standard frequency response of the filter to be tested; the standard frequency response refers to the ideal frequency response of the filter to be tested, including standard passband characteristics, standard stopband attenuation, standard transition band slope, standard insertion loss and standard bandwidth. The filter to be tested refers to the filter that needs to be evaluated. The standard passband characteristics, standard stopband attenuation, standard transition band slope, standard insertion loss and standard bandwidth can respectively refer to the relevant parameters when the filter to be tested is designed.

[0018] Step S2: Input the test signal into the filter to be tested, and process the filtered signal output by the filter to be tested through a network analyzer to obtain a test frequency response; the test frequency response refers to the actual frequency response of the filter to be tested. The test signal may refer to a signal used to test the filter to be tested, and the test signal may be generated by a signal generator. The filtered signal may refer to a signal obtained after the filter to be tested filters the input test signal.

[0019] Step S3: Compare the standard frequency response with the test frequency response to determine the filtering performance of the filter to be tested; the filtering performance is used to reflect the quality of the filter to be tested. The filtering performance is: ; in, Indicates the score of filtering performance. The higher the score, the better the filtering performance of the tested filter. represents the cut-off frequency error; represents the passband ripple error; represents the stopband attenuation error; represents the slope factor; represents the linearity factor; , , , and They respectively represent the first weight coefficient, the second weight coefficient, the third weight coefficient, the fourth weight coefficient and the fifth weight coefficient.

[0020] Figure 2 An exemplary flow chart of obtaining a test frequency response is provided by the present invention. Figure 2 As shown, the process of obtaining the test frequency response includes the following: Step S2.1: Based on the standard frequency response, determine multiple sets of initial frequency point sets and initial scanning time. The initial frequency point set refers to multiple frequency points used to perform frequency response testing on the filter. For example, frequency points can be selected from the test frequency range in a uniform distribution or logarithmic distribution manner to obtain multiple sets of initial frequency point sets. The initial scanning time can refer to the time for the network analyzer to scan the filter when it is initially set. For example, the initial scanning time can be the response time.

[0021] Determining multiple sets of initial frequency point sets includes: obtaining a design circuit diagram of the filter to be tested, and extracting multiple components (e.g., components such as resistors, capacitors, and inductors) of the design circuit diagram. Determining the frequency response characteristics of the filter to be tested based on the design parameters of the multiple components. Determining the frequency response characteristics by a circuit theory analysis method. Determining key frequency points based on the frequency response characteristics; the key frequency points include passband edge points, stopband starting points, and high sensitivity area starting points. Based on the key frequency points, generating the multiple sets of initial frequency point sets.

[0022] It also includes optimizing key frequency points, including: based on the frequency response characteristics, obtaining the theoretical frequency response curve of the filter to be tested, and based on the key frequency points, dividing the theoretical frequency response curve into multiple sub-theoretical frequency response curves. The theoretical frequency response curve can be a theoretical frequency response curve of the filter analyzed according to the values ​​of components and the design circuit diagram. For example, the design frequency response curve of the filter. The theoretical frequency curve can be divided into multiple sub-theoretical frequency response curves such as passband, stopband, and high-sensitivity area through key frequency points. Based on the key frequency points, multiple sub-reconstructed frequency response curves are generated. The reconstructed frequency response curve can refer to a frequency response curve reconstructed based on the selection of key frequency points. The sub-reconstructed frequency curves can include multiple response curves corresponding to the sub-theoretical frequency response curves such as passband, stopband, and high-sensitivity area. Calculate the mean square error of the sub-theoretical frequency response curve and the corresponding sub-reconstruction frequency response curve respectively; when the mean square error is greater than the error threshold, perform interpolation to the key frequency points within the range to obtain new key frequency points, generate a new sub-reconstruction frequency response curve, and repeat the mean square error calculation and judgment operation; when the mean square error is less than or equal to the error threshold, stop the loop, and use the new key frequency point obtained as the final key frequency point. The error threshold may refer to a preset maximum value of the mean square error allowed. The method of performing interpolation to the key frequency points within the range may be to interpolate the midpoints between each key frequency point within the range.

[0023] The method of determining the frequency response characteristics of the filter to be tested based on the design parameters of the multiple components respectively includes: determining the nominal values ​​and tolerance ranges of the multiple components respectively based on the design parameters; performing Monte Carlo analysis based on the nominal values ​​and the tolerance ranges to generate a plurality of groups of component values ​​with random distribution, and simulating the changes of component values ​​through normal distribution or uniform distribution; calculating the response of the filter at different frequency points for each group of component values; and determining the frequency response characteristics based on the response of the filter at different frequency points.

[0024] Step S2.2: Optimize the initial scanning time through the multiple initial frequency point sets respectively to obtain multiple initial optimized scanning times. The initial optimized scanning time may refer to the scanning time obtained after optimizing the initial scanning time based on the number of frequency points. For example, the scanning time may be gradually increased based on the initial frequency point set until the measurement structure is no longer significantly improved, and the scanning time at this time is used as the initial optimized scanning time.

[0025] Step S2.3: Based on the initial frequency point set and the initial optimized scanning time corresponding thereto, the network analyzer determines multiple groups of initial frequency responses. The initial frequency response may refer to the frequency response of the filter obtained by the network analyzer based on the initial frequency point set and the initial optimized scanning time.

[0026] Step S2.4: construct a fitness function based on the actual frequency response and the standard frequency response, and optimize the initial frequency point set through a genetic algorithm to obtain a test frequency point set. The actual frequency response may refer to the frequency response obtained by testing the filter with a network analyzer. The test frequency point set may refer to the frequency point set finally determined for testing the filter.

[0027] Among them, the genetic algorithm includes: using frequency points as genes and frequency point sets as chromosomes to construct an initial population; determining the fitness values ​​of multiple chromosomes in the initial population respectively; extracting multiple parent chromosomes from the multiple chromosomes based on the fitness values; performing crossover and mutation operations on the parent chromosomes to obtain a new population; calculating the fitness values ​​of multiple offspring chromosomes in the new population, repeating the population update operation until the loop stop condition is reached, and using the chromosome that reaches the loop stop condition as the test frequency point set. The loop stop condition can be that the fitness value is less than a preset fitness threshold or the number of iterations is greater than a preset maximum number of iterations.

[0028] Wherein, the mutation operation includes: obtaining the parent frequency response of the parent chromosome. The parent frequency response may refer to a frequency response outputted by a network analyzer based on a frequency point selection scheme of the parent. The parent frequency response is processed to obtain a first parent frequency response and a second parent frequency response; the first parent frequency response is related to the first-order derivative of the parent frequency response; the second parent frequency response is related to the second-order derivative of the parent frequency response. The first parent frequency response is identified to obtain a first point set and a second point set; the first point set is related to the corner point of the parent frequency response; the second point set is related to the maximum point of the parent frequency response. The second parent frequency response is identified to obtain a third point set; the third point set is related to the inflection point of the parent frequency response. The parent frequency points in the parent chromosome that are closest to the frequency points in the first point set, the second point set, and the third point set are respectively determined, and the point distances are determined. When the point distance is greater than or equal to the resolution of the network analyzer, a new frequency point is added between the closest parent frequency point and the corresponding set point; the set point refers to the points in the first point set, the second point set and the third point set; when the point distance is less than the resolution of the network analyzer, the set point is used to replace the corresponding nearest parent frequency point. For example, the closest unselected parent frequency point to set point A is 124.8MHz. When the point distance (frequency difference) between the two points is greater than or equal to the resolution, a new point is added at the bisection point between point A and 124.8MHz, otherwise, 124.8MHz is used as set point A.

[0029] The fitness function is: ; in, represents the fitness function; N represents the total number of frequency points of the actual frequency response; i represents the frequency point variable; Indicates the value of frequency point i in the actual frequency response; Represents the value of frequency point i in the standard frequency response; A set of key frequency point features representing a standard frequency response; A set of key frequency point features representing the actual frequency response; represents the feature position accuracy function; represents the rate of change function; M represents the population size; j represents the population variable; Indicates the selected chromosome Not the current chromosome ; Represents the feature position accuracy function.

[0030] The rate of change function is: ; in, Indicates the value of the frequency point i+1 in the actual frequency response; It represents the average value of the rate of change; represents the standard deviation of the rate of change; Represents an indicator function that returns 1 if the condition inside the parentheses is true, otherwise it returns 0.

[0031] The feature position accuracy function is: ; in, A set of key frequency point features representing the standard frequency response Elements in A set of key frequency point features representing the actual frequency response Elements in Indicates taking the maximum value; represents the exponential function; Indicates an adjustable parameter.

[0032] Step S2.5: Determine a test scan time based on the test frequency point set. The test scan time may refer to a scan time finally determined for testing the filter.

[0033] Step S2.6: Based on the test frequency point set and the test sweep time, determine the test frequency response by the network analyzer.

[0034] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A filter evaluation method for a filter, characterized in that: include: Obtaining a standard frequency response of the filter to be tested; the standard frequency response refers to an ideal frequency response of the filter to be tested, including a standard passband characteristic, a standard stopband attenuation, a standard transition band slope, a standard insertion loss, and a standard bandwidth; A test signal is input into the filter to be tested, and the filter signal output by the filter to be tested is processed by a network analyzer to obtain a test frequency response; the test frequency response refers to the actual frequency response of the filter to be tested; the test frequency response is obtained, including: Based on the standard frequency response, determining multiple groups of initial frequency point sets and initial scanning times; Optimizing the initial scanning time through the multiple initial frequency point sets respectively to obtain multiple initial optimized scanning times; Based on the initial frequency point set and the initial optimized scanning time corresponding thereto, determining multiple groups of initial frequency responses by the network analyzer; Constructing a fitness function based on the actual frequency response and the standard frequency response, optimizing the initial frequency point set through a genetic algorithm to obtain a test frequency point set; Determining a test scan time based on the test frequency point set; Determining the test frequency response by the network analyzer based on the test frequency point set and the test scan time; The standard frequency response is compared with the test frequency response to determine the filtering performance of the filter to be tested; the filtering performance is used to reflect the quality of the filter to be tested.

2. The filter evaluation method of the filter according to claim 1, characterized in that: The genetic algorithm comprises: The frequency points are used as genes and the frequency point sets are used as chromosomes to construct the initial population; Respectively determining the fitness values ​​of multiple chromosomes in the initial population; Based on the fitness values, extracting a plurality of parent chromosomes from the plurality of chromosomes; Performing crossover and mutation operations on the parent chromosome to obtain a new population; The fitness values ​​of multiple offspring chromosomes in the new population are calculated, and the population update operation is repeated until a cycle stop condition is reached, and the chromosomes that meet the cycle stop condition are used as the test frequency point set.

3. The filter evaluation method of the filter according to claim 2, characterized in that: The mutation operation includes: Obtaining a parent frequency response of the parent chromosome; Processing the parent frequency response to obtain a first parent frequency response and a second parent frequency response; the first parent frequency response is related to a first-order derivative of the parent frequency response; and the second parent frequency response is related to a second-order derivative of the parent frequency response; Identify the first parent frequency response to obtain a first point set and a second point set; the first point set is related to the corner points of the parent frequency response; the second point set is related to the maximum value points of the parent frequency response; Identifying the second parent frequency response to obtain a third point set; the third point set is related to the inflection point of the parent frequency response; Respectively determine the parent frequency points in the parent chromosome that are closest to the frequency points in the first point set, the second point set, and the third point set, and determine the point distances; When the point distance is greater than or equal to the resolution of the network analyzer, a new frequency point is added between the closest parent frequency point and the corresponding set point; the set point refers to a point in the first point set, the second point set and the third point set; When the point distance is smaller than the resolution of the network analyzer, the aggregation point is used to replace the corresponding nearest parent frequency point.

4. The filter evaluation method of the filter according to claim 1, characterized in that: The fitness function is: ； in, represents the fitness function; N represents the total number of frequency points of the actual frequency response; i represents the frequency point variable; Indicates the value of frequency point i in the actual frequency response; Represents the value of frequency point i in the standard frequency response; A set of key frequency point features representing a standard frequency response; A set of key frequency point features representing the actual frequency response; represents the feature position accuracy function; represents the rate of change function; M represents the population size; j represents the population variable; Indicates the selected chromosome Not the current chromosome ; Represents the feature position accuracy function.

5. The filter evaluation method of the filter according to claim 4, characterized in that: The rate of change function is: ； in, Indicates the value of the frequency point i+1 in the actual frequency response; It represents the average value of the rate of change; represents the standard deviation of the rate of change; Represents an indicator function that returns 1 if the condition inside the parentheses is true, otherwise it returns 0.

6. The filter evaluation method of the filter according to claim 4, characterized in that: The feature position accuracy function is: ； in, A set of key frequency point features representing the standard frequency response Elements in A set of key frequency point features representing the actual frequency response Elements in Indicates taking the maximum value; represents the exponential function; Indicates an adjustable parameter.

7. The filter evaluation method of the filter according to claim 1, characterized in that: Determine multiple sets of initial frequency points, including: Obtaining a design circuit diagram of the filter to be tested, and extracting a plurality of components of the design circuit diagram; Determining the frequency response characteristics of the filter to be tested based on the design parameters of the multiple components respectively; Based on the frequency response characteristics, determining key frequency points; the key frequency points include passband edge points, stopband starting points and high sensitivity area starting points; Based on the key frequency points, the multiple groups of initial frequency point sets are generated.

8. The filter evaluation method of claim 7, characterized in that: It also includes optimization of key frequency points, including: Based on the frequency response characteristics, a theoretical frequency response curve of the filter to be tested is obtained, and based on the key frequency points, the theoretical frequency response curve is divided into a plurality of sub-theoretical frequency response curves; Based on the key frequency points, generating a plurality of sub-reconstruction frequency response curves; respectively calculating the mean square error between the sub-theoretical frequency response curve and the corresponding sub-reconstructed frequency response curve; When the mean square error is greater than the error threshold, interpolation is performed on the key frequency points within the range to obtain new key frequency points, and a new sub-reconstruction frequency response curve is generated, and the calculation and judgment operations of the mean square error are repeated; When the mean square error is less than or equal to the error threshold, the loop is stopped, and the obtained new key frequency point is used as the final key frequency point.

9. The filter evaluation method of the filter according to claim 7, characterized in that: The determining the frequency response characteristics of the filter to be tested based on the design parameters of the plurality of components respectively comprises: Based on the design parameters, respectively determine the nominal values ​​and tolerance ranges of the plurality of components; Based on the nominal value and the tolerance range, a Monte Carlo analysis is performed to generate a plurality of groups of component values ​​in a random distribution, and a change in the component value is simulated by a normal distribution or a uniform distribution; For each set of component values, calculate the filter response at different frequencies; The frequency response characteristic is determined based on the response of the filter at different frequency points.

10. The filter evaluation method of the filter according to claim 1, characterized in that: The filtering performance is: ; in, Indicates the score of filtering performance. The higher the score, the better the filtering performance of the tested filter. represents the cut-off frequency error; represents the passband ripple error; represents the stopband attenuation error; represents the slope factor; represents the linearity factor; , , , and They respectively represent the first weight coefficient, the second weight coefficient, the third weight coefficient, the fourth weight coefficient and the fifth weight coefficient.

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