CN109302362A - Utilize the high-speed link equalization methods of DFE and CTLE - Google Patents
Utilize the high-speed link equalization methods of DFE and CTLE Download PDFInfo
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- CN109302362A CN109302362A CN201811222841.1A CN201811222841A CN109302362A CN 109302362 A CN109302362 A CN 109302362A CN 201811222841 A CN201811222841 A CN 201811222841A CN 109302362 A CN109302362 A CN 109302362A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03012—Arrangements for removing intersymbol interference operating in the time domain
- H04L25/03019—Arrangements for removing intersymbol interference operating in the time domain adaptive, i.e. capable of adjustment during data reception
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03012—Arrangements for removing intersymbol interference operating in the time domain
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03178—Arrangements involving sequence estimation techniques
- H04L25/03248—Arrangements for operating in conjunction with other apparatus
- H04L25/03254—Operation with other circuitry for removing intersymbol interference
- H04L25/03267—Operation with other circuitry for removing intersymbol interference with decision feedback equalisers
Abstract
The present invention discloses a kind of high-speed link equalization methods using adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE, the steps include: (1) input waveform；(2) transmission function of discrete complex frequency domain is generated；(3) waveform after obtaining LINEAR CONTINUOUS time equalizer CTLE equilibrium；(4) waveform values (6) of each sample point obtain the waveform after equilibrium in waveform after calculating weighted value (5) calculating generation adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE is balanced.The present invention effectively improves the versatility of high-speed link equilibrium, reduces the computational complexity of high-speed link equilibrium.
Description
Technical field
The invention belongs to field of computer technology, further relate to one in computer high-speed link balancing technique field
Kind is equal using adaptive decision feedback equalizer DFE (Decision Feedback Equalization) and LINEAR CONTINUOUS time
The high-speed link equalization methods of weighing apparatus CTLE (Continuous Time Linear Equalization).The present invention can be achieved
Equilibrium to high speed link signal carries out signal integrity analysis using the signal before and after equilibrium.
Background technique
Currently, the transmission speed of signal has become to be getting faster in computer high-speed link, it will cause apparent
Intersymbol interference ISI (Inter Symbol Interference) and reflection.Therefore it needs to carry out high speed link signal equal
Weighing apparatus, to regain workable signal.
In the patent document of its application, " a kind of low complex degree is sentenced for No.54 Institute of China Electronics Science & Technology Group
Certainly feedback equalization algorithm " (applying date: 2017.11.28, application number: 201711214380.9, application publication number: CN
107911322 A) in a kind of decision feedback equalization algorithm of low complex degree is provided.This method will receive signal in receiving end first
Frequency-domain transform is carried out, linear equalization is then carried out and is transformed into time domain, noise predictor is input to after judgement and carries out noise prediction, from
And reduce the noise jamming of unenforced symbol, improve the performance of communication system.But the shortcoming that this method still has
Be: the algorithm needs to establish prediction model according to channel characteristic, and different channels needs to establish different prediction models, so that should
The versatility of high-speed link equilibrium reduces.
A kind of patent document " Channel Equalization Algorithm that time-domain and frequency-domain combine " (application of the Zhongshan University in its application
Day: 2018.03.20, application number: 201810232190.8, application publication number: 108418771 A of CN) in a kind of single carry is provided
The channel equalization method of wave system system.This method comprises the concrete steps that: (1) in receiving end, fitting in the time domain to reception data
Work as segmentation, time-domain calculation is transformed by frequency domain using overlap-save method；(2) it is slightly adjudicated using MMSE equalization methods；(3) with
Based on thick court verdict, further thin judgement is carried out to thick court verdict using time domain exhaustive search method.This method is deposited
Shortcoming be: the algorithm needs adjudicated twice so that the computational complexity of high-speed link equilibrium increases.
Summary of the invention
It is a kind of equal using adaptive decision feedback it is an object of the invention in view of the above shortcomings of the prior art, propose
The high-speed link equalization methods of weighing apparatus DFE and LINEAR CONTINUOUS time equalizer.This method can be realized to the equal of high speed link signal
Weighing apparatus carries out signal integrity analysis using the signal before and after equilibrium, while guaranteeing balanced device precision, reducing balanced device operation complexity
Degree increases balanced device versatility.
To achieve the goals above, concrete thought of the invention is to carry out Fast Fourier Transform (FFT) to input waveform first,
It is balanced to generate laggard line continuous time for the transmission function that discrete complex frequency domain is generated after transformation；Then ideal decision wave is generated
Shape calculates the weighted value of each sample point in waveform using adaptive algorithm after generation, generate adaptive decision-feedback equalization
The tap coefficient of device DFE；It is equal finally to calculate generation adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE
After weighing apparatus in waveform each sample point waveform values, generate it is balanced after waveform.
The present invention realizes that specific step is as follows:
(1) input waveform:
The waveform of one high-speed link of (1a) stochastic inputs, as time domain input waveform；
(1b) carries out Fast Fourier Transform (FFT) to time domain input waveform, obtains frequency domain input waveform；
(2) transmission function of discrete complex frequency domain is generated:
The zero point and pole frequency value of input linear continuous-time equalizer CTLE are converted to the transmitting of complex frequency domain by (2a)
Function；
The transmission function discretization of complex frequency domain is obtained discrete complex frequency domain transmission function by (2b)；
(3) waveform after obtaining LINEAR CONTINUOUS time equalizer CTLE equilibrium:
Frequency domain input waveform is multiplied by (3a) with discrete complex frequency domain transmission function, obtains frequency domain output waveform；
Frequency domain output waveform is carried out an inverse fast fourier by (3b), is obtained by LINEAR CONTINUOUS time equalizer CTLE
Waveform after equilibrium；
(4) weighted value of each sample point in waveform after being truncated is calculated:
The intermediate point of the waveform peak point of (4a) by LINEAR CONTINUOUS time equalizer CTLE after balanced, as rising for waveform
Point, the Wave data before deleting starting point, waveform after being truncated；
Sample points greater than threshold value all in waveform after truncation are disposed as high value by (4b), institute in waveform after truncation
There is the sample point less than threshold value to be disposed as low level value, the waveform after all be provided with is formed into ideal decision waveform；
The waveform values of each sample point are corresponding with each in ideal decision waveform in waveform after (4c) calculating truncation takes
The difference of the waveform values of sampling point；
(4d) utilizes adaptive algorithm formula, passes through the waveform values and ideal decision of each sample point in waveform after truncation
The difference of the waveform values of each corresponding sample point in waveform calculates the weighted value of each sample point in waveform after being truncated；
(5) waveform after generating adaptive decision feedback equalizer DFE and the CTLE equilibrium of LINEAR CONTINUOUS time equalizer is calculated
In each sample point waveform values:
(5a) chooses the weighted value of last N number of sample point in waveform after truncation, forms adaptive decision feedback equalizer DFE
Tap coefficient, wherein the value of 1≤N≤n, N are determined by balanced required accuracy；
(5b) utilizes waveform values calculation formula, by the tap coefficient of adaptive decision feedback equalizer DFE, calculates and generates
After adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE is balanced in waveform each sample point waveform
Value；
(6) waveform after equilibrium is obtained:
By all samplings in waveform after adaptive decision feedback equalizer DFE and the CTLE equilibrium of LINEAR CONTINUOUS time equalizer
The waveform values of point, it is equal according to sampling sequence composition adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE
Waveform after weighing apparatus.
Compared with the prior art, the present invention has the following advantages:
First, since present invention employs the taps that adaptive algorithm formula calculates adaptive decision feedback equalizer DFE
Coefficient overcomes the tap existing in the prior art for needing channel estimating model to calculate adaptive decision feedback equalizer DFE
Coefficient causes different channels to need to establish different channel estimating models, so that high-speed link equilibrium is directed to different channels
It needs to carry out different modifications, thus the problem of versatility reduction, so that the present invention expands the versatility of high-speed link equilibrium.
Second, it does not need further to be adjudicated after generating ideal decision waveform due to the present invention, overcomes the prior art
It also needs further to be adjudicated using time domain exhaustive search method after middle generation ideal decision waveform, so that high-speed link is balanced
Computational complexity increase deficiency so that the present invention guarantee high-speed link equilibrium precision simultaneously, reduce high-speed link
Balanced computational complexity.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is analogous diagram of the present invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
Referring to attached drawing 1, the step of present invention realization, is further described.
Step 1, input waveform.
It exports the wave file being made of periodic sampling point at random from circuit simulation tools, reads in this document
Waveform, as time domain input waveform.
Fast Fourier Transform (FFT) is carried out to time domain input waveform, obtains frequency domain input waveform.
Step 2, the transmission function of discrete complex frequency domain is generated.
By zero point, the pole frequency value of the LINEAR CONTINUOUS time equalizer CTLE of input, the transmitting letter of complex frequency domain is converted to
Number.
By the transmission function discretization of complex frequency domain, the transmission function of discrete complex frequency domain is obtained.
The LINEAR CONTINUOUS time equalizer CTLE is is a kind of analog filter, so needing to convert zero pole point to multiple
The transmission function of frequency domain.Reuse the transmitting letter that Bilinear transformation method converts the transmission function of complex frequency domain to discrete complex frequency domain
Number, physical significance are that analog filter is converted to digital filter.
Step 3, the waveform after obtaining LINEAR CONTINUOUS time equalizer CTLE equilibrium.
Frequency domain input waveform is multiplied with the transmission function of discrete complex frequency domain, obtains frequency domain output waveform.
Frequency domain output waveform is subjected to an inverse fast fourier, is obtained balanced by LINEAR CONTINUOUS time equalizer CTLE
Waveform afterwards.
Step 4, the weighted value of each sample point in waveform after being truncated is calculated.
The intermediate point of waveform peak point of the LINEAR CONTINUOUS time equalizer CTLE after balanced is deleted as the starting point of waveform
Except the Wave data before starting point, waveform after being truncated.
Sample points greater than threshold value all in waveform after truncation are disposed as high value, it is all small in waveform after truncation
It is disposed as low level value in the sample point of threshold value, the waveform after all be provided with is formed into ideal decision waveform.
The threshold value refers to, the average value of the ideal low and high level value of adaptive decision feedback equalizer DFE.
Calculate after truncation in waveform each corresponding sample point in the waveform values of each sample point and ideal decision waveform
Waveform values difference.
Using adaptive algorithm formula, pass through the waveform values and ideal decision waveform of each sample point in waveform after truncation
In each corresponding sample point waveform values difference, calculate the weighted value of each sample point in waveform after truncation.
The adaptive algorithm formula is as follows:
+ 2 μ e (k) y of w (k+1)=w (k)d(h)
Wherein, w (k+1) indicates the weighted value of+1 sample point of kth in waveform after being truncated, after k=1...n, n indicate truncation
The sample point sum of waveform, w (k) indicate the weighted value of k-th of sample point in waveform after being truncated, and μ expression takes arbitrary constant value
Step value, e (k) indicate the waveform values and the waveform of corresponding sample point in ideal decision waveform of k-th of sample point of waveform after truncation
The difference of value, yd(h) waveform values of h-th of sample point in ideal decision waveform are indicated, the value of h and the value of k are equal to each other.
The adaptive algorithm formula principle is least-mean-square error algorithm, and least-mean-square error algorithm is nineteen sixty
What B.Widrow and Hoff et al. were proposed on the basis of most trembling descent algorithm, the algorithm is simple, is easily achieved, therefore extensive
It uses.Rule used by least-mean-square error algorithm be make it is square between the desired output of balanced device and real output value
The criterion minimized the error.
Mean square error function is the quadratic equation of tap coefficient, and the hyperparaboloid of a multidimensional is consequently formed, similar bowl-shape
Curved surface, and there is unique smallest point.Adaptive algorithm is exactly to keep tap coefficient mobile towards curved bottom portion smallest point direction, finally
Bottom smallest point is reached, obtains making the smallest best tap coefficients value of error.
Least-mean-square error algorithm is the optimal algorithm for realizing above-mentioned movement, it analyzes adaptive-filtering using gradient information
Performance and tracking optimum filtering state.Tap coefficient is adjusted according to the direction of gradient decline.
Step 5, it calculates and generates adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE equilibrium postwave
The waveform values of each sample point in shape.
The weighted value for choosing last N number of sample point in waveform after being truncated, forms the pumping of adaptive decision feedback equalizer DFE
Head coefficient, wherein the value of 1≤N≤n, N are determined by balanced required accuracy.
It is adaptive to be calculated by the tap coefficient of adaptive decision feedback equalizer DFE for generation using waveform values calculation formula
After answering decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE balanced in waveform each sample point waveform values.
The waveform values calculation formula is as follows:
Wherein, ye(g) adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE equilibrium postwave are indicated
The waveform values of g-th of sample point in shape, g=1...n, x (f) indicate waveform values of the waveform in f-th of sample point after truncation, w (j-
I) weighted value of-i sample points of jth in waveform after being truncated, i=1...N, y are indicatedd(l-i) it indicates the in ideal decision waveform
The waveform values of l-i sample point, the value of f, j, l are equal to each other with the value of g.
Step 6, the waveform after equilibrium is obtained.
By all samplings in waveform after adaptive decision feedback equalizer DFE and the CTLE equilibrium of LINEAR CONTINUOUS time equalizer
The waveform values of point, it is equal according to sampling sequence composition adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE
Waveform after weighing apparatus.
Effect of the invention can be further illustrated by following emulation.
1. simulated conditions:
Emulation experiment of the invention uses MATLAB R2016b simulation software, 2014 circuit simulating software of ADS, in ADS
The high-low voltage of waveform is respectively 1.2V-1.2V in circuit simulating software, and the data transfer rate of waveform is 8Gbps, and waveform contains 5000
A bit, the time span of each bit are 125ps, and the sampled point of each bit is 32.Adaptively
The tap number of decision feedback equalizer DFE is set as 4, and step-length is set as 0.001, the zero point of LINEAR CONTINUOUS time equalizer CTLE
It is set as 1.26Ghz, two poles are set to 19.4GHz and 9.803Ghz.
2. emulation content and its analysis of simulation result:
Emulation experiment of the invention is using the equilibrium side carried in equalization methods of the invention and ADS circuit simulating software
Method, respectively to the processing of high-speed link receiving end wave shape equalization, comparing result is as shown in Figure 2.Wherein, Fig. 2 (a) is to high-speed chain
Road uses the waveform diagram before equalization methods.Fig. 2 (b) is using the LINEAR CONTINUOUS time equalization carried in ADS circuit simulating software
Waveform diagram of the device CTLE to high-speed link after balanced.Fig. 2 (c) is anti-using self-adaptive decision is carried in ADS circuit simulating software
Present waveform diagram of the balanced device DFE to high-speed link after balanced.Fig. 2 (d) is using the LINEAR CONTINUOUS time equalizer in the present invention
Waveform diagram of the CTLE to high-speed link after balanced.Fig. 2 (e) is using DFE pairs of adaptive decision feedback equalizer in the present invention
Waveform diagram after high-speed link is balanced.The ADS circuit simulating software be released by Agilent Technologies of the U.S. it is a at
Ripe business software, included equalization methods have been subjected to the approval of many companies,
Abscissa in Fig. 2 indicates the time, and unit is picosecond.The voltage value that ordinate in Fig. 2 indicates, unit are volt.
Automatic measurement is carried out to waveform diagram in Fig. 2 (a), Fig. 2 (b), Fig. 2 (d) respectively using MATLAB R2016b simulation software, is obtained
The data that the eye of respective waveforms figure is high, eye is wide, see Table 1 for details.CTLE refers to LINEAR CONTINUOUS time equalizer in table 1.
Eye height, the wide contrast table of eye after table 1. uses the present invention balanced with CTLE in the prior art
Distinguish that Fig. 2 (a), Fig. 2 (c), waveform diagram measures in Fig. 2 (e) using MATLAB R2016b simulation software, obtains
The data wide to eye height, the eye of respective waveforms figure, see Table 2 for details.DFE refers to adaptive decision feedback equalizer in table 2.
According to following two formula, linear continuous-time equalizer CTLE equilibrium postwave in the present invention is calculated separately in table 1
The eye of shape figure is high, eye it is wide it is balanced with the LINEAR CONTINUOUS time equalizer CTLE carried in ADS after waveform diagram the wide mistake of eye height, eye
Difference:
(0.850-0.845)/0.850 ≈ 1%
(111.9-111.3)/111.9 ≈ 1%
The eye of waveform diagram is high after linear continuous-time equalizer CTLE is balanced in the present invention, eye is wide with the line carried in ADS
Property continuous-time equalizer CTLE it is balanced after waveform diagram eye is high, error that eye is wide is each about 1%.In Practical Project field
Error within 10% is acceptable error, it can be seen that 1% error is very little, illustrates the present invention compared to existing skill
Art significantly improves balanced precision.
Eye height, the wide contrast table of eye after table 2. uses the present invention balanced with DFE in the prior art
According to following two formula, adaptive decision feedback equalizer DFE equilibrium postwave in the present invention is calculated separately in table 2
The eye of shape figure is high, eye it is wide it is balanced with the adaptive decision feedback equalizer DFE carried in ADS after waveform diagram eye height, eye it is wide
Error:
(0.578-0.5456)/0.546 ≈ 5.7%
(112.5-109.4)/112.5 ≈ 2.7%
After adaptive decision feedback equalizer DFE is balanced in the present invention eye of waveform diagram is high, eye it is wide with carried in ADS from
The error that the eye of waveform diagram is high after adaptation decision feedback equalizer DFE is balanced, eye is wide respectively may be about 5.7% and 2.7%.In reality
Error within 10% in engineering field is acceptable error range, it can be seen that 5.7% and 2.7% error is smaller
, illustrate that the present invention significantly improves balanced precision compared with prior art.
Claims (4)
1. a kind of high-speed link equilibrium side using adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE
Method, which is characterized in that the transmission function for generating discrete complex frequency domain is calculated each in waveform after being truncated using adaptive algorithm formula
The weighted value of a sample point calculates and generates adaptive decision feedback equalizer DFE and the CTLE equilibrium of LINEAR CONTINUOUS time equalizer
Afterwards in waveform each sample point waveform values；The step of this method includes the following:
(1) input waveform:
The waveform of one high-speed link of (1a) stochastic inputs, as time domain input waveform；
(1b) carries out Fast Fourier Transform (FFT) to time domain input waveform, obtains frequency domain input waveform；
(2) transmission function of discrete complex frequency domain is generated:
The zero point and pole frequency value of input linear continuous-time equalizer CTLE are converted to the transmitting letter of complex frequency domain by (2a)
Number；
The transmission function discretization of complex frequency domain is obtained discrete complex frequency domain transmission function by (2b)；
(3) waveform after obtaining LINEAR CONTINUOUS time equalizer CTLE equilibrium:
Frequency domain input waveform is multiplied by (3a) with discrete complex frequency domain transmission function, obtains frequency domain output waveform；
Frequency domain output waveform is carried out an inverse fast fourier by (3b), is obtained balanced by LINEAR CONTINUOUS time equalizer CTLE
Waveform afterwards；
(4) weighted value of each sample point in waveform after being truncated is calculated:
The intermediate point of the waveform peak point of (4a) by LINEAR CONTINUOUS time equalizer CTLE after balanced is deleted as the starting point of waveform
Except the Wave data before starting point, waveform after being truncated；
Sample points greater than threshold value all in waveform after truncation are disposed as high value by (4b), all small in waveform after truncation
It is disposed as low level value in the sample point of threshold value, the waveform after all be provided with is formed into ideal decision waveform；
(4c) calculates after truncation in waveform each corresponding sample point in the waveform values of each sample point and ideal decision waveform
Waveform values difference；
(4d) utilizes adaptive algorithm formula, passes through the waveform values and ideal decision waveform of each sample point in waveform after truncation
In each corresponding sample point waveform values difference, calculate the weighted value of each sample point in waveform after truncation；
(5) it calculates every in waveform after generating adaptive decision feedback equalizer DFE and the CTLE equilibrium of LINEAR CONTINUOUS time equalizer
The waveform values of a sample point:
(5a) chooses the weighted value of last N number of sample point in waveform after truncation, forms the pumping of adaptive decision feedback equalizer DFE
Head coefficient, wherein the value of 1≤N≤n, N are determined by balanced required accuracy；
(5b) utilizes waveform values calculation formula, and by the tap coefficient of adaptive decision feedback equalizer DFE, it is adaptive to calculate generation
After answering decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE balanced in waveform each sample point waveform values；
(6) waveform after equilibrium is obtained:
By all sample points in waveform after adaptive decision feedback equalizer DFE and the CTLE equilibrium of LINEAR CONTINUOUS time equalizer
Waveform values, after forming adaptive decision feedback equalizer DFE and the CTLE equilibrium of LINEAR CONTINUOUS time equalizer according to sampling sequence
Waveform.
2. according to claim 1 utilize adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE
High-speed link equalization methods, which is characterized in that threshold value described in step (4b) refers to, adaptive decision feedback equalizer
The average value of the ideal low and high level value of DFE.
3. according to claim 1 utilize adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE
High-speed link equalization methods, which is characterized in that adaptive algorithm formula described in step (4d) is as follows:
+ 2 μ e (k) y of w (k+1)=w (k)d(h)
Wherein, w (k+1) indicates the weighted value of+1 sample point of kth in waveform after being truncated, and k=1...n, n indicate waveform after truncation
Sample point sum, w (k) indicates that the weighted value of k-th of sample point in waveform after truncation, μ indicate to take the step-length of arbitrary constant value
Value, e (k) indicate the waveform values of k-th of sample point of waveform and the waveform values of corresponding sample point in ideal decision waveform after being truncated
Difference, yd(h) waveform values of h-th of sample point in ideal decision waveform are indicated, the value of h and the value of k are equal to each other.
4. according to claim 1 utilize adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE
High-speed link equalization methods, which is characterized in that waveform values calculation formula described in step (5b) is as follows:
Wherein, ye(g) after expression adaptive decision feedback equalizer DFE and LINEAR CONTINUOUS time equalizer CTLE are balanced in waveform
The waveform values of g-th of sample point, g=1...n, x (f) indicate waveform values of the waveform in f-th of sample point after truncation, w (j-i) table
Show the weighted value of jth-i sample point in waveform after being truncated, i=1...N, yd(l-i) l-i are indicated in ideal decision waveform
The waveform values of sample point, the value of f, j, l are equal to each other with the value of g.
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