Abstract:
The invention provides an electrocardiogram signal compression and de-compression system. The invention uses the sign characteristics of the coefficients of the discrete cosine transform type IV and the characteristics of quantization of spectrum to perform the differential pulse code modulation of the spectrum for preserving the high frequency characteristics of the spectrum of the discrete Fourier transform. The invention also uses the Huffman coding to increase the compression ratio. Different from the conventional compression technology, the invention uses the fact that the quantization values of the spectrum in the high frequency are almost the same to increase the compression ratio and preserve the characteristics of high frequency components of the spectrum.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to the technical field of digital signal processing and, more particularly, to an electrocardiogram signal compression and de-compression system. 
     2. Description of Related Art 
     Because the generation of electrocardiogram (ECG) requires continuously recording electrocardiogram signals, typical medical instruments usually do not have enough memory for processing the signals. Taking the existent multi-lead-tapeless ECG Holter system as an example, it uses semiconductor memory as storage media. The semiconductor memory has to store a system program and three ECG signal recordings each for continuous 24 hours. The storage of such data requires a great amount of memory, resulting in high cost for many medical instruments. 
     Due to the great amount of data and long recording time for ECG, there are lots of ECG signal compressing methods proposed for reducing the cost. As a result, current medical instruments generally use a data compressing method to reduce the cost. By compressing the ECG signals, the memory space can be saved and thus the ECG data can be conveniently added into a central database, so as to perform analysis and comparison data for therapy subsequently. Because the amount of the compressed data is small, it is able to transmit the data in real time via a wired or wireless channel, whereby the prior heart rate monitoring system can be integrated into a portable device to facilitate in monitoring the heart rate of a patient at any time. 
       FIG. 1  is a schematic diagram illustrating the ECG signals, wherein the important information in the ECG signals focuses on P, Q, R, S and T waveforms, including their positions, shapes, sizes, etc. The P waveform stands for the effect of an atrium (of the heart), in which the left atrium receives the blood full of oxygen from the lung and the right atrium receives the blood without oxygen from the hole body, and this effect continues for about 90 ms. The next part of ECG is QRS-complex waveform, which stands for the effect of a chamber (of the heart), in which the left chamber sends the blood full of oxygen to the whole body and the right chamber sends the blood without oxygen to the lung, and this effect continues for about 80 ms. During the period of time that the QRS-complex waveform appears, the atrium of the heart gradually resumes and prepares to repeat another cycle. During the T waveform, the chamber of the heart also gradually resumes and prepares to repeat another cycle. The time between two adjacent QRS-complex waveforms or R waveforms is a reciprocal of the heartbeat frequency. These data should be reserved to the best no matter what compressing method is used. 
     The prior art only considers compression of the ECG signals and thus devotes to increasing the compression ratio (CR) of the technique. However, with the advance of the technology, no matter for the flash memory, the dynamic random access memory or the hard disk, the storage capacity has been greatly increased, so that the compression ratio is no longer the major target for ECG compression. In turn, the depression of distortion can provide excellent reconstructed signals for allowing the doctors to make a most correct decision. Therefore, it is desirable to provide an improved electrocardiogram signal compression and de-compression system to mitigate and/or obviate the aforementioned problems. 
     SUMMARY OF THE INVENTION 
     The object of the present invention is to provide an electrocardiogram signal compression and de-compression system, which has excellent compression ratio and low distortion rate, as well as excellent quality score after de-compression. 
     In one aspect of the present invention, there is provided an electrocardiogram signal compression system, which includes: a normalization device for receiving N electrocardiogram signals and performing normalization operation on the N electrocardiogram signals to generate N normalized signals, where N is a positive integer; a discrete cosine transform device connected to the normalization device for receiving the N normalized signals and performing discrete cosine operation to generate N discrete cosine signals; an absolute value and quantization device connected to the discrete cosine transform device for receiving N discrete cosine signals and performing absolute value operation and quantization operation to generate N quantized amplitude signals; a difference coding device connected to the absolute value and quantization device for receiving the N quantized amplitude signals and performing differential pulse code modulation (DPCM) on the N quantized amplitude signals to generate N difference signals; a first variable length coding device connected to the difference coding device for performing variable length coding operation on the N difference signals to generate a first data stream; a sign and difference device connected to the discrete cosine transform device for receiving the N discrete cosine signals and recoding signs of the N discrete cosine signals, so as to generate three sign signals; a second variable length coding device connected to the sign and difference device for performing variable length coding operation on the three sign signals to generate a second data stream; and a mixer connected to the first variable length coding device and the second variable length coding device for mixing the first data stream and the second data stream to generate a compressed electrocardiogram data stream. 
     In another aspect of the present invention, there is provided an electrocardiogram signal de-compression system includes: a parser device for receiving a compressed electrocardiogram data stream and analyzing the compressed electrocardiogram data stream, so as to generate a first data stream and a second data stream; a first variable length decoding device connected to the parser device for performing variable length decoding operation on the first data stream to generate N difference signals, where N is a positive integer; a difference decoding device connected to the first variable length decoding device for receiving the N difference signals and performing differential pulse code modulation (DPCM) operation on the N difference signals to generate N quantized amplitude signals; an inverse quantization device connected to the difference decoding device for receiving the N quantized amplitude signals and performing inverse quantization operation to generate inverse quantization signals of N discrete cosine signals; a second variable length decoding device connected to the parser device for performing variable length decoding operation on the second data stream to generate three sign and difference signals; a restored difference and sign prediction device connected to the second variable length decoding device for receiving the three sign and difference signals and performing restored difference and sign prediction operation to generate signs of the N discrete cosine signals; an inverse discrete cosine transform device connected to the inverse quantization device and the restored difference and sign prediction device for receiving the inverse quantization signals of the N discrete cosine signals and the signs of the N discrete cosine signals to generate the N discrete cosine signals, and performing inverse discrete cosine operation on the N discrete cosine signals so as to generate N normalized signals; and an inverse normalization device connected to the inverse discrete cosine transform device for receiving the N normalized signals and performing inverse normalization operation on the N normalized signals to generate N electrocardiogram signals. 
     Other objects, advantages, and novel features of the invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram illustrating the ECG signals; 
         FIG. 2  is a block diagram showing the ECG signal compression system in accordance with a preferred embodiment of the present invention; 
         FIG. 3  shows the data format of the compressed bit stream in accordance with the present invention; 
         FIG. 4  schematically illustrates the operation of the normalization device in accordance with the present invention; 
         FIG. 5(A)  schematically illustrates the ECG signals normalized to −1 to 1; 
         FIG. 5(B)  schematically illustrates the ECG signals normalized to 0 to 1; 
         FIG. 5(C)  schematically illustrates the ECG signals normalized to DCT-IV coefficient of −1 to 1; 
         FIG. 5(D)  schematically illustrates the ECG signals normalized to DCT-IV coefficient of 0 to 1; 
         FIG. 6  schematically illustrates the calculation result of applying input constant value 1 and N=64 into DCT-IV mathematics model; 
         FIG. 7  shows the pseudo code for applying input constant value 1 and N=64 into DCT-IV mathematics model; 
         FIG. 8(A)  and  FIG. 8(B)  respectively illustrate the N discrete cosine signals X[k] and the spectrum thereof in accordance with the present invention; 
         FIG. 9(A) ,  FIG. 9(B)  and  FIG. 9(C)  schematically illustrate the operation of the absolute value and quantization device; 
         FIG. 10  schematically illustrates the DCT-IV spectrum quantization value Q in accordance with the present invention; 
         FIG. 11(A)  and  FIG. 11(B)  schematically illustrate the operation of the difference coding device  240  in accordance with the present invention; 
         FIG. 12(A)  and  FIG. 12(B)  schematically illustrate the DCT-IV spectrum quantization value Q and the difference Diff of quantization values of the present invention, respectively; 
         FIG. 13  shows a difference table in accordance with the present invention; 
         FIG. 14  shows a Huffman code table in accordance with the present invention; 
         FIG. 15  schematically illustrates the total bit number of difference coding in accordance with the present invention; 
         FIG. 16(A)  and  FIG. 16(B)  schematically illustrate the operation of the sign and difference device in accordance with the present invention; 
         FIG. 17  shows another difference table in accordance with the present invention; 
         FIG. 18  shows another Huffman code in accordance with the present invention; 
         FIG. 19  schematically illustrates the difference table address for the difference bit number being 3; 
         FIG. 20  shows the bit number for sign compression flow in accordance with the present invention; 
         FIG. 21  is a block diagram of the ECG signal decompression system in accordance with a preferred embodiment of the present invention; 
         FIG. 22  schematically illustrates the compressed ECG data stream in accordance with the present invention; 
         FIG. 23  schematically illustrates Huffman decompression in accordance with the present invention; 
         FIG. 24  schematically illustrates the operation of the difference decoding device in accordance with the present invention; 
         FIG. 25  schematically illustrates the operation of the inverse quantization device in accordance with the present invention; 
         FIG. 26  schematically illustrates the operation of the restored difference and sign prediction device in accordance with the present invention; 
         FIG. 27  schematically illustrates the operation of the inverse discrete cosine transform device; 
         FIG. 28  schematically illustrates the operation of the inverse normalization device; and 
         FIG. 29 ,  FIG. 30  and  FIG. 31  schematically illustrate the results of testing each set of database with the measurement indexes. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       FIG. 2  is a block diagram showing the electrocardiogram (ECG) signal compression system  200  in accordance with a preferred embodiment of the present invention. The system  200  includes normalization device  210 , a discrete cosine transform (DCT) device  220 , an absolute value and quantization device  230 , a difference coding device  240 , a first variable length coding device  250 , a sign and difference device  260 , a second variable length coding device  270 , and a mixer  280 . 
     There are 64 samples of signals per frame inputted to the ECG signal compression system  200  of the present invention and, after compression, there are 67 compressed bit streams generated for output, each compressed bit stream being composed of Huffman coding and difference table address, wherein three of the compressed bit streams are provided for recording signs and the remaining 64 of the compressed bit streams are the result of the input signals after being transformed and compressed. The data format of the compressed bit stream is shown in  FIG. 3 . 
     The normalization device  219  receives N ECG signals for performing a normalization operation on the N ECG signals x(n), where N is a positive integer and, in this embodiment, N is 64. 
     The normalization device  210  first normalizes the 64 samples of input ECG signals for the purpose of controlling the dynamic range (i.e., the maximum and minimum value) of the coefficient after the discrete cosine transform device  220  perform a DCT-IV operation to be in a smaller range. If no normalization is done, the dynamic range of transformed coefficients will be very large, resulting in requiring more bits for representation. 
     There are two choices for normalization, one being normalized to −1 to 1 and the other one being normalized to 0 to 1. In the present invention, the normalization device  210  uses the scheme of being normalized to −1 to 1 due to that, after transformation, the present invention has a smaller dynamic range in comparison with the scheme of being normalized to 0 to 1. 
     According to the ECG signals in MIT-BIH database, the value is between 0 and 2048 and thus, if it is to be normalized to −1 to 1, the original signal has to be minus 1024 and then divided by 1024, as shown in  FIG. 4 .  FIG. 4  schematically illustrates the operation of the normalization device  210  in accordance with the present invention; that is, the N ECG signals are respectively minus 2 K−1  and then divided by 2 K−1  by the normalization device  210 , so as to generate the N normalized signals x(n), where K is the bit number of the N ECG signals. 
     The discrete cosine transform device  220  is connected to the normalization device  210  for receiving the N normalized signals so as to perform a discrete cosine transform operation thereby generating N discrete cosine transform signals X[k]. The discrete cosine transform device  220  is a DCT-IV device, wherein the N discrete cosine transform signals X[k] can be expressed as: 
                       X   ⁡     [   k   ]       =       ∑     n   =   0       N   -   1       ⁢           ⁢       x   ⁡     (   n   )       ×     cos   ⁡     (         (       2   ⁢   n     +   1     )     ⁢     (       2   ⁢   k     +   1     )     ⁢   π       4   ⁢   N       )             ,     n   =   0     ,   1   ,   …   ,     N   -   1     ,           (   1   )               
where x(n) represents the normalized signals.
 
     The N discrete cosine transform signals X[k] are also known as DCT-IV coefficient, wherein k is an index for coefficient X[k]. In the present invention, N is 64, i.e., 64-point DCT-IV coefficients being calculated, X[0] is known as DC value, and X[1] X[63] are known as AC value. 
     Taking the front 512 samples of ECG signals in number-100 data of MIT-BIH database as an example,  FIG. 5(A)  schematically illustrates the ECG signals normalized to −1 to 1,  FIG. 5(B)  schematically illustrates the ECG signals normalized to 0 to 1,  FIG. 5(C)  schematically illustrates the ECG signals normalized to DCT-IV coefficient of −1 to 1, and  FIG. 5(D)  schematically illustrates the ECG signals normalized to DCT-IV coefficient of 0 to 1. 
     From the dynamic ranges of  FIG. 5(C)  and  FIG. 5(D) , it is observed that the dynamic range normalized to −1 to 1 is smaller than the dynamic range normalized to 0 to 1. The coefficient of small dynamic range has the advantage in that, after subsequent spectrum transformation and quantization step, the quantization values have small difference and are concentrated, so as to have better compression effect. Therefore, the present invention adopts the normalization of −1 to 1. 
     From  FIG. 5(C)  and  FIG. 5(D) , it is observed that, after signals are transformed by DCT-IV, the value of DCT-IV coefficient is alternative between positive one and negative one. As shown in  FIG. 1 , ECG is composed of PQRST waveforms, and the above unique phenomenon usually occurs when the ECG is not QRS-complex waveform, due to that, when the input waveform is not QRS waveform, the magnitudes of signals are very close but violently swung (high frequency). Therefore, in order to explore and explain this phenomenon, it is assumed that the input signal is a constant value 1 which is applied into DCT-IV mathematics model, i.e., x(n)=1 being applied into equation (1), we have: 
     
       
         
           
             
               
                 
                   
                     
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     Equation (2) is equivalent to summing up 
             cos   ⁢       (         (       2   ⁢   n     +   1     )     ⁢     (       2   ⁢   k     +   1     )     ⁢   π       4   ⁢   N       )     .           
The result of summing up
 
             cos   ⁢     (         (       2   ⁢   n     +   1     )     ⁢     (       2   ⁢   k     +   1     )     ⁢   π       4   ⁢   N       )           
is shown in  FIG. 6 .  FIG. 6  schematically illustrates the calculation result of applying input constant value 1 and N=64 into DCT-IV mathematics model, which has the same feature of alternative positive and negative value as that in  FIG. 5(C)  and  FIG. 5(D) . This physical feature means that, when there is non-QRS-complex waveform occurred, signals will slightly and frequently swing. After signals are multiplied by the cosine function
 
             cos   ⁡     (         (       2   ⁢   n     +   1     )     ⁢     (       2   ⁢   k     +   1     )     ⁢   π       4   ⁢   N       )           
in DCT-IV mathematics model and summed up, the cosine function
 
             cos   ⁡     (         (       2   ⁢   n     +   1     )     ⁢     (       2   ⁢   k     +   1     )     ⁢   π       4   ⁢   N       )           
causes the phenomenon of having positive and negative signs alternatively occurred and this regularity helps in increasing the compression ratio.  FIG. 7  shows the pseudo code for applying input constant value 1 and N=64 into DCT-IV mathematics model.
 
     The absolute value and quantization device  230  is connected to the discrete cosine transform device  220  for receiving the N discrete cosine signals X[k] to execute absolute value and quantization operation, so as to generate N quantization amplitude signals. The absolute value and quantization device  230  has a first quantization step, denoted as step 1 , and a second quantization step, denoted as step 2 , for performing absolute value operations to the N discrete cosine signals to generate N absolute-value discrete cosine signal coefficients, and then performs quantization operations to N absolute-value discrete cosine signal coefficients based on the first quantization step and the second quantization step, so as to generate the N quantization amplitude signals. 
     The sign and difference device  260  records the sign of the DCT-IV coefficient, and the absolute value and quantization device  230  takes the absolute value of the coefficient. By observing the characteristics of spectrum,  FIG. 8 ) is obtained. 
       FIG. 8(A)  and  FIG. 8(B)  respectively illustrate the N discrete cosine signals X[k] and the spectrum thereof, i.e., DCT-IV coefficients and DCT_IV spectrum. From  FIG. 8(B) , it can be seen that, after taking absolute value of the coefficient, the spectrum energy of ECG is concentrated on low frequency while energy level of middle/high frequency is relatively low. In order to achieve low distortion rate, the subsequent quantization strategy adopts non-uniform quantization scheme, in which the quantization interval (Step) for middle/low frequency is relatively large and the first quantization step “step 1 ” is adopted, and the quantization interval (Step) for high frequency is relatively small and the second quantization step “step 2 ” is adopted. 
     Based on the DCT-IV spectrums of 48 sets of arrhythmic ECG signals in MIT_BIH database, the value domain for the 48 sets of DCT-IV spectrums is in the range of 0 to 40. Due to considering on the characteristics of spectrum, the present invention adopts non-uniform quantization. When DCT-IV spectrum index value is (0)-(39), it uses 10 bits to record spectrum quantization value Q and uses the first quantization step “step 1 ” to be 0.039, i.e., Q=10 bit, step 1 =0.039. When DCT-IV spectrum index value is (40)-(63), it uses 11 bits to record spectrum quantization value Q and uses the second quantization step “step 2 ” to be 0.02, i.e., Q=11 bit, step 2 =0.02.  FIG. 9(A) ,  FIG. 9(B)  and  FIG. 9(C)  schematically illustrate the operation of the absolute value and quantization device  230 , in which the DCT-IV spectrum value is divided by the quantization step (step 1 , step  2 ) and then the closet integer value is taken, so as to determine the spectrum quantization value Q by rounding up or down.  FIG. 10  schematically illustrates the DCT-IV spectrum quantization value Q in accordance with the present invention. 
     The difference coding device  240  is connected to the absolute value and quantization device  230  for receiving the N quantization amplitude signals, so as to perform a differential pulse code modulation (DPCM) operation to the N quantization amplitude signals thereby generating N difference signals. 
     After quantizing the DCT-IV spectrum values in non-uniform manner, the DCT-IV spectrum quantization values Q in  FIG. 10  are observed. Because the adjacent Q values are very close, it is suitable to use difference coding for compression. Such a method is a lossless compression and allows the compression ratio to increase. The method for recording the difference between the current quantization value and the previous quantization value is known as differential pulse code modulation (DPCM), i.e. Diff(i)=Q(i)−Q(i−1). However, as the difference between several Q values in front is relatively large, it may require more bits by using the method of taking difference between adjacent values. Therefore, the front two data are minus a fixed value (64, 16).  FIG. 11(A)  and  FIG. 11(B)  schematically illustrate the operation of the difference coding device  240 . As shown, we have:
 
Diff(0)= Q (0)−64,
 
Diff(1)= Q (1)−16,
 
Diff( i )= Q ( i )− Q ( i− 1),  i= 2 to 63.  (3)
 
       FIG. 12(A)  and  FIG. 12(B)  schematically illustrate the DCT-IV spectrum quantization value Q and the difference Diff of quantization values of the present invention, respectively, in which the number of bits can be effectively saved by using difference. By taking  FIG. 12(B)  as an example, the use of difference coding in  FIG. 12(B)  results in a covered range of −10 to 10, which is much smaller than the covered range of 0 to 70 of the quantization value in  FIG. 12(A) . Therefore, the use of difference Diff to substitute the original quantization value Q can effectively reduce the number of bits required. 
     The first variable length coding device  250  is connected to the difference coding device  240  for performing variable length coding operation to the N difference signals so as to generate a first data stream, wherein the first variable length coding device  250  performs Huffman coding to the N difference signals to generate the first data stream. 
       FIG. 13  shows a difference table in accordance with the present invention.  FIG. 14  shows a Huffman code table in accordance with the present invention. After determining the difference Diff, the first variable length coding device  250  depends on whether it is larger than 0 or smaller than 0, to calculate the address and difference bit number corresponding to the difference Diff in the difference table of  FIG. 13  and then to find out the Huffman code corresponding to the difference bit number in the Huffman code table. 
     Taking the front four spectrum quantization values Q(0)=70, Q(1)=26, Q(2)=15 and Q(3)=10 in  FIG. 12(A)  as an example, the differences can be represented as: Diff(0)=Q(0)−64, Diff(1)=Q(1)−16, Diff(2)=Q(2)−Q(1), and Diff(3)=Q(3)−Q(2), and thus Diff(0)=6, Diff(1)=10, Diff(2)=−11, and Diff(3)=−5. Then, the corresponding fields and addresses in the difference table of  FIG. 13  are calculated as follows:
 
Diff(0)=6=110(binary), difference bit number=3, address=110;
 
Diff(1)=10=1010(binary), difference bit number=4, address=1010;
 
Diff(2)=−11 inversed to 11=1011(binary) which becomes 0100 by taking 1&#39;s complement, difference bit number=4, address=0100;
 
Diff(3)=−5 inversed to 5=101(binary) which becomes 010 by taking 1&#39;s complement, difference bit number=3, address=010.
 
     Finally, the difference bit numbers are mapped to the Huffman codes in  FIG. 14  as follows:
 
Diff(0), difference bit number=3, Huffman code=01000;
 
Diff(1), difference bit number=2, Huffman code=011;
 
Diff(2), difference bit number=4, Huffman code=01010;
 
Diff(3), difference bit number=3, Huffman code=01000.
 
     The first variable length coding device  250  uses Huffman code+difference table address as the first data stream for output as follows:
 
01000 110 (1st), 011 10 (2nd), 01010 0100 (3rd), 01000 010 (4th), . . . .
 
       FIG. 15  schematically illustrates the total bit number of difference coding in accordance with the present invention. From  FIG. 15 , it is known that the possibility of difference being 0 is 43.28%, indicating that 43.28% of data can be compressed to 1 bit. Similarly, the possibility of difference being 1 is 32.03%, indicating that 32.03% of data can be compressed to 3 bits. Therefore, about 75% of data can be compressed to less than 3 bits. 
     The sign and difference device  260  is connected to the discrete cosine transform device  220  for receiving the N discrete cosine signals to record the signs and differences of the N discrete cosine signals, so as to generate three sign signals (FIRST, SECOND and THIRD), wherein the sign and difference device  260  modifies part of the signs of the N discrete cosine signals so as to generate three modified sign signals Diff_FIRST, Diff_SECOND and Diff_THIRD. 
     The characteristics of the aforementioned DCT-IV coefficient can be applied in compression with the use of unique sign regularity of ECG DCT-IV coefficient. Because DCT-IV coefficient is alternative between positive sign and negative sign, simplification can be used to only record part of the signs so as to achieve the effect of compression, without having to record all 64 signs. In the present invention, there are only 33 signs recorded, which have index values of (0)-(31) and index value of (63). Such a method can increase the compression ratio up to about 13.04%. These 33 data are further compressed. The sign and difference device  260  divides the 33 signs into three parts, each having 11 signs, which are denoted as FIRST, SECOND and THIRD. Subsequently, difference operation and Huffman coding are performed to further increase the compression efficiency, and the compression ratio can be further increased by about 5.76%. 
     FIRST represents sign data string with DCT-IV coefficient index value of 0-10, SECOND represents sign data string with index value of 11-21, and THIRD represents sign data string with index value of 63 and index value of 22-31, wherein the most significant bit of THIRD is the sign of the discrete cosine signal (X[63]) with index value of 63. However, in most cases, the phenomenon of having alternative positive sign and negative sign occurs as shown in  FIG. 5(C) , in which the sign of X[0] is 1, the sign of X[1] is 0, the sign of X[2] is 1, . . . , the sign of X[63] is 0, where 0 represents positive and 1 represents negative. 
     Therefore, the sign and difference device  260  subtracts a fixed value from or adds a fixed value to FIRST, SECOND and THIRD, described in the following. 
     In most cases, FIRST is −683, SECOND is 682 and THIRD is 682, expressed as follows:
 
FIRST=101010101012=−683, 0:positive, 1:negative;
 
SECOND=010101010102=682;
 
THIRD=010101010102=682.  (3)
 
Therefore, we have:
 
FIRST+683=Diff_FIRST;
 
SECOND−682=Diff_SECOND;
 
THIRD−682=Diff_THIRD.  (4)
 
     With a simple addition, the values of FIRST, SECOND and THIRD are controlled in a smaller dynamic range.  FIG. 16(A)  and  FIG. 16(B)  schematically illustrate the operation of the sign and difference device  260  in accordance with the present invention; i.e., for difference values Diff_FIRST, Diff_SECOND and Diff_THIRD, it calculates the difference table address and difference bit number based on whether the difference is larger than 0 or smaller than 0. As shown in  FIG. 16(B) , if the difference is larger than 0, the difference is the difference table address and the number of bits for representing the address is the difference bit number; if the difference is smaller than 0, the value has to be inversed to a positive one and then 1&#39;s complement thereof is taken to thus obtain a value equal to the difference table address, and the number of bits for representing the address is the difference bit number. 
     The second variable length coding device  270  is connected to the sign and difference device  260  for performing a variable length coding operation to the three sign and difference signals, so as to generate a second data stream, wherein the second variable length coding device  270  performs a Huffman coding to the three modified sign signals so as to generate the second data stream. 
       FIG. 17  shows another difference table in accordance with the present invention.  FIG. 18  shows another Huffman code in accordance with the present invention. The second variable length coding device  270  is able to determine the table address and difference bit number form the difference, corresponding to the difference table as shown in  FIG. 17 . Next, the occurrence probability of difference bit number is used to generate the Huffman code as shown in  FIG. 18 . Then, the difference bit number is represented by Huffman code. Finally, the second variable length coding device  270  generates the second data stream based on the Huffman code+difference table address. 
     Taking the field of the difference table with the difference bit number being 3 as an example, the difference table address 000 corresponds to a value of −7, address 001 corresponds to a value of −6, and so on. As shown in  FIG. 19 ,  FIG. 19  schematically illustrates the difference table address for the difference bit number being 3. 
     In case of the difference being positive, taking Diff_FIRST=5 as an example, 5 is expressed as 101 in binary code and the bit number of 101 is 3. By looking up  FIG. 17  and  FIG. 19 , it is known that the difference of 5 appears at the field with difference bit number being 3 and the address is 101. Then, the obtained difference bit number is encoded with the Huffman code table shown in  FIG. 18 , wherein difference bit number=3 corresponds to Huffman code of 1001110. Therefore, the final compressed bit stream is expressed as 1001110 101. 
     In case of the difference being negative, taking Diff_FIRST=−5 as an example, the negative difference value is first inversed to a positive one, and 5 is expressed as 101 in binary code. Then, the 1&#39;s complement of 101 is 010 and the bit number of 010 is 3. By looking up  FIG. 17  and  FIG. 19 , it is known that the difference of −5 appears at the field with difference bit number being 3 and the address is 101. Then, the obtained difference bit number is encoded with the Huffman code table shown in  FIG. 18 . Therefore, the final compressed bit stream is expressed as 1001110 010. 
     Based on the occurrence probability of difference bit number 0-11, the Huffman code table, as shown in  FIG. 18 , is manufactured. The use of Huffman code to replace the difference bit number can increase the coding efficiency. After calculating the difference and analyzing the result, the probability of having 0 for the difference after addition/subtraction is over 50%. That is, each of FIRST, SECOND and THIRD requires 11 bits for recording. After taking difference, the number of times of having 0 for the results of FIRST, SECOND and THIRD is more than ½ of the total number of times. Then, after performing Huffman coding, the original 11-bit data is compressed to require only one bit for recording.  FIG. 20  shows the bit number for sign compression flow in accordance with the present invention, wherein there is a probability of 56.8% to express 11-bit data by one bit, and there is a probability of 38% to use more bits than the original one, at most 15 bits, for expression. The use of difference and lossless Huffman can obtain effect in compression ratio. The recorded 33 DCT-IV coefficient signs are compressed to generate three compressed bit streams. 
     The mixer  280  is connected to the first variable length coding device  250  and the second variable length coding device  270  for mixing the first data stream and the second data stream, so as to generate a compressed ECG data stream. That is, after the compression flow, there are 67 compressed bit streams in total for output, wherein 3 of them are sign compressed bit streams and the remaining 64 of them are coefficient-converted compressed bit streams. 
       FIG. 21  is a block diagram of the ECG signal decompression system  2100  in accordance with a preferred embodiment of the present invention. The decompression system  2100  includes a parser device  2110 , a first variable length decoding device  2120 , a difference decoding device  2130 , an inverse quantization device  2140 , a second variable length decoding device  2150 , a restored difference and sign prediction device  2160 , an inverse discrete cosine transform device  2170 , and an inverse normalization device  2180 . 
     The decompression system can be divided into three parts. The first part relates to decompression of 3 sign compressed bit streams and decompression of the remaining 64 compressed bit streams. Then, the second part relates to how to restore the sign and DCT-IV coefficient. Finally, the third part performs inverse DCT-IV and inverse normalization to the restored DCT-IV coefficient, so as to obtain a reconstruction signal. 
     The parser device  2110  receives a compressed ECG data stream and analyzes the compressed ECG data stream, so as to generate a first data stream and a second data stream. 
       FIG. 22  schematically illustrates the compressed ECG data stream in accordance with the present invention. When the decompression system  2100  receives 67 compressed bit streams each time, it uses the Huffman code table of  FIG. 18  and the difference table of  FIG. 17  to resolve the sign difference for the front 3 compressed bit streams (second data stream). For the remaining 64 compressed bit streams (first data stream), the Huffman code table of  FIG. 14  and the difference table of  FIG. 13  are used to resolve the quantization difference. 
     The first variable length decoding device  2120  is connected to the parser device  2110  for performing a variable length decoding operation to the first data stream so as to generate N difference signals, where N is a positive integer. The first variable length decoding device  2120  performs Huffman coding operation to the first data stream so as to generate N difference signals, where N is 64 in the present invention. 
     Because Huffman coding has the feature of uniqueness, when receiving a series of compressed stream, the decoding end first uses Huffman coding and the Huffman code table of  FIG. 14  to find out the difference bit number and, at this moment, is aware of the number of bits occupied by the difference address following the Huffman code, thereby obtaining the difference via the difference table of  FIG. 13 . 
     Taking the decoding end receiving a sign compressed bit stream 01000 010xxx . . . as an example, by looking up the Huffman code table of  FIG. 14 , it can determine the difference bit number corresponding to the Huffman code 01000 to be 3, indicating that the next three bits (=010) following 01000 represent the difference table address. Therefore, from the difference table of  FIG. 13 , the filed with difference bit number=3 and difference table address=010, it can resolve a difference of −5. 
       FIG. 23  schematically illustrates Huffman decompression in accordance with the present invention. No matter for the sign compressed bit stream or the compressed bit stream of DCT-IV transform coefficient, the decompression method is illustrated in  FIG. 23 . Both of them have the same difference table, but each of them has its own Huffman table. Further, after obtaining the differences, the methods for restoring sign and spectrum quantization value are slightly different. 
     The difference decoding device  2130  is connected to the first variable length decoding device  2120  for receiving the N difference signals and performing a differential pulse code modulation (DPCM) operation to the N difference signals, so as to generate 63 quantization amplitude signals. 
     The decoding end receives the compressed bit stream of DCT-IV coefficient absolute value and decodes the corresponding differences, i.e., Diff(i), i=0-63. Then, similar to the aforementioned difference coding device  240 , addition/subtraction and difference coding are used to restore the spectrum quantization values (or 64 quantization amplitude signals).  FIG. 24  schematically illustrates the operation of the difference decoding device  2130  in accordance with the present invention. As shown, we have:
 
 Q (0)=Diff(0)+64,
 
 Q (1)=Diff(1)+16,
 
 Q ( i )=Diff( i )+ Q ( i− 1),  i= 2−63.  (5)
 
     The inverse quantization device  2140  is connected to the difference decoding device  2130  for receiving the N quantization amplitude signals and performing an inverse quantization operation, so as to generate inverse quantization signals of the N discrete cosine signals, wherein the inverse quantization device includes a first quantization step, denoted as step  1 , and a second quantization step, denoted as step  2 . The inverse quantization device performs an inverse quantization operation to the N quantization amplitude signals based on the first quantization step and the second quantization step, so as to generate inverse quantization signals of the N discrete cosine signals. 
       FIG. 25  schematically illustrates the operation of the inverse quantization device  2140  in accordance with the present invention. The operation of inverse quantization is to multiply the spectrum quantization value Q with a quantization step (step 1 , step 2 ) for restoring. However, the values after inverse quantization are all positive ones, but not the true DCT-IV coefficients. It is necessary to correspond the 64 signs restored and predicted by the second variable length decoding device  2150  and the restored difference and sign prediction device  2160  to each of the indexes, so as to obtain the restored DCT-IV coefficients. 
     The second variable length decoding device  2150  is connected to the parser device  2110  for performing a variable length decoding operation to the second data stream, so as to generate three sign and difference signals, wherein the second variable length decoding device  2150  performs a Huffman coding to the second data stream to generate the three modified sign signals. 
     Taking the decoding end receiving a sign compressed bit stream 1001110 010xxx . . . as an example, by looking up the Huffman table shown in  FIG. 18 , it is determined that the Huffman code 1001110 corresponds to a difference bit number=3, indicating that the next three bits (=010) following 1001110 represent a difference table address. Therefore, from the difference table of  FIG. 17 , the column of difference bit number=3 in  FIG. 18 , and difference table address=010 in  FIG. 19 , it is able to solve the difference=−5. 
     The restored difference and sign prediction device  2160  is connected to the second variable length decoding device  2150  for receiving difference signals of the three signs, so as to execute a restored difference and sign prediction operation thereby generating the signs of the N discrete cosine signals 
     The restored difference and sign prediction device  2160  subtracts a first constant from the first modified sign signal, and adds a second constant to the second and third modified sign signals, so as to generate first to third temporal signals. The restored difference and sign prediction device  2160  performs sign prediction to the first to third temporal signals, so as to generate the signs of the N discrete cosine signals. 
       FIG. 26  schematically illustrates the operation of the restored difference and sign prediction device  2160  in accordance with the present invention. The restored difference and sign prediction device  2160  receives the differences decoded from the sign compressed bit streams, i.e., Diff_FIRST, Diff_SECOND and Diff_THIRD. Then, as shown in  FIG. 26 , the restored difference and sign prediction device  2160  restores FIRST, SECOND and THIRD through addition and subtraction as follows:
 
FIRST=Diff_FIRST−683,
 
SECOND=Diff_SECOND+682,
 
THIRD=Diff_THIRD+682.  (6)
 
     After obtaining FIRST, SECOND and THIRD, the restored difference and sign prediction device  2160  restores 33 signs for DCT-IV coefficients X[0] to X[31] and X[63] of the original signal, while the remaining 31 signs are restored by prediction. 
     In the flow of compression, due to the alternation of positive sign and negative sign, only 33 signs are recorded. Therefore, in compression, the 32-th to 62-th signs are restored by prediction, which is based on the 63-th sign. 
     When X[63] is positive, i.e., sign(63)=0, X[62] is predicted to be negative, i.e., predict_sign(62)=1; X[61] is predicted to be positive, i.e., predict_sign(61)=0; similar prediction is applied until X[33] is positive, i.e., predict_sign(33)=0 and X[32] is negative, i.e., predict_sign(32)=1. 
     When X[63] is negative, i.e., sign(63)=1, X[62] is predicted to be positive, i.e., predict X[61] sign(62)=0; X[61] is predicted to be negative, i.e., predict_sign(61)=1; similar prediction is applied until X[33] is negative, i.e., predict_sign(33)=1 and X[32] is positive, i.e., predict_sign(32)=0. The flow of sign restoring is shown in  FIG. 26 . 
     The inverse discrete cosine transform device  2170  is connected to the inverse quantization device  2140  and the restored difference and sign prediction device  2160  for receiving the inverse quantization signals of the N discrete cosine signals and the signs of the N discrete cosine signals so as to generate the N discrete cosine signals X[k], and performing inverse discrete cosine operation to the N discrete cosine signals X[k] so as to generate N normalized signals X[n], wherein the inverse discrete cosine transform device  2170  is an type IV inverse discrete cosine transform (IDCT-IV) device. 
     After obtaining the restored DCT-IV coefficients, it then computes type IV inverse discrete cosine transformation, as shown in  FIG. 27 .  FIG. 27  schematically illustrates the operation of the inverse discrete cosine transform device  2170 . An IDCT-IV mathematics model of N points is defined as follows: 
                       x   ⁡     (   n   )       =       2   N     ⁢       ∑     k   =   0       N   -   1       ⁢       X   ⁡     [   k   ]       ×     cos   ⁡     (         (       2   ⁢   k     +   1     )     ⁢     (       2   ⁢   n     +   1     )     ⁢   π       4   ⁢   N       )               ,     k   =   0     ,   1   ,   …   ,     N   -   1     ,           (   7   )               
where X[n] represents N normalized signals and X[k] represents the N discrete cosine signals.
 
     The inverse normalization device  2180  is connected to the inverse discrete cosine transform device  2170  for receiving N normalized signals and performing inverse normalization operation to the N normalized signals so as to generate N ECG signals. 
       FIG. 28  schematically illustrates the operation of the inverse normalization device  2180 , wherein the N normalized signals are respectively multiplied by 2 K−1  and then added with 2 K−1 , so as to generate the N ECG signals, where K is the bit number of the N ECG signals. 
     In signal compression, some comparison indexes are provided as follows: 
     (1) Compression ratio: 
     
       
         
           
             
               
                 
                   
                     CR 
                     = 
                     
                       
                         Number 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         of 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         original 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         data 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         bits 
                       
                       
                         Number 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         of 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         compressed 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         bits 
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     (2) Percent rms difference: 
     
       
         
           
             
               
                 
                   
                     
                       PRD 
                       ⁡ 
                       
                         ( 
                         % 
                         ) 
                       
                     
                     = 
                     
                       100 
                       × 
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         X 
                                         s 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         n 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         X 
                                         r 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         n 
                                         ) 
                                       
                                     
                                   
                                   ] 
                                 
                                 2 
                               
                             
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   [ 
                                   
                                     
                                       X 
                                       s 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                   ] 
                                 
                                 2 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     (3) Quality score: 
     
       
         
           
             
               
                 
                   
                     QS 
                     = 
                     
                       CR 
                       PRD 
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     (4) Percent rms difference normalized: 
     
       
         
           
             
               
                 
                   
                     
                       PRDN 
                       ⁡ 
                       
                         ( 
                         % 
                         ) 
                       
                     
                     = 
                     
                       100 
                       × 
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         X 
                                         s 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         n 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         X 
                                         r 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         n 
                                         ) 
                                       
                                     
                                   
                                   ] 
                                 
                                 2 
                               
                             
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         X 
                                         s 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         n 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       X 
                                       _ 
                                     
                                   
                                   ] 
                                 
                                 2 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     (5) Root mean square: 
     
       
         
           
             
               
                 
                   
                     RMS 
                     = 
                     
                       
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               [ 
                               
                                 
                                   
                                     X 
                                     s 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     X 
                                     r 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                               ] 
                             
                             2 
                           
                         
                         N 
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     (6) Signal to noise ratio: 
                     SNR   =     10   ×     log   ⁡     (         ∑     n   =   0       N   -   1       ⁢           ⁢       [         X   s     ⁡     (   n   )       -     X   _       ]     2           ∑     n   =   0       N   -   1       ⁢           ⁢       [         X   s     ⁡     (   n   )       -       X   r     ⁡     (   n   )         ]     2         )           ;           (   13   )               
wherein X s  represents the original signal, X r  represents the constructed signal,  X  represents the averaged original signal, and N is the total number of original signals.
 
     The present invention performs analysis for three relatively important measurement indexes CR, PRD and QS as follows: 
     CR value is the compression ratio. According to expression (6), the numerator is in the original signal storage format that is 16-bit, and the denominator is the total bit number of the compressed signal, representative of the amount of data being compressed, a larger value indicating a smaller storage space. 
     PRD value is the power rate distortion representative of the degree of error between the constructed signal and the original, a lower value indicating a smaller distortion. 
     QS value represents the quality score, a higher score indicating a better compression efficiency. Because CR and PRD value will influence with each other, high CR value means high PRD value and low CR value means low PRD value. Therefore, since it is desired to have high CR value and low PRD value, the compression method of the compression must have a trade-off therebetween. QS value can directly reflect whether the compression method of a compression system is efficient or not. If the trade-off is excellent, the score is high. 
     For each index of the compression method, 48 sets of MIT-BIH arrhythmia database files are used as test signals. The results of testing each set of database with the measurement indexes are respectively illustrated in  FIG. 29 ,  FIG. 30  and  FIG. 31 . 
     In the presentation of all data, the 201-st set has the best CR value 6.40, and the worst CR value 4.29 appears at the 107-th set. The 201-st set has best PRD value 0.18, and the worst PRD value 0.21 appears at the 116-th set. For the QS value, the 201-st set has the best QS value 35.60, and the worst QS value 21.07 appears at the 116-th set. The detailed measurement index data is shown in Table 1. 
     The compression system of the present invention has a window size 100% identical to that in article 1 (SangJoon Lee; Jungkuk Kim; Myoungho Lee “A Real-Time ECG Data Compression and Transmission Algorithm for an e-Health Device”, Biomedical Engineering, IEEE Transactions on, vol. 58, no. 9, pp. 2448-2455, September 2011), which can conserve all DCT-IV coefficients and the input signal has a 16-bit storage format. The data is shown in Table 2. The present invention has a better CR value, a relatively lower PRD value, and a higher QS value, while the presentation of other indexes is also excellent. 
     Besides, in article 2 (Bendifallah, A.; Benzid, R.; Boulemden, M. “Improved ECG compression method using discrete cosine transform”, Electronics Letters, vol. 47, no. 2, pp. 87-89, January 2011), and article 3 (Alam, M. S.; Rahim, N. M. S. “Compression of ECG signal based on its deviation from a reference signal using discrete cosine transform”, Electrical and Computer Engineering 2008, International Conference, pp. 53-58, 20-22 Dec. 2008), the input uses 11-bit data format. For comparison, the original CR value is multiplied with 16/11 and asterisk (*) indicates the result that has been compressed to the same scale, 
     Although articles 2 and 3 have better compression ratio, the relatively larger PRD value will cause low QS value and thus the overall compression efficiency is degraded by 3 to 4 times. 
     The present invention makes use of the sign relation of DCT-IV coefficients and the characteristics of spectrum quantization to represent each data by recording the difference while retaining all high-frequency information, and further uses Huffman coding to increase compression efficiency. Different from the prior conversion coding, the present invention selects to retain high-frequency component so as to effectively reduce the rate of distortion. Further, the spectrum quantization values of DCT-IV are close in high-frequency region, which can facilitate in increasing the compression ratio. 
     The ECG signal compression system and decompression system of the present invention use 48 sets of arrhythmia data in MIT-BIH database as test signals. The MIT-BIH database has a sampling rate of 360 Hz and an A/D converting resolution of 11 bits. Test results for all 48 sets are CR=5.2, PRD=0.19, QS=29.93. In comparison with articles 1, 2 and 3, the compression method of the present invention is excellent in terms of QS value. QS is a measurement index involving CR value and PRD value. A high QS value indicates that an algorithm has good trade-off between CR value and PRD value, i.e., the compression method of the present invention has excellent representation. 
     
       
         
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                   
                 Measurement Index 
               
             
          
           
               
                   
                   
                 PRD 
                 PRDN  
                   
                   
                   
               
               
                 Data 
                 CR 
                 (%) 
                 (%) 
                 RMS  
                 SNR 
                 QS 
               
               
                   
               
             
          
           
               
                 100 
                 5.86 
                 0.18 
                 4.48 
                 1.73 
                 26.98 
                 32.61 
               
               
                 101 
                 5.69 
                 0.18 
                 3.39 
                 1.77 
                 29.40 
                 31.13 
               
               
                 102  
                 5052 
                 0.18 
                 4.64  
                 1.77 
                 26.67 
                 30.44 
               
               
                 103 
                 5.55 
                 0.18 
                 2.75 
                 1.77 
                 31.23 
                 30.76 
               
               
                 104 
                 5.16  
                 0.20 
                 3.84 
                 1.92 
                 28.32 
                 26.35 
               
               
                 105 
                 5.18 
                 0.18 
                 2.20 
                 1.78 
                 33.16 
                 28.57 
               
               
                 106 
                 5.10 
                 0.18 
                 2.48 
                 1.83 
                 32.11 
                 27.67 
               
               
                 107 
                 4.29 
                 0.18 
                 1.04 
                 1.78 
                 39.67 
                 23.87 
               
               
                 108 
                 5.37 
                 0.18 
                 3.01 
                 1.81 
                 30.44 
                 29.08 
               
               
                 109 
                 5.22 
                 0.18 
                 1.81 
                 1.81 
                 34.85 
                 28.40 
               
               
                 111 
                 5.53 
                 0.18 
                 3.57 
                 1.83 
                 28.95 
                 29.91 
               
               
                 112 
                 5.37  
                 0.20 
                 3.94 
                 1.76 
                 28.08 
                 26.21 
               
               
                 113 
                 5.09 
                 0.20 
                 2.45 
                 2.02 
                 32.22 
                 25.12 
               
               
                 114 
                 5.70 
                 0.19 
                 5.48 
                 1.88 
                 25.23 
                 30.16 
               
               
                 115 
                 5.38 
                 0.19  
                 2.44 
                 1.77 
                 32.27 
                 28.26 
               
               
                 116 
                 4.40 
                 0.21 
                 1.33 
                 1.77 
                 37.50 
                 21.07 
               
               
                 117 
                 5.31 
                 0.21 
                 3.68 
                 1.76 
                 28.69 
                 25.83 
               
               
                 118 
                 4.57 
                 0.21 
                 2.06 
                 1.76 
                 33.72 
                 22.20 
               
               
                 119 
                 4.86 
                 0.20  
                 1.64 
                 1.76  
                 35.69 
                 23.74 
               
               
                 121 
                 5.55 
                 0.20 
                 2.92 
                 1.76  
                 30.68 
                 27.23 
               
               
                 122 
                 4.80 
                 0.20 
                 2.40 
                 1.76 
                 32.39 
                 23.45 
               
               
                 123 
                 5.15 
                 0.20 
                 3.02 
                 1.76 
                 30.39 
                 25.93 
               
               
                 124 
                 5.27 
                 0.20 
                 1.90 
                 1.76 
                 34.40 
                 25.99 
               
               
                 200 
                 4.91 
                 0.19 
                 2.45 
                 1.86 
                 32.21 
                 26.51 
               
               
                 201 
                 6.40 
                 0.18 
                 4.60 
                 1.79  
                 26.74 
                 35.61 
               
               
                 202 
                 5.67 
                 0.18  
                 3.05 
                 1.82 
                 30.31 
                 30.99 
               
               
                 203 
                 4.65 
                 0.19 
                 1.92 
                 1.90 
                 34.34 
                 24.37 
               
               
                 205 
                 6.04 
                 0.18 
                 4.43 
                 1.74  
                 27.07 
                 33.39 
               
               
                 207 
                 5.52 
                 0.18 
                 2.59 
                 1.83  
                 31.75 
                 29.90 
               
               
                 208 
                 4.91 
                 0.18 
                 1.87 
                 1.81 
                 34.55 
                 27.08 
               
               
                 209 
                 4.92 
                 0.19 
                 3.49 
                 1.87  
                 29.13 
                 26.05 
               
               
                 210 
                 5.65 
                 0.18 
                 3.50 
                 1.83 
                 29.13 
                 30.75 
               
               
                 212 
                 4.66 
                 0.19 
                 2.82 
                 1.87  
                 30.98 
                 24.77 
               
               
                 213 
                 4.56 
                 0.18 
                 1.33 
                 1.79  
                 37.50 
                 25.18 
               
               
                 214 
                 5.13 
                 0.18 
                 1.93 
                 1.82  
                 34.28 
                 28.11 
               
               
                 215 
                 4.79 
                 0.18  
                 3.23 
                 1.82 
                 29.82 
                 26.20 
               
               
                 217 
                 4.68 
                 0.18 
                 1.49 
                 1.83 
                 36.57 
                 25.56 
               
               
                 219 
                 5.19 
                 0.19 
                 1.60 
                 1.77  
                 35.91 
                 26.84 
               
               
                 220 
                 5.19 
                 0.19 
                 2.74 
                 1.75  
                 31.23 
                 27.24 
               
               
                 221 
                 5.47 
                 0.18 
                 3.04 
                 1.83 
                 30.34 
                 29.68 
               
               
                 222 
                 5.51 
                 0.19 
                 5.08 
                 1.89 
                 25.88 
                 29.01 
               
               
                 223 
                 5.36 
                 0.19 
                 2.17 
                 1.76 
                 33.29 
                 28.12 
               
               
                 228 
                 5.21 
                 0.19 
                 2.67 
                 1.85 
                 31.46 
                 28.10 
               
               
                 230 
                 5.53 
                 0.18  
                 2.52 
                 1.78 
                 31.98 
                 30.75 
               
               
                 231 
                 5.78 
                 0.18 
                 3.31  
                 1.80 
                 29.61 
                 31.94 
               
               
                 232 
                 5.93 
                 0.18  
                 5.47 
                 1.80 
                 25.25 
                 32.66 
               
               
                 233 
                 4.92 
                 0.18 
                 1.64 
                 1.78 
                 35.70 
                 27.57 
               
               
                 234 
                 5.54 
                 0.18 
                 2.64 
                 1.78 
                 31.57 
                 30.94 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                 Invention 
                 Article 1 
                 Article 2 
                 Article 3 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 CR 
                 5.25 
                 5.19 
                  6.11* 
                  5.82* 
               
               
                   
                 PRD(%) 
                 0.19 
                 0.23 
                 0.78 
                 0.8  
               
               
                   
                 PRDN(%) 
                 2.88 
                 3.56 
                 — 
                 — 
               
               
                   
                 RMS 
                 1.81 
                 2.22 
                 — 
                 — 
               
               
                   
                 SNR 
                 31.45 
                 29.67 
                 — 
                 — 
               
               
                   
                 QS 
                 29.93 
                 22.56 
                 7.83 
                 7.27 
               
               
                   
                   
               
             
          
         
       
     
     Although the present invention has been explained in relation to its preferred embodiment, it is to be understood that many other possible modifications and variations can be made without departing from the spirit and scope of the invention as hereinafter claimed.