GB1580178A - Digital measurement - Google Patents

Description

(54) IMPROVEMENTS IN OR RELATING TO DIGITAL MEASUREMENT (71) We, THE POST OFFICE, a British corporation established by Statute, of 23 Howland Street, London WIP 6HQ, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement:- This invention relates to digital measurement. In particular, but not exclusively, it relates to the digital measurement of electrical potentials.

It is known that in the conversion of electical potential measurements to digital forms, the digital values obtained each represent a range of possible electrical potentials, rather than any specific value.

The resulting uncertainty in the digital measurement can be important in certain applications, such as cable testing or medical electronics, where a large range of possible values in some cases exceeding the ratio 1:1010 can be met. Thermal instability of apparatus, noise in the apparatus and problems of component tolerances can prevent the accuracy of measurement being easily increased, and, in any case, it is advantageous to be able to improve the resolution of existing apparatus for making digital measurement.

According to one aspect of the present invention there is provided a method of digital measurement comprising adding to a first quantity a second varying quantity to produce a third quantity, sampling said third quantity repetitively to generate a plurality of samples, said sampling being carried out asynchronously with respect to any periodicity of said second quantity, digitally encoding the values of the samples, and averaging a plurality, greater than a predetermined number, of the digitally encoded values so that the average is more accurate digital measurement of the first quantity than if the second quantity were not added to it.

The second quantity may have a zero mean and a probability distribution which is symmetrical about the mean.

Said second quantity may have a Gaussian probability distribution or a rectangular probability distribution. The sampling rate may be periodic.

The method may include applying a correction to the average value according to a known parameter of the second quantity. The first quantity may be a Fourier transform.

According to another aspect of the invention there is provided apparatus for digital measurement of a first quantity comprising generator means for generating a second varying quantity, addition means for adding said first and second quantities, sampling means for sampling repetitively the sum of said first and second quantities such that the sampling in asynchronous with respect to any periodicity of the second quantity, means for digitally encoding ~ the sampled values, averaging means for averaging a plurality greater than a predetermined number of the digital sample values to produce an average value which is a more accurate digital measurement of the first quantity than if said second quantity were not added to it.

The second quantity may have a zero mean and a probability distribution which is symmetrical about the mean.

The invention will be described now by way of example only with reference to the accompanying drawings. In the drawings: Figure 1 is a schematic block diagram of apparatus for digital measurement according to an embodiment of the invention; Figure 2 is a probability diagram to illustrate the operation of the apparatus shown in Figure 1; Figure 3 is an enlarged portion of Figure 2, and Figure 4, 5 and 6 show fast Fourier transforms of an impulse illustrating the use of the method of the invention.

Referring now to Figure 1, an input port I is connected to sampling means 5 by way of adding means 3. The adding means 3 is also connected to a white noise generating means 4. Sampling means 5 is connected to digital encoding means 6, which digital encoding means 6 is in turn connected to a storage means 7. The storage means 7 is connected to averaging means 8 which averaging means 8 is in turn connected to an output port 2.

In operation the first electric potential, which is to be represented digitally is applied to the input port 1. The white noise generating means 4 produces a second electrical potential which has a white noise amplitude characteristic. The first and the second electrical potentials are added in the adding means 3. The sum of the signals is sampled periodically by the sampling means 5, and the digital values of the samples are produced by the digital encoding means 6. The digital values are stored in the storage means 7, and when a predetermined number have been stored they are averaged in the averaging means 8.

The average value is then passed to the output port 2 where it can be used by further apparatus, not shown, as the digital measurement of the first electrical potential. Provided that the predetermined number is sufficiently large the digital measurement output from the port 2 will be more precise than a digital measurement of the first electrical potential made by the same apparatus but where the second electrical potential has not been added to the first electrical potential. It will of course be appreciated that the first electrical potential must remain constant during a sufficiently long time for the sampling means 5 to produce a number of samples greater than or equal to the predetermined number.

It is important to appreciate the conditions under which the addition of the second electrical potential and the process of averaging can produce an improvement in the accuracy of the digital measurement.

These conditions can be explained by reference to Figure 2.

The second electrical potential which is generated by the white noise generating means, referenced 4 in Figure 1, has a Gaussian potential probability distribution.

This is shown by the dashed curve 9 in Figure 2. The Gaussian distribution has a zero mean and the distribution is symmetrical about the mean. Line 11 in Figure 2 represents the first electrical potential V, applied to the input port 1 and it will be apparent that curve 10 which has been obtained by adding the value V to the value of every point on the curve 9, will be the potential probability curve for the potential at the output from the adding means 3 of Figure 1. Dashed lines 12 in Figure 2 represent the divisions between potential ranges represented by the same digital word, each potential range being of the width as shown bP.

The action of the sampling means 5 and the encoding means 6 is to produce a number of digital measurments of the potential at the input to the sampling means. The number of times that each particular digital value occurs, over a long period of time, approaches the mean height of the curve 10 in each of the potential ranges AP between the dashed lines 12.

Referring now to Figure 3, which is an enlarged version of a portion of Figure 2, and in which the same reference numerals have been used, where appropriate, the mean values of the curve 10 have been shown in each potential range by the dashed lines 13. When the numbers representing the digital measurement are passed to the averaging means 8 in which the arithmetical mean of a predetermined number of measurements is computed, the averaging process will tend to remove both the fluctuations of the white noise deliberately introduced in the processing and also the uncertainties inherent in the digitising process. Referring again to Figure 3, it will be seen that, because the mean potential V (reference 11) is towards the lefthand side of the range 15, the Gaussian curve 10 is unequally distributed in the adjacent ranges 14 and 16. The weighted mean of the mid-range values, which is produced in the averaging process, will give a value nearer to V than the mid-range value of the range 15. The mid-range value of the range 15 is of course the value that would be obtained if the addition of white noise and the averaging process has been omitted.

Although the apparatus described in the example is shown as having a separate adding means and white noise generating means, it will be apparent to those skilled in the art that an alternative arrangement would be to have an inherent noisy component, or components, in the part of the apparatus preceding the sampling means 5 of Figure 1.

It will also be apparent to those skilled in the art that although a white noise electric potential generator has been used in the example, for convenience, many other waveforms, will work in a similar manner.

In any particular case, a knowledge of the statistical parameters of the noise waveform will enable a correction to be applied to the calculated average to compensate for, for example, a non-zero mean or an asymmetrical probability distribution. It will also be apparent that there must be asynchronism between the sampling means and any periodicity in the noise potential. In the example, this is ensured by having a white noise electrical potential with a Gaussian probability distribution, which because of its random nature, has no periodicity. An alternative method of ensuring asynchronism would be to use a periodic noise potential, for example a sinusoidal fluctuation, and to use a random or pseudo-random sampling interval.

One application of method described in this Specification is to the improvement of the accuracy of fast Fourier transforms.

One such application is illustrated in Figures 4, 5 and 6. Each of these Figures shows the fast Fourier transform of an impulse from the same impulse generator.

A Tektronics digital processing oscilloscope type WP1221 was used to produces the original transform shown in Figure 4. In this case the digital measurements of the potentals were made without using the method of the invention.

In Figure 5 there is shown the same Fourier transform as in Figure 4, but in which the method described in this Specification has been used, with averaging over 32 samples.

Figure 6 is similar to Figure 5 except that the averaging is over 128 samples. It is estimated that the effective dynamic ranges shown in each of the Figures 4, 5 and 6 are respectively 45dB, 50dB and 58dB.

In any particular application of the present method it will be necessary to determine, from the statistical parameters of the system, the precise number of samples which must be averaged in order to achieve any required degree of accuracy.

Although the example described in this Specification relates to the measurement of electrical potentials, and the method is particularly suitable for such applications, it will be appreciated that the method is of much more general application. In particular a non-electrical application might be the measurement of the intensity of a light beam, where the noise added is also a light beam. It will usually be found that the digital numbers are stored in an electrical form, such as in an electronic computer, but there is no reason why this must be the case.

A further application of the present method might be to the measurement of a quantity by a warning type device. In strip mills and other plants where there is a flat product, it is common practice to use a thickness monitoring gauge which gives a warning when the thickness of the product is outside the range of acceptable values.

Using the present method such a 3-stage output could measure the thickness of the sheet, if the white noise input was sufficient to cause the combined signal to exceed the range sufficiently frequently. An additional warning device set with a narrower range of operation is required and the thickness is varied randomly within the specification range but outside the range of the additional device. The average thickness would then be estimated and this information used to apply corrections before the product is outside its desired specification.

It will be appreciated of course that a noise waveform could be generated by the addition of 2 or more other waveforms; there is no reason why these 2 or more other waveforms should not be added separately to the quantity to be measured.

WHAT WE CLAIM IS: 1. A method of digital measurement comprising adding to a first quantity a second varying quantity to produce a third quantity, sampling said third quantity repetitively to generate a plurality of samples, said sampling being carried out asynchronously with respect to any periodicity of said second quantity, digitally encoding the values of the samples, and averaging a plurality, greater than a predetermined number, of the digitally encoded values so that the average is a more accurate digital measurement of the first quantity than if the second quantity were not added to it.

2. A method as claimed in claim 1 wherein said second quantity has a zero mean and a probability distribution which is symmetrical about the mean.

3. A method as claimed in claim 2, wherein said second quantity has a Gaussian probability distribution.

4. A method as claimed in any preceding claim where the sampling rate is periodic.

5. A method as claimed in any preceding claim, including applying a correction to the average value according to a known parameter of the second quantity.

6. A method as claimed in any preceding claim, wherein the first quantity is a fast Fourier transform.

7. Apparatus for digital measurement of a first quantity comprising generator means for generating a second varying quantity, addition means for said first and second quantities, sampling means for sampling repetitively the sum of said first and second quantities such that the sampling is asynochronous with respect to any periodicity of the second quantity, means for digitally encoding the sampled values, averaging means for averaging a plurality greater than a predetermined number, of the digital sample values to produce an average value which is a more accurate digital measurement of the first quantity

**WARNING** end of DESC field may overlap start of CLMS **.

Claims (10)

**WARNING** start of CLMS field may overlap end of DESC **. sampling means and any periodicity in the noise potential. In the example, this is ensured by having a white noise electrical potential with a Gaussian probability distribution, which because of its random nature, has no periodicity. An alternative method of ensuring asynchronism would be to use a periodic noise potential, for example a sinusoidal fluctuation, and to use a random or pseudo-random sampling interval. One application of method described in this Specification is to the improvement of the accuracy of fast Fourier transforms. One such application is illustrated in Figures 4, 5 and 6. Each of these Figures shows the fast Fourier transform of an impulse from the same impulse generator. A Tektronics digital processing oscilloscope type WP1221 was used to produces the original transform shown in Figure 4. In this case the digital measurements of the potentals were made without using the method of the invention. In Figure 5 there is shown the same Fourier transform as in Figure 4, but in which the method described in this Specification has been used, with averaging over 32 samples. Figure 6 is similar to Figure 5 except that the averaging is over 128 samples. It is estimated that the effective dynamic ranges shown in each of the Figures 4, 5 and 6 are respectively 45dB, 50dB and 58dB. In any particular application of the present method it will be necessary to determine, from the statistical parameters of the system, the precise number of samples which must be averaged in order to achieve any required degree of accuracy. Although the example described in this Specification relates to the measurement of electrical potentials, and the method is particularly suitable for such applications, it will be appreciated that the method is of much more general application. In particular a non-electrical application might be the measurement of the intensity of a light beam, where the noise added is also a light beam. It will usually be found that the digital numbers are stored in an electrical form, such as in an electronic computer, but there is no reason why this must be the case. A further application of the present method might be to the measurement of a quantity by a warning type device. In strip mills and other plants where there is a flat product, it is common practice to use a thickness monitoring gauge which gives a warning when the thickness of the product is outside the range of acceptable values. Using the present method such a 3-stage output could measure the thickness of the sheet, if the white noise input was sufficient to cause the combined signal to exceed the range sufficiently frequently. An additional warning device set with a narrower range of operation is required and the thickness is varied randomly within the specification range but outside the range of the additional device. The average thickness would then be estimated and this information used to apply corrections before the product is outside its desired specification. It will be appreciated of course that a noise waveform could be generated by the addition of 2 or more other waveforms; there is no reason why these 2 or more other waveforms should not be added separately to the quantity to be measured. WHAT WE CLAIM IS:

1. A method of digital measurement comprising adding to a first quantity a second varying quantity to produce a third quantity, sampling said third quantity repetitively to generate a plurality of samples, said sampling being carried out asynchronously with respect to any periodicity of said second quantity, digitally encoding the values of the samples, and averaging a plurality, greater than a predetermined number, of the digitally encoded values so that the average is a more accurate digital measurement of the first quantity than if the second quantity were not added to it.

2. A method as claimed in claim 1 wherein said second quantity has a zero mean and a probability distribution which is symmetrical about the mean.

3. A method as claimed in claim 2, wherein said second quantity has a Gaussian probability distribution.

4. A method as claimed in any preceding claim where the sampling rate is periodic.

5. A method as claimed in any preceding claim, including applying a correction to the average value according to a known parameter of the second quantity.

6. A method as claimed in any preceding claim, wherein the first quantity is a fast Fourier transform.

7. Apparatus for digital measurement of a first quantity comprising generator means for generating a second varying quantity, addition means for said first and second quantities, sampling means for sampling repetitively the sum of said first and second quantities such that the sampling is asynochronous with respect to any periodicity of the second quantity, means for digitally encoding the sampled values, averaging means for averaging a plurality greater than a predetermined number, of the digital sample values to produce an average value which is a more accurate digital measurement of the first quantity

than if said second quantity were not added to it.

8. Apparatus as claimed in claim 8, wherein said second quantity has a zero mean and a probability distribution which is symmetrical about said mean.

9. A method of digital measurement substantially as hereinbefore described.

10. Apparatus for digital measurement substantially as hereinbefore described with reference to and as shown in the accompanying drawings.