Gain determination for correlation processes

The present invention relates generally to systems used for computing the correlation between two signals and, more particularly, to methods of setting the gain of amplifiers used in such systems.

Digital transmission systems for communication usually include links in which many slower data streams are multiplexed together onto a single higher speed link. This higher speed link may be implemented by an optical transmission system. Such systems can be end-to-end links, or networks of optical links, with switching elements. Testing and verifying the operation of switching elements of such an optical network can pose problems, particularly because the data rates are often very high.

It is known that connectivity through a network can be guaranteed by network layer protocols such as TCP/IP, which can request retransmission if some data does not arrive. At the physical data transfer level, path trace bytes can be inserted and checked to ensure that a frame of data is routed correctly. However, such methods require decoding the data stream, which usually only takes place at a terminal at the end of the path through the optical network.

With a view to performing connection verification in a non-intrusive manner at an intermediate switching element, developments have been made in the field of testing using pattern matching. For example, as disclosed in U.S. Pat. No. 6,005,695 issued to Roberts, assigned to the assignee of the present invention and incorporated by reference herein, pattern matching can be carried out by a correlation process involving the low frequency components of an input signal and a switched signal. Since the connection map being applied by the switching element is known, it is a simple matter to determine the expected result (i.e., low or high) of the correlation process. By performing a comparison of the measured and expected correlation values, one can assess whether the switching element is operating properly or is malfunctioning.

It should therefore be apparent that obtaining a reliable correlation value from the correlation process is essential to making a correct decision as to whether or not the switching element is operating correctly. Since the input signal and the switched signal often have different signal levels, for example due to losses suffered within the switching element, it is important to provide appropriate amplification or attenuation (i.e., “level setting”) prior to computing the correlation value. One way of providing level setting relies on a pair of programmable-gain amplifiers, one on the input signal side and another one on the switched signal side. A significant challenge lies in appropriately setting the gains of the two amplifiers such that the ensuing correlation results are reliable.

It has been found that when clipping occurs at least part of the time, the correlation result obtained for a pair of truly correlated signals remains virtually unaffected, while there is actually a beneficial effect on the correlation result obtained for a pair of truly uncorrelated signals. Accordingly, the present invention provides for each signal to be amplified to such an extent that the amplified version of the signal will be clipped by a subsequent analog-to-digital converter for a desired percentage of the time, on average. A correlation value is then computed in the digital domain based on the clipped signals. To determine the amplifier gain needed to attain the desired amount of clipping, the present invention capitalizes on the availability of power measurements taken from the signal before it was amplified. In this way, reliance on feedback from the amplifier output is not required, thus simplifying the gain computation process.

Accordingly, the invention may be summarized broadly as a method of setting the level of an analog signal supplied to an electronic device having a maximum input level, including computing a gain which, when applied to the analog signal, causes the resulting amplified signal to exceed the maximum input level for a percentage of time which is greater than zero, and applying the gain to the analog signal.

The invention may also be broadly summarized as a combination which includes an electronic device having an input terminal and characterized by a maximum input level, and an amplifier connected to the input terminal of the electronic device, for applying a gain to an analog input signal, the gain being selected such that the percentage of time during which the signal supplied to the electronic device exceeds the maximum input level is greater than zero.

The invention may also be broadly summarized as a method of jointly processing a first signal and a second signal, including applying a first gain to the first signal and applying a second gain to the second signal, thereby to produce first and second amplified signals, respectively; limiting the amplitude of the first amplified signal to within a first fixed range and limiting the amplitude of the second amplified signal to within a second fixed range; digitally correlating the amplitude-limited signals; and controlling the first gain so as to cause the first amplified signal to fall outside the first fixed range during a first percentage of time that is greater than zero and controlling the second gain so as to cause the second amplified signal to fall outside the second fixed range during a second percentage of time that is greater than zero.

The invention may further be broadly summarized as a system for processing a pair of analog signals, including a first unit for applying a gain to each signal; a second unit for limiting the amplitude of each amplified signal to within a maximum range; a third unit for digitally correlating the amplitude-limited signals; and a fourth unit for controlling the gain applied to each signal so as to cause the corresponding amplified signal to fall outside the maximum range during a percentage of the time that is greater than zero.

In addition, the invention may be broadly summarized as a correlation engine, including a first analog-to-digital converter (ADC) having a fixed input range, a first programmable-gain amplifier connected to an input of the first ADC, a second ADC having a fixed input range, a second programmable-gain amplifier connected to an input of the second ADC, a correlator connected to the first and second ADCs, and a control element connected to the first and second amplifiers, for setting the gain of the first and second amplifiers to such a value that the average percentage of time during which the signal amplified by the each amplifier falls outside the input range of the respective ADC is greater than zero.

The invention may also be broadly summarized as computer-readable media tangibly embodying a program of instructions executable by a computer to perform a method of computing a gain of an amplifier used for amplifying an analog signal to be fed to an electronic device having a maximum input level V MAX , wherein the analog signal is the result of low-pass filtering an F C -bps bit stream to F B hertz, the method including continuously reading a mean level V AVG of the analog signal and computing the gain as substantially equal to the quotient of (V MAX ×V AVG ×(2 F LP ) ½ ) and (β×(R CLK ) ½ ), where β is chosen such that the value of the complementary error function (erfc) at β corresponds to a desired probability of clipping.

These and other aspects and features of the present invention will now become apparent to those of ordinary skill in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram of an optical switching element that uses correlation processes to verify connections through the switching element;

FIG. 2 is a block diagram of the functional elements within a correlation unit in the switching element of FIG. 1;

FIG. 3A shows the effect of controlled clipping of two signals on the correlation result obtained when the two signals are correlated; and

FIG. 3B shows the effect of controlled clipping of two signals on the correlation result obtained when the two signals are uncorrelated.

With reference to FIG. 1, there is shown an optical switching element, comprising a switching unit 102 and a connection verification unit 104 . A plurality of input optical fibers 106 carry respective wavelength-division-multiplexed (WDM) input signals to the switching unit 102 and a plurality of output optical fibers 108 carry respective WDM switched signals out of the switching unit 102 . The single-wavelength signal occupying a given wavelength could be a high-speed digital optical signal (for example a 10 gigabit-per-second non-return-to-zero optical pulse stream) with a clock rate denoted F C .

The switching unit 102 performs switching of the single-wavelength signals occupying individual wavelengths on each of the input WDM fibers 106 . The type of switching performed by the switching unit 102 may preserve the wavelengths of the individual signals being switched. In some embodiments, the switching unit 102 may also allow a change in wavelength to take place, thus permitting any single-wavelength signal on any input optical fiber 106 to appear on any wavelength and on any of the output optical fibers 108 . An example of a suitable switching unit 102 is described in U.S. patent application Ser. #09/511,065 to Graves et al., entitled “Switch for Optical Signals”, filed on Feb. 23, 2000, assigned to the assignee of the present invention and incorporated by reference herein.

An optical tap splitter 110 X is connected in the path of each input optical fiber 106 and allows a portion of the respective WDM input signal to be fed to the connection verification unit 104 . Similarly, an optical tap splitter 110 Y is connected in the path of each output optical fiber 108 and allows a portion of the respective WDM switched signal to be fed to the connection verification unit 104 .

In the connection verification unit 104 , the tapped WDM input signal received from each tap splitter 110 X is fed to a respective optical demultiplexer 112 X (only one of which is shown). Each demultiplexer can be of standard design and, as such, the optical signal emerging at each output of the demultiplexer associated with a particular input optical fiber is a distinct one of the plurality of single-wavelength optical signals travelling on that fiber, although at a lower intensity due to the presence of the corresponding splitter.

Considering the demultiplexer 112 X, each of its outputs is connected to a respective one of a plurality of photodiodes 114 X (only one of which is shown). Each photodiode 114 X is arranged to convert incoming photons into an electrical potential at its output and could be a PIN diode, for example. The output of the photodiode 114 X will be a wideband analog voltage signal representing a digital optical signal with a clock rate (already denoted F C ). However, the connection verification unit 104 may operate in a frequency range limited by several tens of MHz. To avoid aliasing problems during sampling, a suitable anti-alias filter 116 X is connected to the output of the photodiode 114 X. The signal at the output of the anti-alias filter 116 X, denoted X(t), is supplied to a correlation unit 120 .

Also connected to the output of the photodiode 114 X is an averaging unit 118 X. The averaging unit 118 X estimates the mean level (i.e., the DC voltage) of the signal at the output of the photodiode 114 X. Since the mean level of the voltage signal at the output of the photodiode 114 X is directly related to the mean optical intensity impinging on the photodiode 114 X, the output of the averaging unit 118 X is in fact an estimate of the optical intensity of the corresponding single-wavelength signal being admitted by the demultiplexer 112 X. The mean intensity estimate produced by the averaging unit 118 X, denoted A X , is supplied to the correlation unit 120 and to a controller 130 . If A X is provided in digital form, the connection between the averaging unit 118 X, the correlation unit 120 and the controller 130 could be established via a data bus.

Having described an input signal “arm” of the connection verification unit 104 for a particular output of a particular demultiplexer 112 X, an analogous structure is provided in a corresponding switched signal “arm”. Specifically, each tapped WDM switched signal is fed to a respective one of a plurality of optical demultiplexers 112 Y (only one of which is shown). Each output of the demultiplexer 112 Y is connected to a respective one of a plurality of photodiodes 114 Y (only one of which is shown). The photodiode 114 Y is connected to an anti-alias filter 116 Y having a suitable bandwidth. As with the anti-alias filter 116 X, the signal at the output of the anti-alias filter 116 Y, denoted Y(t), is supplied to the correlation unit 120 . An averaging unit 118 Y also receives the voltage signal at the output of the photodiode 114 Y. The mean intensity estimate produced by the averaging unit 118 Y, denoted A Y , is supplied both to the correlation unit 120 and to the controller 130 .

The inputs of the correlation unit 120 therefore include the mean intensity estimates A X and A Y supplied by the averaging units 118 X and 118 Y, as well as the low-pass filtered analog signals X(t) and Y(t) supplied by the anti-alias filters 116 X and 116 Y. The output of the correlation unit 120 at sample time “m” is a correlation value, denoted R O (m) , which is supplied to the controller 130 . More details regarding the structure and operation of the correlation unit 120 shall be given later on.

For its part, the controller 130 accepts the correlation value R O (m) from the correlation unit 120 , as well as the mean intensity estimates A X and A Y from the averaging units 118 X and 118 Y. Based on these values, on the coordinates (input optical fiber and wavelength) of the single-wavelength input signal entering the input signal arm, on the coordinates (output optical fiber and wavelength) of the single-wavelength switched signal entering the switched signal arm, and on the connection map being applied by the switching unit 102 , the controller 130 makes a decision as to whether the connection involving the two corresponding single-wavelength signals is valid. Access to the connection map may be provided via a fabric control unit (not shown) that is commonly used to control the switching unit 102 .

For example, consider the p th wavelength on the q th input optical fiber, and the p th wavelength on the Q th output optical fiber. The connection map will indicate whether a connection is supposed to exist between these two signals. If a connection is indeed supposed to exist, then the ideal value of R O (m) will be high (close to 1) and if not, the ideal value of R O (m) will be low (close to 0). By comparing the value of R O (m) received from the correlation unit 120 , the controller 130 can decide to what degree the computed value of R O (m) matches its ideal value. If there is a match, then the switching unit 102 is deemed to be functioning properly for this particular combination of fibers and wavelengths. Conversely, if there is no match, then the switching unit 102 is deemed to have malfunctioned for this particular combination.

The correlation unit 120 is now described in greater detail with additional reference to FIG. 2 . Specifically, along an input signal path, there is provided a programmable-gain amplifier 122 X, which accepts the low-pass filtered analog input signal X(t) from the anti-alias filter 116 X. The programmable-gain amplifier 122 X has a gain, denoted G X , which is controllable by a gain control functional element 124 X. The gain G X of the programmable-gain amplifier 122 X can be defined as the ratio of the level of the amplified analog signal (denoted X′ (t)) to the level of the low-pass filtered analog input signal X(t).

Based on the mean intensity estimate A X output by the averaging unit 118 X, the gain control functional element 124 X computes the gain G X to be applied by the programmable-gain amplifier 122 X. For reasons that will be explained later on in connection with FIGS. 3A and 3B, computation of G X need not rely on information about the amplified analog signal X′ (t), which affords a considerable simplification of the gain control loop as compared to traditional level setting approaches.

The amplified analog signal X′ (t) is sampled and quantized by an analog-to-digital converter (ADC) 126 X. The ADC 126 X limits the amplitude of X′ (t) to an input range that is bound by a minimum input level and a maximum input level. The output of the ADC 126 X is a digital sample stream, denoted X(n), which is fed to a first input of a digital correlation engine 128 .

Similarly, in a switched signal “arm” of the correlation unit 120 , there is provided a programmable-gain amplifier 122 Y, which accepts the low-pass filtered analog switched signal Y(t) from the anti-alias filter 116 Y. The programmable-gain amplifier 122 Y has a gain, denoted G Y , which is controllable by a gain control functional element 124 Y. The gain control functional element 124 Y is arranged (e.g., programmed) to compute the gain G Y to be applied by the programmable-gain amplifier 122 Y, as a function of the mean intensity estimate A Y supplied by the averaging unit 118 Y. The amplified analog signal, denoted Y′ (t), is sampled and quantized by an ADC 126 Y, whose output sample stream, denoted Y(n), is fed to a second input of the correlation engine 128 .

The characteristics of sample-and-hold circuits within the ADCs 126 X, 126 Y should be chosen to as to ensure compatibility with the bandwidth of the anti-alias filters 116 X, 116 Y (or vice-versa). In correlating the two signals (i.e., the input signal and the switched signal), aliasing in itself does not present a problem; indeed, the folding of spectral information at a frequency higher than half the sampling rate can be beneficial as it provides even more information to the correlation. However, if the passband of the anti-alias filters 116 X, 116 Y is too high, the sample-and-hold circuits will not be synchronized between the two correlation “arms” and the data may appear to be less correlated. Thus, in general, the bandwidth of the anti-alias filters 116 X, 116 Y could be chosen such that it has a time constant that is somewhat greater than the temporal uncertainty of the sample-and-hold circuits.

The correlation engine 128 computes a function of the two sample streams X(n) and Y(n) in order to produce a correlation value, denoted R O (m) , for the present sample time m. In one embodiment of the present invention, the correlation value can be computed in a computationally efficient manner, for example:

R O (m) =Σ( X ( m−j )· Y ( m−j ))/Σ| X ( m−j )· Y ( m−j )|, 0 ≦j≦N,   (1)

for some finite value of N. Of course, it is also within the scope to use other functions, some of which are less computationally efficient, for example: R O ( m ) = ∑ ( X  ( m - j ) · Y  ( m - j ) ) sqrt  ( ∑ X 2  ( m - j ) · ∑ Y 2  ( m - j ) ) ,    0 ≤ j ≤ N . (2)

Still other correlation functions will be known to those skilled in the art and any of these is suitable for use with the present invention.

The correlation value R O (m) for the current value of m is output by the correlation engine 128 to the controller 130 . Because the correlation function being performed is digital in nature, the correlation engine 128 could be implemented in a micro-controller or digital signal processor.

Since the controller's decisions as to whether or not a connection is valid are based on the correlation value R O (m) , it is important to provide a reliable value of R O (m) to the controller 130 . It turns out that reliability of R O (m) is dependent on the amount of “clipping” that the amplified analog signals X′ (t), Y′ (t) undergo as they are sampled and quantized by the ADCs 126 X, 126 Y. The amount of clipping performed by the ADCs 126 X, 126 Y is, in turn, dependent upon the gains G X , G Y of the programmable-gain amplifiers 122 X, 122 Y. It is therefore important to understand the effect of the gains G X , G Y of the two programmable-gain amplifiers 122 X, 122 Y on the reliability of the resulting correlation value R O (m) .

To this end, it is helpful to begin by analyzing the properties of the voltage signal at the output of the photodiode 114 X. (An analogous analysis applies to the single-wavelength switched signal entering the photodiode.) It is recalled that the signal at the output of the photodiode 114 X is a wideband analog voltage signal representative of a digital optical signal having a clock rate F C . For a truly random pattern of zeroes and ones in the digital optical signal, the power spectrum of the voltage signal at the output of the photodiode 114 X denoted S(f), will obey approximately the following relationship (see Horowitz and Hill, The Art of Electronics, Cambridge University Press, ISBN 0 521 23151 5, p.441):

S ( f )=((sin (π f/F C ))/(π f/F C )) 2 .  (3)

It can be easily seen that for f<</F C , S(f) is approximately equal to one. Therefore, after low-pass filtering at a bandwidth of F B hertz where F B <</F C , the resultant power spectrum will be substantially flat.

It can further be shown (again see Horowitz and Hill, The Art of Electronics, Cambridge University Press, ISBN 0 521 23151 5, p.441) that the voltage level of the low-pass filtered analog input signal X(t) is no longer limited to between zero and a maximum voltage but instead has a Gaussian probability density function (pdf) with zero mean. By virtue of the low-pass filtered analog input signal X(t) having a Gaussian pdf, it becomes a simple matter to compute the probability that X(t) will exceed a given voltage V MAX . Specifically, this probability is given by the value of the complementary error function “erfc” evaluated at V MAX /σx 2 , where σx 2 is the variance of the X(t) and where erfc(a) can be defined as: ( 2        pi ) - 1 2  ∫ a ∞  (  - 1 2  t 2    )      t . (4)

(The above definition was take from Helstrom, Carl W., Probability and Stochastic Processes for Engineers , 2 nd edition, New York, Macmillan Publishing Company, 1991. It is to be appreciated that different texts may use slightly different definitions for the complementary error function.)

Next, it is noted that the standard deviation σ X of X(t) is in fact the root-mean-square (RMS) value of X(t) since the latter is a zero-mean random process. It follows that the low-pass filtered analog input signal X(t) will exceed V MAX during a percentage of the time equal to:

100 ·erfc ( V MAX /σ X )=100 ·erfc ( V MAX /V RMS,X ).  (5)

Applying a gain of G X at the amplifier 122 X and setting the maximum input level of the ADC to V MAX , it is seen that control of G X directly provides control over the percentage of the time during which the amplified signal X′ (t) is clipped by the ADC. Specifically, this percentage of time may be denoted by P CLIP and is equal to:

P CLIP =100 ·erfc ( G X ·V MAX /V RMS,X ).  (6)

The effects of controlled clipping (i.e., setting G X and G Y to achieve a desired percentage of clipped samples in the input signal arm and the switched signal arm of the connection verification unit 104 ) on the value of R O (m) computed by the correlation engine 128 are now discussed with reference to FIGS. 3A and 3B.

Specifically, with reference to FIG. 3A, simulations were 10 performed having regard to two truly correlated signals, i.e., the ideal value of R O (m) was unity. The signals were clipped to varying degrees and the value of R O (m) using equation (1) above was plotted as a function of the percentage of samples that had undergone clipping. The curve shows that R O (m) remains to within 10% of its ideal value of unity, even as the percentage of clipped samples approaches 90%. This shows that reliability of the correlation value R O (m) is virtually unaffected by mild or even severe clipping, when the input and switched signals are truly correlated.

With reference now to FIG. 3B, a similar simulation was performed, but with two truly uncorrelated signals, i.e., the ideal value of R O (m) was zero. Again, the signals were clipped to varying degrees and the value of R O (m) using equation (1) above was plotted as a function of the percentage of samples that had undergone clipping. In this case, the curve shows that R O (m) actually decreases as the percentage of samples which undergo clipping is increased. This effect occurs even when the gain is so high that 50% of the samples are being clipped. The implication is that clipping causes the computed correlation value R O (m) to be more reliable, since it is closer to its ideal value.

In view of the above results, it should be apparent to one of ordinary skill in that art that introducing a certain amount of clipping improves reliability of the correlation value R O (m) . The beneficial effects of clipping start at a very low percentage of clipped samples and continue as clipping reaches 10% of the samples or even 50% or higher.

To achieve a desired percentage of clipping and, one may exert control over the gains G X , G Y of the amplifiers 122 X, 122 Y. Specifically, to achieve a desired percentage P CLIP of samples clipped at the ADC, the gain G X to be applied by the amplifier 122 X can be derived from equation (6) above to be the following:

G X =( V RMS,X /V MAX )· erfc −1 ( P CLIP /100).  (7)

An analogous analysis applies to computation of the desired gain G Y for amplifier 122 Y, resulting in the following expression:

G Y =( V RMS,Y /V MAX )· erfc −1 ( P CLIP /100).  (8)

Now, assuming the duty cycle of the single-wavelength input signal to be approximately 50% (that is to say, the laser spends—on average—as much time “on” as it does “off”), it can be shown that V RMS,X is given by (see Horowitz and Hill, The Art of Electronics, Cambridge University Press, ISBN 0 521 23151 5, p.441):

V RMS,X =A X ·sqrt( 2 F B /F C ).  (9)

Therefore, it should be apparent that equation (7) for G X involves only the parameters A X , F B , F C and P CLIP . The only dynamically changing parameter is A X , which is obtained from the averaging unit 118 X without reliance on the amplified analog signal X′ (t). Similarly, the only time-varying parameter used in equation (8) for G Y is A Y , which is conveniently supplied by the averaging unit 118 Y. This results in a level setting technique which not only provides the above-mentioned advantages related to reliability of the correlation value R O (m) arising from controlled clipping of the low-pass filtered analog signals X(t), Y(t), but which is also stable and robust because the parameters it requires are computed without reliance on feedback techniques.

Of course, various modifications of the invention are possible. For example, it is within the scope of the invention to replace the plurality of demultiplexers 112 X in the input signal arm with a single-output wavelength selection device. The wavelength selection device could be designed to controllably pass the optical signal occupying a single selected wavelength from a single selected one of the input optical fibers 104 . A suitable example of a wavelength selection device has been described as a “front end” in U.S. patent application Ser. #60/207,292 to Graves et al., entitled “Optical Switch with Connection Verification”, filed on May 30, 2000, assigned to the assignee of the present invention and incorporated by reference herein. Control of the wavelength selection device could be achieved from the controller 130 , which would also have access to the connection map of the switching unit 102 . An analogous arrangement could be provided at the switched signal “arm” of the connection verification unit 104 . In this way, connection verification could be achieved on a sequential basis, thus reducing the processing requirements. However, it would take much longer to verify all the connections through the switching unit 102 .

Furthermore, it is to be appreciated that the improvements in the reliability of the correlation value R O (m) resulting from controlled clipping extends to situations in which the signals are already in digital form prior to clipping. In this case, the amplitude-limiting function would not be performed by an analog-to-digital converter but instead could be performed in software.

In some embodiments, it may be advantageous to use a high-pass filter in addition to each of the low-pass anti-alias filters 116 X, 116 Y. The roll-off frequency of the high-pass filters should be roughly equal to the sampling rate divided by N, the number of samples in the correlation vector. The high pass filter prevents loss of dynamic range due to large swings of the entire data stream in the correlation vector. If the correlation vector is sufficiently large (e.g., 50 samples) then the effects of this additional filter on the gain calculation (see equations (7) and (8) above) are negligible.

Other embodiments of the invention could include a plurality of connection verification units 104 sharing a common controller. Thus, the common controller could receive multiple correlation values R O,1 (m) , R O,2 m) , . . . R O,P (m) from multiple correlation engines. The controller could then make a decision as to the true value of R O (m) by evaluating a function (e.g., the product, mean, median or mode) of the multiplicity of correlation values.

Those skilled in the art should also appreciate that in some embodiments of the invention, all or part of the functionality previously described herein with respect to the gain control functional elements 124 X, 124 Y and the correlation engine 128 may be implemented as pre-programmed hardware or firmware elements (e.g., application specific integrated circuits (ASICs), electrically erasable programmable read-only memories (EEPROMs), etc.), or other related components. In other embodiments of the invention, all or part of the functionality previously described herein with respect to the gain control functional elements 124 X, 124 Y and the correlation engine 128 may be implemented as software consisting of a series of instructions for execution by a computer system.

The series of instructions could be stored on a medium which is fixed, tangible and readable directly by the computer system, (e.g., removable diskette, CD-ROM, ROM, or fixed disk), or the instructions could be stored remotely but transmittable to the computer system via a modem or other interface device (e.g., a communications adapter) connected to a network over a transmission medium. The transmission medium may be either a tangible medium (e.g., optical or analog communications lines) or a medium implemented using wireless techniques (e.g., microwave, infrared or other transmission schemes).

Those skilled in the art should further appreciate that the series of instructions may be written in a number of programming languages for use with many computer architectures or operating systems. For example, some embodiments may be implemented in a procedural programming language (e.g., “C”) or an object oriented programming language (e.g., “C++” or “JAVA”).

While specific embodiments of the present invention have been described and illustrated, it will be apparent to those skilled in the art that numerous modifications and variations can be made without departing from the scope of the invention as defined in the appended claims.