Abstract:
A measured signal, such as a high-speed digital pulse, transmitted through a system is corrected. The measured signal is sampled to a sampled signal sequence, and a signal series is provided as a plurality of the sampled signal sequences put together successively. The signal series is windowed with a window function, and a corrected measured signal is recalculated from the windowed signal series using information about the frequency-dependency of the system.

Description:
BACKGROUND OF THE INVENTION 
   The present invention relates to correcting a measured signal transmitted through a system. 
   Effective and accurate measuring of high-speed pulses requires careful design of the measuring setups and methods. Increased measurement accuracy of signals with increasing frequencies together with a high degree of automatization is getting more and more difficult to achieve. While reaching ranges of above 1 GHz, signal distortion resulting from each connection, cables, switches or other elements in the transmission path is influencing the pulse performances significantly, for example with respect to pulse rise and/or fall time, ringing, droop, overshoot, or the like. Such kind of distortion is generally tried to be minimized by using (usually more expensive) high-speed cables, high-frequency connectors, switches, etc. and/or by optimizing the measurement set-up to minimize signal connection lengths. Moreover, a certain trade off between measurement accuracy and the degree of measurement automatization is often required. 
   Another approach for improving measuring signals can be accomplished by determining the distortion of the signal transmission path and recalculating an ideal signal (i.e. without being distorted by the signal transmission path) from the actually measured signal. The techniques for recalculating the ideal signal are well established in the theory of communications. The response of a linear system to a signal can be determined in the time domain by using the principle of convolution, and in the frequency domain by applying the principle of superposition to responses produced by the individual frequency components applied for the frequency domain representation. Multiplication in the frequency domain is equivalent to convolution in the time domain, and vice versa. A detailed break down of the theory, both for time domain and frequency domain analysis, can be readily taken e.g. from the introductory chapter “Signals and Channels” in “Telecommunications engineering”, ISBN 0-412-38190-7, by J. Dunlop. 
   For the sake of simplicity and since signal recalculations are mainly applied in the frequency domain, the principle of signal recalculation shall be explained in the following mainly with respect to frequency domain analysis. It is clear, however, that signal recalculations in the time domain applying convolution techniques can be applied accordingly. 
     FIG. 1  illustrates the principle of signal recalculation in the frequency domain. An input signal  10  provided from a signal source  20  is transmitted through a communication channel generally represented herein as a system  30 . In general, the system  30  modifies or distorts the waveform of the input signal  10  transmitted through the system  30  to an output signal  40 . The amount of distortion produced by the system  30  is thereby determined by the transfer function (i.e. attenuation and phase shift as a function of frequency) of the system  30 . The determination of the transfer function will be explained in more detail with respect to  FIG. 2 . The output signal  40  is measured by a measuring device  50  such as an oscilloscope. 
   Before recalculating the input signal  10  from the output signal  40  by a recalculation unit  60 , a window function W is usually applied to the measured output signal  40  for reducing spectral leakage effects. Typical window functions are Hanning-Window, Blackman Window, or Hamming Window. The recalculation unit  60  then transforms the windowed signal from the time domain into the frequency domain usually by applying a Fast Fourier Transformation (FFT). The transformed signal is then divided by the transfer function T(f) of the system  30 , and the result thereof is retransformed from the frequency domain back into the time domain usually by applying an Inverse Fast Fourier Transformation (IFFT). The result of the retransformation represents a recalculated signal  70 , which substantially corresponds to the input signal  10 . The recalculated signal  70  might be applied to a signal source  80  for generating a physical signal  90  from the recalculated signal  70  or could be applied for analyzing the recalculated signal  70  with respect to its characteristics and properties. 
   It is clear that the recalculated signal  70  ideally equals the input signal  10  in case that:
         the transfer function T(f) applied in the recalculation unit  60  fully equals the transfer function of the system  30 ,   The transformation and retransformation steps are completely inverse,   the measuring device  50  and the recalculation unit  60  have no transfer function(s) further modulating the signals, and   the window function W has no influence on the signals.       

   It is clear that any deviation from the ideal situation as outlined above will adversely affect the signal recalculation process and lead to deviations of the recalculated signal  70  from the input signal  10 . 
     FIG. 2  illustrates the principle for determining a transfer function. A reference signal generator  100  applies a reference signal  110  to the system  30  for which the transfer function T(f) is to be determined. The reference signal  110  transmitted through the system  30  is distorted to a signal response  120  measured by a first measuring device  130 . The measured signal response  120  is modulated by a window function (block W) and transformed into the frequency domain (block FFT) as a function O(f). Accordingly, the reference signal  110  is measured by a second measuring device  140 , modulated by a window function (block W) and transformed into the frequency domain (block FFT) as a function I(f). The transfer function T(f) of the system  30  is then determined in a calculation unit  150  by dividing the frequency-transformed signal response O(f) by the frequency-transformed reference signal I(f). 
   It is clear that—dependent on the characteristics of the respective signals—the window functions W applied in  FIGS. 1 and 2  can either be the same or different window functions. 
   Another way for determining the transfer function T(f) would be to measure the response of the system  30  to an applied Dirac pulse. 
   As noted above, the frequency domain analysis executed by the recalculation unit  60  in  FIG. 1  can also be undertaken in the time domain, since the time domain and the frequency domain are linked by the Fourier transform. In that case, the recalculation unit  60  would provide a convolution analysis, however, leading correspondingly to the recalculated signal  70 . 
   When performing the recalculation as outlined for  FIG. 1 , several difficulties are encountered:
         Firstly, sampling oscilloscopes are generally applied as standard measurement instruments for characterizing (digital) signals, e.g. for determining overshoot or ringing of a digital pulse. For achieving highest accuracy on signal performance measurements, it is necessary to set the time base of the oscilloscope to a value that shows only a few signal periods or even less than one signal period on the screen. This allows maximizing the sampling density of the measured signal. On the other hand, for performing the frequency transformation (such as FFT) a significant number of periods of the measured signal should be used for minimizing the effect of the signal windowing on the measurement accuracy.   High sampling resolution and to put a huge number of signal periods into one screen shot for minimizing windowing effects, however, are contravening requirements, and a certain trade off between those requirements has to be made. However, it is apparent that any limitation of the sampling accuracy in the measuring process of  FIG. 1  will correspondingly lead to a reduced accuracy of the recalculated signal  70  with respect to the input signal  10 . Accordingly, any inaccuracy in the sampling process of  FIG. 2  (by the measuring devices  130  and  140 ) will lead to a reduced accuracy of the transfer function T(f), which again reduces the accuracy of the recalculation process in the recalculation unit  60  of  FIG. 1 .   Secondly, the transfer function T(f) can only be determined for discrete frequencies and a limited frequency range. That means, that if the time base of the measuring device  50  has to be changed, the transfer function should be determined again. That requires a huge effort for characterizing each measurement path for all different time bases used.   Thirdly, even with highest accuracy for the sampling process and determination of the transfer function, the recalculated signal  70  is still slightly distorted under the influence of the windowing function.   Fourthly, the determination of the transfer function is strongly dependent on the quality of the reference signal generator  100  providing the reference signal  110 . Any frequency limitation of the reference source  110  will automatically reduce the accuracy of the determined transfer function.       

   SUMMARY OF THE INVENTION 
   It is therefore an object of the present invention to provide an improved correction of measured signals. The object is solved by the independent claims. Preferred embodiments are shown by the dependent claims. 
   According to the invention, the signal correction process can be significantly improved in that—before modulating the corrected measured signal with a window function and recalculating the corrected measured signal—the measured signal is sampled, and the sample sequence is reproduced (preferably copied) to a series of several successive sequences. This signal series of a plurality of the sampled signal sequences is then applied for the windowing process. This allows that the measured signal can be sampled with highest accuracy, while windowing effects can be encountered by choosing a sufficiently high number of the sampled signal sequences put together to the signal series. 
   Since the invention does not depend on the specific method applied for recalculating corrected measured signals, frequency domain analysis as well as time domain analysis can be applied, as described in the introductory part of the description. Preferably, the recalculation process is performed using a frequency domain transformation of the windowed signal series, and by multiplying the transformed signal series with the inverse transfer function of the system. The result is retransformed into the time domain, and the corrected measured signal can be extracted therefrom preferably by selecting one sequence corresponding to the sequence of the measured signal. 
   In a preferred embodiment, the corrected signal sequence is selected substantially from a middle range of the signal series resulting from the recalculation process of the windowed signal series. 
   In another preferred embodiment, a demodulation process inverse to the modulation of the signal series with the window function is applied to the results of the recalculation process of the windowed signal series. This allows further reducing distortion effects resulting from the windowing process. 
   It is to be understood that the inventive signal sampling and accumulation is not limited to signal recalculations but can be applied in order to reduce windowing effects in any kind of application. 
   It is clear that the invention can be partly or entirely embodied by one or more suitable software programs, which can be stored on or otherwise provided by any kind of data carrier, and which might be executed in or by any suitable data processing unit. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other objects and many of the attendant advantages of the present invention will be readily appreciated and become better understood by reference to the following detailed description when considering in connection with the accompanied drawings. Features that are substantially or functionally equal or similar will be referred to with the same reference sign(s). 
       FIG. 1  illustrates the principle of signal recalculation in the frequency domain, 
       FIG. 2  illustrates the principle for determining a transfer function, and 
       FIG. 3  shows a preferred embodiment of the invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 3  shows a preferred embodiment of the invention, whereby the lower part depicts the signal recovery process for correcting a measured signal, and the upper part illustrates the calibration process for determining the transfer function for the signal recovery process.  FIG. 3  substantially corresponds to the measuring principles as depicted for  FIGS. 1 and 2 . 
   The measuring device  50  in  FIG. 3 , as explained for  FIG. 1 , measures and samples the output signal  40  of the system  30 . However, in contrast with the explanation as given for  FIG. 1 , the output signal  40  can be sampled with highest accuracy as provided by the measuring device  50 . This allows that sampling distortion can be minimized to a high degree. In case of a periodic output signal, e.g. one period can be sampled with maximum sample density for achieving highest accuracy. 
   The sampled output signal  40  is then applied to a signal multiplication unit  200 , which captures the sampled output signal  40  and appends it thereto (n−1)-times. This results in an n-periodic signal, whereby each period represents the sampled output signal  40 . In the example of  FIG. 3 , the sampled output signal  40  is added (or copied) nineteen times to the “original” sampled output signal  40 , thus resulting in a 20-periods signal 
   The n-period signal provided from the multiplication unit  200  is then modulated with a window function W and supplied to the recalculation unit  60 . The recalculation unit  60 , as explained for  FIG. 1 , provides a Fourier transform (block FFT) of the windowed n-period signal, divides (block *Xfer) the frequency transformed signal by the transfer function T(f) of the system  30 , and finally retransforms (block IFFT) the result back into the time domain. 
   The recalculated n-periodic signal provided from the recalculation unit  60  now contains n-times the recalculated signal  70 , which again can be received e.g. by selecting one period. 
   In a preferred embodiment, the recalculated n-period signal provided from the recalculation unit  60  will be demodulated from the windowing function W in a demodulation unit  210 . The demodulation unit  210  preferably divides the n-period signal from the recalculation unit  60  by the windowing function W (as applied in the previous windowing process). 
   In another embodiment, the n-periodic signal from the recalculation unit  60  is applied either directly or via the demodulation unit  210  to a period selection unit  220 . The period selection unit  220  selects one period of the n-periodic signal, preferably in a middle range of the n-periodic signal. In the example of  FIG. 3 , the period selection unit  220  will select the eleventh period of the 20-period signal. 
   The upper part of  FIG. 3  illustrates the calibration process preferably applied for determining the transfer function T(f) of the system  30 . It is clear, however, that the transfer function T(f) can also be determined by other processes as known in the art, and that the invention is not limited to the specific embodiment as depicted in the upper part of  FIG. 3 . In accordance with the above said for  FIG. 2 , the first measuring device  130  measures and samples the signal response  120  of the system  30 , while the second measuring device  140  measures and samples the reference signal  110  applied to the system  30 . Also in accordance with the above said, a multiplication unit  200 A provides an n-period signal from the sampled signal response  120 , and a multiplication unit  200 B provides an n-period signal from the sampled reference signal  110 . The signal response  120  as well as the reference signal  110  are preferably sampled with highest accuracy achievable by the measuring devices  130  and  140 . The n-periods signals from the multiplication units  200 A and  200 B are each modulated with a window function W and transformed into the frequency domain, as indicated by the respective blocks W and FFT, to a transformed signal response  210 A and a transformed reference signal  210 B. 
   The transfer function T(f) can then be determined by dividing the transformed signal response  210 A by the transformed reference signal  210 B. However, instead of directly dividing the transformed signal response  210 A by the transformed reference signal  210 B, a cross spectrum and an auto spectrum can be determined, as shown in the upper part of  FIG. 3 . A cross spectrum unit  225  determines the cross spectrum by complex multiplying the spectra of the transformed signal response  210 A and the transformed reference signal  210 B. An auto spectrum unit  230  determines the auto spectrum by complex multiplying the spectrum of the transformed reference signal  210 B with itself. A transfer function determining unit  240  can then determine the transfer function T(f) by dividing the determined cross spectrum by the determined auto spectrum. This allows eliminating white noise effects thus increasing accuracy. 
   The determined transfer function T(f) is then preferably stored in a storage  250  and can be used by the recalculation unit  60 . 
   In a preferred embodiment, an interpolation unit  260  provides an interpolation of the transfer function T(f) from discrete frequency values to a continued frequency spectrum. This is preferably accomplished by a linear interpolation between two discrete frequency points or a spline interpolation.