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  Adaptive interpolationThe Patent Description & Claims data below is from USPTO Patent Application 20070273567. Brief Patent Description - Full Patent Description - Patent Application Claims
BACKGROUND OF THE INVENTION [0001] The present invention is directed to real time oscilloscopes, and more particularly to real time oscilloscopes employing a bandwidth extension scheme (i.e. Digital Bandwidth Interleaving), such as that described in U.S. patent application Ser. No. 11/281,075, titled HIGH BANDWIDTH OSCILLOSCOPE, filed Nov. 17, 2005 ("the '075 application"), currently pending, the entire contents thereof being incorporated herein by reference. In accordance with the disclosure of this pending patent application, each of a plurality of channels (two, for example, which will be referred to as LF (low frequency) and HF (high frequency)) receive a portion of an input signal corresponding to a specific frequency band. As described in the above application, additional processing is performed on this split signal for acquiring and digitizing the signal. In accordance with the present invention, further modification to this process of the '075 application is presented. [0002] The DBI technique referenced above allows extending the bandwidth of Digital Storage Oscilloscopes (DSO's) by using bandwidth available in additional channels of the DSO to augment the bandwidth of a primary channel or channels. The application of such a DBI technique is limited not only by the bandwidth available on each channel but also by the necessity to leave sufficient distance between the bands for upsampling. Also, to allow for the use of the greatest amount of theoretically available bandwidth, the cross-over regions between adjacent bands have to be narrow, causing various challenges such as large group delay variations. [0003] Ideally, two bands of width f.sub.S/2, one extending between 0 and f.sub.S/2 and the other extending between f.sub.S/2 and f.sub.S, can be combined into a channel of width f.sub.S and sampling rate 2 f.sub.S. However, such a scheme appears to be physically impossible because no hardware filter structure can be made to transmit 100% frequencies below f.sub.S/2, and transmit 0% frequencies above f.sub.S/2, and vice versa. Furthermore, software filters encounter a similar challenge: no finite-length linear digital filter can upsample (interpolate) leaving the original frequency 100% intact and create 0% spur, when the frequency is nearly equal to Nyquist. [0004] The invention is a method for setting the imperfections of software interpolation filter to be commensurate with the hardware filter imperfections. When the samplings of the channel connected with the low frequency are staggered in between the samplings of the high frequency channel, and the interpolation filter taps are set equal to the other channel's input response scaled values, a substantially perfect cancellation (to the level of precision of the instrument) of terms appearing at the wrong frequency can be achieved in accordance with the invention. This is analogous to the well-known aliasing-canceling condition of filterbanks, and the description will show similarities and differences between the present invention and this specific digital filtering technique. [0005] As presented in the '075 application, f.sub.LO represents the frequency of the mixer's LO (element 43 of FIG. 2 in the '075 application). f.sub.S represents the sampling frequency of the digitizers (elements 5, 6, 7, 8 of FIG. 1 in the '075 application). In such a system, f.sub.LO would be equal to f.sub.S, with half the bandwidth [0 to f.sub.S/2] going to the LF channel and half the bandwidth [f.sub.S/2 to f.sub.S] going to the HF channel. As noted above, it has been determined by the inventor of the present invention that when one tries to build such a system employing the maximum theoretical bandwidth, two phenomena impede optimal operation, namely the width of the hardware filters and the width of the software interpolation filters. In accordance with the present invention, the inventor herein presents a technique that circumvents these limitations. SUMMARY OF THE INVENTION [0006] As noted above, when attempting to build the above described system using maximum theoretical channel bandwidth by setting f.sub.S=f.sub.LO, the inventor of the present invention has determined that two phenomena hinder optimal operation. [0007] First, any filter or diplexer employed to split the input signal into the two specific frequency bands will always have a non-zero "crossover bandwidth." (the element highlighted by FIGS. 23 and 24 in the '075 application). There will, therefore, be a particular portion of the bandwidth that will be included in the signal sent into both channels, even though this portion of the bandwidth should be properly included in only one of the frequency bands, and thus sent to only one of the channels, either LF or HF. Any signal within this crossover bandwidth will pass through to both the high frequency channel and the low frequency channel with comparable power and amplitude. As a result, for example, a portion of the signal that is within the high band, and therefore belongs in the high frequency channel, will arrive in the low frequency channel, and will be interpreted as if it were a low-frequency signal, along with all of the other signals that are actually low frequency and belong in the low frequency channel. The same is true for low frequency signals in the high band. [0008] Such a signal of frequency f arriving in the wrong band causes a large spur (.about.0 dB, meaning the spur is nearly of a size equal to the size of the correct signal) at the wrong frequency, because the frequency received at the channel is above the Nyquist limit of f.sub.S/2. When this occurs, the amount of frequency error is two times f-f.sub.S/2, changing f into f-2 (f-f.sub.S/2), namely into f.sub.S-f. It is well known that the phenomenon of aliasing occurs when frequencies above the Nyquist limit are input into a sampling circuit, and that this phenomenon causes the same frequency error as a function of frequency (see for example the article by Ruwan Welaratna--"Effects of Sampling and Aliasing on the Conversion of Analog Signals to Digital Format"--Sound and Vibration magazine, December 2002). [0009] Secondly, the inventor of the present application has recognized another phenomenon hindering the use of the maximum theoretical available bandwidth. This phenomenon causes a problem even if all signals are received in the correct frequency channel. The sin x/x upsampling referred to in the above '075 application is performed with a finite number of points. Namely, element 95 in FIG. 11 in the '075 application is equal to 30, for example. Such a combination of an upsampler and filter has a non-ideal rejection for artifacts generated at frequency f.sub.S-f, as noted in the discussion by Julius O. Smith III (see Smith, Julius O., MUS420/EE367A Lecture 4A, Interpolated Delay Lines, Ideal Bandlimited Interpolation, and Fractional Delay Filter Design, Stanford University) also referred to by the '075 application. In general, the rejection of unwanted frequency components provided by a truncated Sinc is fairly good. But, when approaching the Nyquist limit (f.sub.S/2), the truncated Sinc filter fails to reject an undesired frequency because it is just too close to the desired frequency, and both are part of a curve with a finite slope. [0010] FIG. 16 of the present application shows an example of an upsampling process performed with an upsample distance of 30 (this upsample distance of 30 defining, in the '075 application, the fact that the Sinc function is truncated at 30 terms). The inventor of the present invention notes that such a truncated Sinc filtering fails to regenerate only the intended frequency when f=0.49 fs. This issue can be mitigated by increasing the upsample distance beyond 30. In any case, however, the issue remains if the input frequency is made equal to f.sub.S/2 to a precision better than the frequency resolution of the truncated Sinc filter, as long as the filter has a finite number of taps, i.e. a finite upsample distance, such a filter will fail. Ultimately, this second phenomenon results in a large (order 0 dB) spur at f.sub.S-f. (the same frequency noted above). [0011] Therefore, the inventor of the present invention notes that these two sources of spur, one of hardware origin, the other of software origin, result in the presence of the same erroneous frequency. And therefore, in accordance with the invention, the inventor has proposed a method and apparatus that uses these two spurs to cancel each other out. [0012] In such a method and apparatus in accordance with the invention, an adaptive upsampling for the high frequency band acquired data takes the place of the truncated sin x/x upsampler. In other words, element 80 of FIG. 10 in the '075 application is preferably replaced by block 80 of FIG. 11 in the present application. The interpolation thus preferably comprises a FIR taps somewhat different from sin x/x used in place of a true sin x/x function to upsample the signal by a factor of 2. The values of the filter taps, instead of being taken from the sin x/x function, are taken from consecutive points on a normalized and averaged low frequency impulse response, measured during a dedicated calibration step that will be shown below (see FIG. 6c). Similarly, an adaptive upsampling of the low frequency band takes the place of the truncated sin x/x upsampler. Namely, element 73 of FIG. 10 in the '075 application is preferably replaced by block 73 of FIG. 11 in the present application. The sin(x)/x-related filter taps are preferably replaced by consecutive points on the averaged high frequency impulse response, as measured during a dedicated calibration step that will be shown below (see FIG. 6b). Thus, in accordance with the invention, it is deliberately chosen to make the software imperfections the same size as the hardware imperfections. [0013] Apart from the small effect of "leakage" or "crosstalk", which will be discussed below, the cancellation between the spurs that results from this process is intrinsically substantially perfect (again, to the level of precision of the instrument). This cancellation between the two spurs then leaves us with a generally simple linear and finite (non-zero) response at all frequencies. [0014] Actually, the finiteness (non-zero-ness) happens only if the samples coming from the LF band and the samples coming from the MF band are independent enough; i.e. if the system is in a "quadrature" condition at fs/2. Such a "quadrature" condition takes place if the samples are at their minimum amplitude in one channel while at their maximum in the other channel and vice-versa, and the interpolated points from one band line up with the original points of the other band, and vice-versa. [0015] With respect to the '075 application, the present invention achieves a number of benefits. Some changes simply related to the change of operation frequencies are first noted. Hardware employed by the DSO to implement the present invention preferably modifies diplexer (elements 29, 31, and 33), and filters (elements 34, 37) of FIG. 2 of the '075 application so that the crossover frequency is 5 GHz instead of 6 GHz (see FIG. 10 of the present application), and the diplexer does not have to have a very narrow crossover. In accordance with the present invention, element 53 of the '075 application is preferably removed, as the full frequency range receivable by the channel dedicated to high frequencies can be used. Element 30 of the '075 application is preferably removed, as the presence of a f.sub.LO signal is no longer a threat to performance. Rather its presence amounts to a shift of the DC level in the channel, which can be calibrated away. The design of the present invention does not need special equipment to generate, track or filter out f.sub.LO, thus preferably avoiding the need for elements 43, 44, 45, 46, 47, 48, 49, 50, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, and 63 of the '075 application. On the software front, many filters used in the '075 application (74, 75, 81, 82, 88) are preferably not needed, as the removal of various spurs is performed differently (i.e. without generic filters) in accordance with the invention. The generation of a software version of f.sub.LO is preferably not needed, justifying the preferred removal of elements 86 and 87 of the '075 application. The most notable changes comprise the preferred modification of elements 73 and 80, and thus the trivialization of elements 83 and 84, of the '075 application. [0016] Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification and the drawings. [0017] The invention accordingly comprises the several steps and the relation of one or more of such steps with respect to each of the others, and the apparatus embodying features of construction, combinations of elements and arrangement of parts that are adapted to effect such steps, all as exemplified in the following detailed disclosure, and the scope of the invention will be indicated in the claims. BRIEF DESCRIPTION OF THE DRAWINGS [0018] For a more complete understanding of the invention, reference is made to the following description and accompanying drawings, in which: [0019] FIG. 1 is a screen shot representation of a number of signals displayed on an oscilloscope depicting the functionality of an embodiment of the invention, when a sinewave is fed to the oscilloscope; [0020] FIGS. 2a and 2b are screen shot representations of a number of signals displayed on an oscilloscope depicting the functionality of an embodiment of the invention, when a negative edge is fed to the oscilloscope; in FIG. 2a, the invention is not employed. In FIG. 2b, the invention is used; [0021] FIGS. 3a-3e represent a technique entitled of "Aliasing-Cancellation Conditions of Filterbanks", and its various modifications in accordance with the present invention; Continue reading... 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