US 20010010500 A1 Abstract A method, arrangement, and system enable adaptive calibration of an analog-to-digital converter (ADC) from reference signals with unknown parameter(s) that may vary (e.g., a varying frequency). An analog reference signal s(t) is supplied to an ADC to be calibrated. The output x(n) of the ADC is used by a, e.g., sine-wave reconstruction filter to reconstruct an estimate ŝ(n) of the sampled instances of the signal s(t). A recursive frequency estimator within the sine-wave reconstruction filter produces a frequency estimate of the analog reference signal s(t) from the signal x(n). An adaptive reconstruction filter uses this frequency estimate and the signal x(n) to produce the estimate ŝ(n). When a convergence detector determines that the adaptive reconstruction filter has converged, the estimate ŝ(n) is used to alter values that are stored in a correction table. During functional operation of the ADC, the correction table is used to correct the output values of the ADC.
Claims(47) 1. An arrangement for calibrating an analog-to-digital conversion, said arrangement comprising:
an analog-to-digital converter adapted for receiving an analog signal and producing a digital signal; a recursive estimator configured for computing at least one parameter related to said analog signal from said digital signal; and an adaptive filter configured for receiving said at least one parameter and said digital signal and producing therefrom a digital representation of said analog signal, said adaptive filter adapting to a change of said at least one parameter. 2. The arrangement of claim 1 3. The arrangement of claim 1 a memory for storing values, said values based, at least in part, on said digital representation of said analog signal. 4. The arrangement of claim 3 5. The arrangement of claim 1 a convergence detector for detecting a convergence of said adaptive filter. 6. The arrangement of claim 5 7. The arrangement of claim 1 8. The arrangement of claim 1 9. The arrangement of claim 1 10. The arrangement of claim 1 11. A method for calibrating an analog-to-digital conversion, said method comprising the steps of:
converting an analog reference signal to a digital signal; recursively estimating at least one parameter related to said analog reference signal from said digital signal; and adaptively reconstructing a digital representation of said analog reference signal from said digital signal and said at least one parameter, said step of adaptively reconstructing comprising the step of adapting to a change of said at least one parameter. 12. The method of claim 11 13. The method of claim 11 storing at least one value responsive to said digital representation in a correction table if the reconstruction of said step of adaptively reconstructing has converged. 14. The method of claim 11 determining if the reconstruction of said step of adaptively reconstructing has converged. 15. The method of claim 14 16. The method of claim 11 17. The method of claim 11 18. The method of claim 11 19. The method of claim 11 generating said analog reference signal using a single tone that is stepped over a plurality of frequencies. 20. The method of claim 11 21. An arrangement for calibrating an analog-to-digital conversion, said arrangement comprising:
an analog-to-digital converter adapted for receiving an analog calibration signal and producing a digital signal; a recursive estimator configured for computing a first parameter related to said analog calibration signal from said digital signal; an adaptive filter configured for receiving said first parameter and said digital signal and producing therefrom a digital representation of said analog calibration signal, said adaptive filter adapting to a change in said first parameter; and a correction table for storing at least one value therein, said at least one value based, at least in part, on said digital representation of said analog calibration signal. 22. The arrangement of claim 21 23. The arrangement of claim 22 24. The arrangement of claim 21 a convergence detector for detecting a convergence of said adaptive filter. 25. The arrangement of claim 21 26. The arrangement of claim 21 27. The arrangement of claim 26 28. The arrangement of claim 26 29. A method for calibrating an analog-to-digital conversion, said method comprising the steps of:
converting an analog calibration signal to a digital signal; recursively estimating a first parameter related to said analog calibration signal from said digital signal; adaptively reconstructing a digital representation of said analog calibration signal from said digital signal and said first parameter, said step of adaptively reconstructing adapting to a change in said first parameter; and storing at least one value in a correction table, said at least one value based, at least in part, on said digital representation, if said step of adaptively reconstructing has converged. 30. The method of claim 29 31. The method of claim 29 determining if said step of adaptively reconstructing has converged. 32. The method of claim 29 33. The method of claim 29 34. The method of claim 33 35. The method of claim 33 36. An arrangement for calibrating analog-to-digital conversion, said arrangement comprising:
an analog-to-digital converter, said analog-to-digital converter adapted to receive an analog input and to produce a digital output, said analog input corresponding to at least one parameter; a recursive estimator, said recursive estimator configured to receive said digital output and to estimate a first version of said at least one parameter therefrom; and an adaptive filter, said adaptive filter associated with a second version of said at least one parameter, said adaptive filter configured to receive said digital output and said first version of said at least one parameter, said adaptive filter further configured to determine at least one value based on, at least in part, said digital output and at least one of said first version of said at least one parameter and said second version of said at least one parameter. 37. The arrangement of claim 36 38. The arrangement of claim 36 39. The arrangement of claim 36 40. The arrangement of claim 36 41. The arrangement of claim 36 42. The arrangement of claim 36 a convergence detector, said convergence detector configured to ascertain whether said adaptive filter has converged. 43. The arrangement of claim 42 44. The arrangement of claim 42 45. The arrangement of claim 42 46. The arrangement of claim 36 a corrective unit, said corrective unit including a correction data structure that stores at least one entry derived from said at least one value. 47. The arrangement of claim 46 Description [0001] 1. Technical Field of the Invention [0002] The present invention relates in general to the field of analog-to-digital converters (ADCs), and in particular by way of example but not limitation, to digital calibration of ADCs in which the calibration may be accomplished adaptively with dynamic estimation of reference signals that have unknown parameters. [0003] 2. Description of Related Art [0004] The natural world operates in an analog domain, but information signals (voice, data, etc.) may frequently be processed, transmitted, or otherwise manipulated more efficiently in the digital domain. The conversion from the analog domain to the digital domain is accomplished with ADCs. An ADC receives as input an analog signal and produces as output a digital signal. However, some information present in the analog signal is necessarily lost during the conversion process even if an ADC is operating in an ideal manner. Unfortunately, real-world ADCs do not operate in an ideal manner. Consequently, the digital output of a real-world ADC does not track the analog input even as accurately an ideal ADC. [0005] It is therefore beneficial to make and/or tune real-world ADCs to approximate ideal ADCs. Techniques have been developed to calibrate real-world ADCs so as to modify their performance to emulate ideal ADCs as closely as possible. For example, ADCs are traditionally calibrated using high precision digital voltmeters to characterize the errors that result from digitizing static or slowly varying analog reference voltages. The outcome from this static testing forms the basis for a hardware or software implemented calibration scheme. Another method of conventional ADC calibration is the use of a sinusoidal reference signal. The reference is sampled, and estimations of the ideal sample values are calculated. These estimations are calculated using a minimum squared error criterion that requires knowledge of the frequency of the calibration signal. The errors (i.e., the difference between the estimated values and the actual sampled values output by the ADC being calibrated) are then used to build a correction table. The correction table may subsequently be used to modify sampled values of actual (e.g., non-calibration, functional, etc.) analog input signals. [0006] Efficient calibration schemes require that the reference signal be dynamically estimated on a sample-by-sample basis during the ADC calibration period(s). No method previously existed for dynamic estimation of a reference signal (e.g., a calibration signal) with one or more unknown parameters (e.g., frequency, phase, etc.) during an ADC calibration. The pre-existing calibration procedures relied on accurate and costly signal generators and/or precise and expensive measuring components. [0007] However, the parent application (U.S. Ser. No. 09/196,811, now U.S. Pat. No. 6,127,955) addressed these deficiencies of pre-existing calibration procedures by dynamically estimating a reference signal having one or more unknown parameters. Nevertheless, the invention of the parent application was primarily directed, with respect to frequency estimation, to the problem of calibrating ADCs that operate in a narrow frequency band. Since the linearity errors in general are frequency dependent, correction tables in accordance with the invention of the parent application are primarily useful for frequencies near the calibration frequency. The invention of the parent application does not therefore address the problem of wide-band calibration of ADCs. Consequently, implementations in accordance with the invention of the parent application do not optimally calibrate ADCs that are to be operated in a broad frequency band. [0008] The deficiencies of the prior art are overcome by the method, arrangement, and system of the present invention. To wit, the present invention is directed to a method, arrangement, and system for enabling adaptive calibration of an analog-to-digital converter (ADC) from reference signals with unknown parameter(s). For example, a reference signal having at least one unknown parameter that varies may be advantageously employed in order to calibrate an ADC over wide ranges of the unknown parameter(s) (e.g., over a wide frequency range). [0009] In certain embodiments, an analog reference signal s(t) is supplied to an ADC to be calibrated. The output x(n) of the ADC is used by a, e.g., sine-wave reconstruction filter to reconstruct an estimate ŝ(n) of the sampled instances of the signal s(t). A recursive frequency estimator within the sine-wave reconstruction filter produces a frequency estimate of the analog reference signal s(t) from the signal x(n) . An adaptive reconstruction filter uses this frequency estimate and the signal x(n) to produce the estimate ŝ(n). When a convergence detector determines that the adaptive reconstruction filter has converged, the estimate ŝ(n) is used to alter values that are stored in a correction table. During functional operation of the ADC, the correction table is used to correct the output values of the ADC. [0010] The above-described and other features of the present invention are explained in detail hereinafter with reference to the illustrative examples shown in the accompanying drawings. Those skilled in the art will appreciate that the described embodiments are provided for purposes of illustration and understanding and that numerous equivalent embodiments are contemplated herein. [0011] A more complete understanding of the method, arrangement, and system of the present invention may be had by reference to the following detailed description when taken in conjunction with the accompanying drawings wherein: [0012]FIG. 1 illustrates an exemplary ADC environment in which the present invention may be advantageously implemented; [0013]FIG. 2A illustrates an exemplary analog input signal versus digital output signal graph of an ideal ADC; [0014]FIG. 2B illustrates an exemplary analog input signal versus digital output signal graph of a practical ADC; [0015]FIG. 3A illustrates an exemplary application of calibration in accordance with the present invention; [0016]FIG. 3B illustrates another exemplary application of calibration in accordance with the present invention; [0017]FIG. 4A illustrates an exemplary ADC and an associated calibrator with selected signals denoted in accordance with the present invention; [0018]FIG. 4B illustrates exemplary details of one embodiment of calibration logic in accordance primarily with the invention of the parent application; [0019]FIG. 4C illustrates exemplary details of another embodiment of calibration logic in accordance primarily with the invention of the parent application; [0020]FIG. 5 illustrates a method in flowchart form for calibrating an ADC in accordance with the invention of the parent application; [0021]FIG. 6A illustrates exemplary details of one embodiment of calibration logic in accordance with the present invention; [0022]FIG. 6B illustrates exemplary details of one embodiment of correction logic in accordance with the present invention; [0023]FIG. 7 illustrates an exemplary embodiment of an adaptive reconstruction filter in accordance with the present invention; [0024]FIG. 8 illustrates an exemplary method in flowchart form for use in an ADC calibration procedure in accordance with the present invention; and [0025]FIGS. 9A and 9B illustrate exemplary corrected and uncorrected performance characteristics in graphical form in accordance with the present invention. [0026] A preferred embodiment of the present invention and its advantages are best understood by referring to FIGS. [0027] Referring now to FIG. 1, an exemplary ADC environment in which the present invention may be advantageously implemented is illustrated. An ADC [0028] The ADC [0029] The ADC [0030] Referring now to FIG. 2A, an exemplary analog input signal versus digital output signal graph of an ideal ADC is illustrated. The ideal ADC graph is shown generally at [0031] Referring now to FIG. 2B, an exemplary analog input signal versus digital output signal graph of a practical ADC is illustrated. The practical ADC graph is shown generally at [0032] Application of the ADC calibration principles of the present invention and/or invention of the parent application provides many advantages over conventional approaches. For example, robustness against variations in the analog calibration signal is provided. There is no need for highly-stable signal generators because the present invention and/or invention of the parent application calculates relevant parametrical information from quantized samples of the calibration signal utilizing prior knowledge of the waveform type. The calibration signal may be generated by a low-complexity, low-precision (but spectrally pure) local oscillator included in the system using the ADC (e.g., the system may be an integrated circuit (IC), BS, etc.). The present invention allows for a design using two ADCs that switches between reference and functional input signals, where one ADC is being calibrated while the other is running functionally. Using this solution, the calibrated ADC(s) may be sensitive to temperature drift without requiring the cessation of functional data conversion while implementing repetitive calibration. [0033] Another exemplary advantage of the present invention and/or invention of the parent application is increased efficiency as compared to conventional solutions. Because the filter (as explained further below) yields a better estimation of the reference signal than prior methods, fewer samples of the reference signal are needed for calibration. Additionally, the calibration scheme may be fully implemented in software. If the system the ADC is connected to has sufficient overflow capacity, then no additional digital signal processing (DSP) resources (e.g., hardware, processing cycles, etc.) are needed. In principle, the calibration may be made transparently during normal operation and delayed by only a memory access by utilizing, for example, a known pilot, as explained further below. The correction table may therefore be trained incrementally with short bursts of samples from the pilot tone used as a reference signal, thus allowing for a design using only one ADC, which is alternately connected to the reference signal and calibrated incrementally during known intermissions of the incoming functional signal. [0034] A pilot is a signal which stands apart from the information portion of the overall signal channel, but is carried by the same physical transmission medium. The pilot may occupy just one frequency in the utilized signal band (a so-called pilot tone), and the information may be spread in frequency to the side or around the pilot, but not on the same frequency as the pilot. A pilot is often used to adjust the system to carry the information with as high a quality as possible. Because the pilot has well-known characteristics, it may be measured and used to adjust signal level, synchronize clocks, etc., regardless of the information carried on the channel. In accordance with the principles of the present invention and/or invention of the parent application, the pilot signal, which may already be present in the relevant system for other purposes, may be used as a reference signal to calibrate the ADC. [0035] A still further advantage provided by application of the principles of the present invention and/or invention of the parent application is that the calibration scheme adapts to the reference signal, requiring knowledge of the waveform type only. This allows for both a calibration procedure using several different frequencies and a design using an extended correction table. The correction table addressing is then extended with addresses depending upon the difference between the value of the previous sample and that of the current sample. This corrects the dynamic aspect of the errors in the ADC. Moreover, improvement of the linearity may be enhanced still further by preloading the correction table and using the output thereof for the calibration scheme. Thus, the calibrator becomes a feedback system. The improvement is due, at least in part, to the more-accurate amplitude estimation of the reference signal. [0036] Referring now to FIG. 3A, an exemplary application of calibration in accordance with the present invention is illustrated. An ADC [0037] Thus, the switch [0038] Referring now to FIG. 3B, another exemplary application of calibration in accordance with the present invention is illustrated. The present invention also enables real-time calibration with two ADCs as shown generally at [0039] It should be noted that the calibration resources may be shared, except for the correction table [0040] Referring now to FIG. 4A, an exemplary ADC and an associated calibrator are illustrated with selected signals denoted in accordance with the present invention. An exemplary ADC [0041] Continuing with FIG. 4A, the ADC [0042] Referring now to FIG. 4B, exemplary details of one embodiment of calibration logic in accordance primarily with the invention of the parent application are illustrated. The calibrator [0043] Third, the correction calculator [0044] During functional operation mode, the digital output signal x(k) continues to be used to address the correction table [0045] Each of the functional units (components) shown in the calibrator [0046] Referring now to FIG. 4C, exemplary details of another embodiment of calibration logic in accordance primarily with the invention of the parent application are illustrated. The exemplary details of this calibration logic embodiment are designated generally by [0047] Multiple schemes have previously been proposed in order to calibrate ADCs. In fact, a calibration scheme has recently been proposed that works in the digital domain only in S. -H. Lee and B. -S. Song, “Digital-domain calibration of multistep analog-to-digital converters”, IEEE Journal on Solid-State Circuits, Vol. 27, No. 12, pp. 1679-1688, 1992, which is hereby incorporated by reference in its entirety herein. One drawback with a method such as the one in Lee and Song's article is that it requires accurate signal generators and measurement devices to measure the code errors. [0048] In contradistinction, the calibration scheme for ADCs in accordance with the present invention and/or invention of the parent application does not require such accurate signal generators and measurement devices. The scheme may be implemented fully digitally and completely in software. Furthermore, it does not require internal calibration circuitry. The calibration scheme does entail, on the other hand, a calibration signal connected to the ADC input. It also may include the storing of code errors directly in memory; consequently, the normal conversion is not slowed by error calculations. [0049] The calibration procedure utilizes a known waveform as the calibration signal, such as a sine wave signal, a sum of several sine wave signals, a saw-tooth signal, a triangle wave signal, etc. In an exemplary embodiment that is described below, the calibration scheme for sinusoidal calibration signals is described, but it should be understood that other waveform types may be employed. The scheme (primarily of the parent application) may be decomposed into the following exemplary functional blocks, each of which is described in further detail below: First is a processor for estimating the frequency of the analog input s(t), where the estimate {circumflex over (ω)} is computed from the quantized output x(k) of the ADC. Second is a linear time invariant FIR filter having as input the output x(k) of the ADC, such that characteristics of the filter include coefficients which are set to minimize the noise gain. The filter output ŝ(k) is a reconstruction of the analog calibration signal at the given sampling instants (in principle, a continuous-amplitude discrete-time signal). And, a third functional block is a processor for computing an updated reconstruction table in dependence upon x (k) and ŝ(k). [0050] A derivation of a calibration scheme primarily in accordance with the invention of the parent application is summarized in Table 1.
[0051] Initially, the calibration signal is sampled and quantized. The calibration signal s(t) is a continuous time (t[s] is the time instant) sine wave with frequency F [Hz], amplitude A [Volts] where A>0, and initial phase ø [radians], that is [0052] [0053] [0054] The frequency F is in the range (0, F [0055] where ω=2πF/F [0056] Consider a b-bits uniform quantizer. For simplicity, but without loss of generality, let the maximum swing of the ADC be ±1. Then, the resolution is
[0057] A b-bit quantized signal x(k)=Q [0058] where Q [0059] The model from (4)-(5), describing the quantized output of the ADC, is known to be valid for small quantization steps [0060] Δ and when s(k) traverses several quantization levels between two successive samples. [0061] A quality measure for ADCs is the signal-to-quantization noise ratio (SQNR) defined as the ratio of the signal power P to the power of the quantization noise, that is
[0062] where (5) was used in the second equality. For s(k) in (2), it holds that P=A [0063] Secondly, in order to reconstruct the calibration signal s(k) from the quantized inputs x(k), an L-th order FIR filter is employed, that is
[0064] Filter coefficients ({c [0065] The optimization problem to be solved is
[0066] where s(k) is the sine-wave in (2). This optimization problem was solved in P. Händel, “Predictive digital filtering of sinusoidal signals”, IEEE Transactions on Signal Processing, Vol. 46, No. 2, pp. 364-375, 1998, which is hereby incorporated by reference in its entirety herein, and the following result holds true
[0067] where
[0068] The reconstruction filter may be composed of (7) where the coefficients are determined by (10)-(13) with ω there replaced by an estimate {circumflex over (ω)}. Obtaining an estimate {circumflex over (ω)} from the A/D output x(k) is described below. [0069] Thirdly, the frequency of the calibration signal s(t) is estimated. The filter coefficients (10)-(13) do not depend on the initial phase or the amplitude of the calibration signal s(t); they only depend on ω. Several methods may be used to estimate the frequency of a noise corrupted sinusoidal signal. For example, D. C. Rife and R. R. Boorstyn, “Single tone parameter estimation from discrete-time observations”, IEEE Transactions on Information Theory, Vol. IT-20, No. 5, pp. 591-598, 1974, which is hereby incorporated by reference in its entirety herein, shows that frequency estimation may be mathematically characterized as
[0070] The maximization of (14) may be performed by aid of the fast Fourier transform followed by an iterative minimization. Using the estimate {circumflex over (ω)} from (14) in place of ω in (10)-(13) completes the reconstruction of s(k) from x(k). [0071] And fourthly, a reconstruction table may be updated using the following exemplary algorithm. The scheme is based on the expression for the optimal, in the sense that E[e(k) [0072] The quantized output, x(k), from the ADC has M=2 {x [0073] where x {s [0074] can be constructed from ŝ(k) as follows: Let s [0075] After the data has been processed, and the table has been updated, the operation of the quantizer becomes: The input signal produces a sample s(k) which is quantized to x(k)= x [0076] The formula in (17) calculates an average of estimates for every encountered level in the input signal x(k). An averaging process may be considered as similar to a low pass filter. Thus, for an implementation in which the number of calibration samples is limited (e.g., due to limited calibration time or arithmetic resolution in average calculation, for example), the averaging may be replaced with a low pass filter. Consequently, for a limited number of calibration samples per level, the formula (17) may be approximated with
[0077] Because the level of x(k) (which defines the variable “i”) acts as the address for the correction table [0078] Referring again to an alternative embodiment of the invention of the parent application as illustrated in FIG. 4C, the correction table [0079] Referring now to FIG. 5, a method in flowchart form for calibrating an ADC in accordance primarily with the invention of the parent application is illustrated. Flowchart [0080] The ADC is therefore calibrated by applying the entries in the correction data structure to the digital ADC outputs of a functional signal. Advantageously, the correction data structure may be updated continuously to account for, e.g., temperature drift. The method described in the flowchart [0081] The invention of the parent applications provides for calibration of ADCs working in a relatively narrow frequency band around the calibration signal frequency. However, the method of the parent application does not solve the problem of wide-band calibration of ADCs because the linearity errors that need to be compensated for are frequency dependent. [0082] The present invention provides for calibration of ADCs intended to operate in a broad frequency band. Certain embodiments of the present invention may involve the following exemplary aspects. Firstly, in order to deal with the frequency dependence of the linearity errors, calibration may be performed using a sequential multi-tone reference signal. That is, the reference signal may include several single-tone sinusoids at different frequencies in sequence. Secondly, the reference signal reconstruction is fully adaptive and performs both the frequency estimation and signal reconstruction on a sample-by-sample basis, enabling a more efficient implementation. The present invention minimizes the communication required between the calibration software and the peripheral calibration equipment (e.g., a sine-wave generator, switching devices, etc.) since the calibration algorithms autonomously detect the reference frequency and the instants at which the frequency changes. Thus, no advanced synchronization between the reference signal generator and the calibration software is needed. All of the calibration procedures can be performed on the digital side of the ADC, requiring only binary control logic/communication to indicate calibration versus correction between the analog and digital side. Thirdly, the calibration may be performed using discontinuous reference sequences of arbitrary length. This allows the ADC system to initiate a calibration sequence whenever suitable (e.g. when work load is low), terminate it at any time, and continue it again when possible. [0083] Referring now to FIG. 6A, exemplary details of one embodiment of calibration logic in accordance with the present invention are illustrated generally at [0084] As shown in FIG. 6A generally at [0085] ADC [0086] Recursive Frequency Estimator [0087] The recursive frequency estimator [0088] 1. Initialize the real scalar parameter {circumflex over (θ)} such that −2<{circumflex over (θ)}<2. [0089] 2. For each sample n, update {circumflex over (θ)} using {circumflex over (θ)}( [0090] 3. Estimate the discrete (angular) frequency ω of the input signal from {circumflex over (θ)}(n) using
[0091] 4. Increase n and repeat from step 2. [0092] The index ω is used to distinguish the step size and frequency estimate associated with the recursive frequency estimator from the same qualities associated with the reconstruction filter. Here μ [0093] where α is the amplitude of the ADC output x(n). Although the least-mean-square algorithm is used in this example, many other recursive algorithms known to those skilled in the art may be used instead. [0094] Adaptive Reconstruction Filter [0095] The signal reconstruction may be performed by a FIR filter, for example, that is updated using a constrained LMS algorithm. Referring now to FIG. 7 an exemplary embodiment of an adaptive reconstruction filter [0096] Let C=[c [0097] where L is the length of the filter, e.g., the number of filter coefficients. The filter coefficients are constrained to
[0098] through the properties of the filter update algorithm. The LMS algorithm may be normalized, e.g., the step size μ is dependent on the signal power ||X(n)|| [0099] As described hereinabove, the adaptive reconstruction filter interacts with the recursive frequency estimator. This interaction is necessary to ensure that the adaptive reconstruction filter converges to the global minimum, and not to any of the numerous local minima in the close neighborhood of the global minimum. The filter algorithm described hereinbelow ensures that the filter converges to a frequency close to that obtained from the recursive frequency estimator (within some tolerance δ{circumflex over (ω)} [0100] Adaptive Reconstruction Filter Algorithm [0101] An adaptive reconstruction filter scheme in accordance with certain embodiments of the present invention may be performed in seven main steps: [0102] 1. Initialize the filter coefficients using Equation 23 and a suitable ω, e.g. ω=π/2. [0103] 2. For each sample n, if {circumflex over (ω)} [0104] 3. Reconstruct ŝ(n):
[0105] If the value of track(n−1)=1 (as explained further hereinbelow under “Convergence Detection”) , then the adaptive reconstruction filter has converged, and the updating steps 4, 5, and 6 are not executed, e.g. processing may continue at step 7. [0106] 4. Calculate the step size μ:
[0107] 5. Update {circumflex over (ω)}:
[0108] 6. Update C:
[0109] 7. Increase n and repeat from step 2. [0110] The algorithm is stable when the normalized step size is 0<{overscore (μ)}<2, although {overscore (μ)} will typically be much less than 2 to achieve low-noise reconstruction of the sine wave. The convergence test threshold δ is a design variable that should be chosen with care. It is preferably small enough not to let {circumflex over (ω)} converge to a false minimum, yet large enough not to let the estimation noise in {circumflex over (ω)} [0111] Convergence Detection [0112] To detect whether the filter has converged or not, a convergence detector in the form of SINAD estimator [0113] where L [0114] The output track(n) of the convergence detector ultimately determines whether the present sample x(n) and the reconstructed signal ŝ(n) are used to update the correction table or not. Although in this example a SINAD detector is used to detect convergence of the adaptive filter, alternatively other convergence detectors known to those skilled in the art may be used. [0115] Updating the Correction Table [0116] The correction table of the correction table update block [0117] Correction table updating involves two main operations: [0118] 1. Initialize the correction table, e.g. s [0119] 2. For each sample n, if track(n)=1, update s [0120] In contradistinction to existing approaches, the correction table of the present invention is not reset when the reference signal changes frequency. Consequently, the correction table may be useable over a greater input frequency range than with prior approaches. One scheme for changing the frequency of the reference signal during calibration is the use of step-wise changes in frequency. The reference signal frequency is kept at a constant frequency for a long enough time for frequency adaptation and some table updates to be accomplished. This time period may be estimated or determined based on experimentation, for example. It should be noted that the step-sizes between calibration frequencies need not be equidistant. For example, frequency steps may be made denser around certain desired frequency subranges and less dense, or nonexistant, in other subranges. [0121] Correction Scheme [0122] Referring now to FIG. 6B, exemplary details of one embodiment of correction logic in accordance with the present invention are illustrated generally at [0123] Referring now to FIG. 8, an exemplary method in flowchart form for use in an ADC calibration procedure in accordance with the present invention is illustrated generally at [0124] Performance [0125] The performance of the calibration method of the present invention was evaluated using experimental data from an Analog Devices AD876 10-bit ADC. The experimental data used was composed of eight 32 K sequences (N=32768). The sequences were obtained using a sampling frequency F [0126] The calibration was performed using seven of the sequences, and correction was performed and evaluated on the eighth. The spurious-free dynamic range (SFDR) was calculated for the test signal before and after correction. Typically, the original converter is characterized by an uncompensated SFDR of 65 dB and a noise floor at approximately −90 dBFS. Referring now to FIGS. 9A and 9B, exemplary corrected (
[0127] The present invention has several advantages over preexisting approaches. One advantage is that the present invention is robust against variations in the analog reference signal because of the adaptivity of the reconstruction algorithms. Hence, the calibration signal generator does not have to be long-term stable, only relatively spectrally pure. Another advantage of the present invention is that the calibration scheme may be fully implemented in software. The calibration procedures are performed on the digital side of the ADC, requiring only binary control logic/communication for calibration and correction between the analog and digital side. Another advantage occurs as a result of the fact that the calibration algorithms are not real-time critical applications. If the sampled reference signal is stored in a memory, the calibration algorithms may be processed in the background on a low priority level while the ADC is in normal operation. Furthermore, sequential multi-tone calibration is advantageous due to its relatively simple implementation. The reference signal may be generated from a single voltage-controlled oscillator, which is a simplification compared to those calibration schemes that require a separate digital-to-analog converter. In another advantage, calibration may be performed using reference sequences of any length that are only longer than the settling time for the reconstruction filter. Moreover, the calibration procedures may be initiated, interrupted, and continued at any time suitable for or convenient to the rest of the system. [0128] Although preferred embodiment(s) of the method, arrangement, and system of the present invention have been illustrated in the accompanying Drawings and described in the foregoing Detailed Description, it will be understood that the present invention is not limited to the embodiment(s) disclosed, but is capable of numerous rearrangements, modifications, and substitutions without departing from the spirit and scope of the present invention as set forth and defined by the following claims. Referenced by
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