US20060092056A1 - Sample rate doubling using alternating adcs - Google Patents
Sample rate doubling using alternating adcs Download PDFInfo
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- US20060092056A1 US20060092056A1 US10/977,833 US97783304A US2006092056A1 US 20060092056 A1 US20060092056 A1 US 20060092056A1 US 97783304 A US97783304 A US 97783304A US 2006092056 A1 US2006092056 A1 US 2006092056A1
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M1/00—Analogue/digital conversion; Digital/analogue conversion
- H03M1/06—Continuously compensating for, or preventing, undesired influence of physical parameters
- H03M1/0617—Continuously compensating for, or preventing, undesired influence of physical parameters characterised by the use of methods or means not specific to a particular type of detrimental influence
- H03M1/0626—Continuously compensating for, or preventing, undesired influence of physical parameters characterised by the use of methods or means not specific to a particular type of detrimental influence by filtering
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M1/00—Analogue/digital conversion; Digital/analogue conversion
- H03M1/12—Analogue/digital converters
- H03M1/1205—Multiplexed conversion systems
- H03M1/121—Interleaved, i.e. using multiple converters or converter parts for one channel
- H03M1/1215—Interleaved, i.e. using multiple converters or converter parts for one channel using time-division multiplexing
Definitions
- IF Intermediate Frequency
- alternating ADCs that each sample at half of the desired sample rate (assuming that the bandwidth of the IF signal is less than or equal to double the first Nyquist intervals of each of the ADCs).
- I In-Phase
- Q Quadrature
- the I and Q signals are then each digitized by one of a pair of alternating ADCs that sample at one half F sample . Distortion is added to the signals because of non-ideal and non-matching frequency responses of the two ADCs. In fact, the frequency response mismatch of the two ADCs can eliminate much of the advantage of a two ADC system over a single ADC system.
- the I and Q signals are then processed by local oscillators that multiply the I digitized signal by a sequence of [1, ⁇ 1, 1 . . . ] and multiply the Q digitized signal by a sequence of [j, ⁇ j, . . . ].
- the frequency response corruption of each ADC can then be associated with the real or imaginary data streams.
- a single Finite Impulse Response (FIR) filter is used to eliminate the corruption of the data paths, with the output of the filter being reassembled into one digital signal that includes all of the information of the original analog signal.
- FIR Finite Impulse Response
- the conceptual separation of distortion into real and imaginary components provides the key to understanding that a single FIR filter can be implemented to correct for the frequency response mismatch of the two ADCs.
- the IF signal solution does not necessarily lead to a solution for correcting for frequency response mismatch between two ADCs in a system that digitizes a single analog baseband input signal. This is because a single analog baseband input signal cannot be separated into real and imaginary components.
- One embodiment of the invention includes a system comprising an analog baseband signal input, a conversion circuit with N Analog to Digital Converters (ADCs) operable to receive the analog baseband signal, and a Finite Impulse Response (FIR) filter operable to receive outputs of the N ADCs and to produce a digital representation of the analog baseband signal corrected for a mismatch in the N ADCs.
- ADCs Analog to Digital Converters
- FIR Finite Impulse Response
- correcting for frequency response mismatch in a dual-ADC system is accomplished by splitting the signal into even and odd paths, wherein the odd path signal is subjected to a time delay.
- the two paths are digitized by separate ADCs to produce even and odd digital representation components of the original analog baseband input signal.
- the even and odd components contain distortion from the frequency response mismatch between the two ADCs.
- the components are then input into a single FIR filter that applies 2 ⁇ 2 matrix filter taps. The result is corrected even and odd components that can be reassembled into a single digital signal that includes all of the information of the original analog baseband input signal.
- FIG. 1 is an illustration of one embodiment of the invention for performing sample rate doubling using alternating ADCs
- FIG. 2 is a flowchart of one embodiment of the invention for correcting for ADC mismatch
- FIG. 3 is an illustration of one embodiment of the invention for performing sample rate doubling using alternating ADCs.
- FIG. 4 is an illustration of one embodiment of the invention for performing sample rate tripling using three ADCs.
- FIG. 1 is an illustration of one embodiment of the invention in which system 100 is shown for performing sample rate doubling using alternating Analog to Digital Converters (ADCs).
- input 120 is an analog baseband signal that is provided to circuit 101 for digital conversion.
- circuit 110 includes an impulse response, illustrated by h(t) 101 .
- Impulse response 101 is the response for ADCs 104 and 105 , delay 102 , and additional components of the circuit that are not shown.
- impulse response 101 is determined by the characteristics of the various components of circuit 110 , it is illustrated as a separate component of circuit 110 for simplicity.
- Input 120 is provided to circuit 110 and split into two paths.
- the top path leads to ADC 104 .
- the bottom path leads to delay 102 and ADC 105 .
- ADCs 104 and 105 are both run by clock 103 . Accordingly, while both paths convert signal 120 into a digital signal, the lower path subjects input 120 to a time delay.
- ADCs 104 and 105 are alternating so that, in a given clock cycle, together they produce a set of samples corresponding to one delay of zero and one delay of T/2. The result is that ADCs 104 and 105 operate respectively to produce even and odd digital representation components 106 of analog input signal 120 .
- components 106 will represent all of the information in analog baseband signal input 120 as long as each ADC 104 and 105 samples input 120 at least at half of the desired sample frequency.
- ADCs 104 and 105 sample analog baseband signal input 120 at exactly the same time and operate with exactly the same parameters. Practical embodiments, however, show some degree of frequency response mismatch. The result of frequency response mismatch is that when components 106 are assembled into a single digital signal, there will be some amount of information distortion. Therefore, the accuracy of the digital representation will be degraded.
- Impulse response 101 includes the frequency response mismatch between ADCs 104 and 105 , and it is possible to use impulse response 101 to design filter 130 to effectively correct for the mismatch.
- System 100 includes Finite Impulse Response (FIR) filter 130 operable to receive outputs 106 of ADCs 104 and 105 , and to produce digital representation 107 of analog baseband signal input 120 corrected for the mismatch between ADCs 104 and 105 .
- FIR Finite Impulse Response
- a problem encountered in correcting for the frequency response mismatch between alternating ADCs is how to design a filter, such as FIR filter 130 , that can account for the fact that each of the digital representation components 106 are not complete representations of analog baseband signal input 120 . It is not as simple as putting a single filter behind each ADC 104 and 105 . A single filter that receives only the even or odd components will not have enough information to correctly filter the component because there is an infinite combination of first and second Nyquist interval signals that could combine to produce the same sequence of samples that are found in that component. Therefore, the filter that is needed is one that receives and conditions both the even and odd sampled components.
- the filter cross-couples both the even and odd components to compute the linear combination of all samples to produce the correct even samples and the linear combination of all samples to produce the correct odd samples.
- FIR filter 130 provides such a solution by incorporating a sequence of 2 ⁇ 2 matrix filter taps that are each computed using even and odd components of system impulse response 101 and are each applied to even and odd components of representation 106 .
- Equation 1 The desired signal processing of analog baseband signal input signal 120 , x(t), is given in Equation 1.
- T the sampling period of each ADC 104 and 105
- g(t) is the impulse response of the desired filtering to be applied to the signal.
- This response, g(t) has a bandwidth of less than 1/T in order for the composite sample rate to eliminate aliasing.
- This may be implemented, for example, as a flat pass band for the first Nyquist interval of x(t) with a transition band that rolls off rapidly to filter out frequencies of the second Nyquist interval.
- the filtering represented by g(t) may be a user's ideal analog-to-digital conversion of analog baseband signal input signal 120 , and it is usually chosen by the user.
- Splitting impulse response 101 into h 1 (t) and h 2 (t) is a way of adapting response 101 to the vector notation used herein.
- each of the two paths have individual impulse responses. It should be noted that, similar to Equation 1, the right hand side represents an array of discrete sample values. Further, the bandwidth of h 1 (t) and h 2 (t) is assumed to be less than 1/T.
- the integration and summation can now be reordered. Also, since the dummy integration variable is the same for both elements of each vector, the integration can be performed with the integrand being a scalar multiplied by a vector, as in Equation 6.
- the impulse responses g, h 1 , and h 2 are all fully specified with time samples spaced at intervals of T/2.
- the constraint at both of these time points can be written into a single matrix equation, as in Equation 8.
- Equation 9 [ h 1 ⁇ ( nT ) h 1 ⁇ ( nT - T / 2 ) h 2 ⁇ ( nT ) h 2 ⁇ ( nT - T / 2 ) ] ( 9 )
- g n [ g ⁇ ( nT ) g ⁇ ( nT - T / 2 ) g ⁇ ( nT + T / 2 ) g ⁇ ( nT ) ] ( 10 )
- Equation 11 The desired set of coefficient matrices, q m , is found by solving a matrix convolution equation, as in Equation 11.
- N The length of the transform, N, should be long enough to encompass the complete impulse responses g, h 1 , and h 2 .
- Equation 15 Making this substitution and limiting the number of filter taps gives Equation 15. Note that the filter taps are non-zero only in the range 0 through N ⁇ 1, such that the non-zero range is implemented cyclically in Equation 15. Thus, N must be chosen to be large enough to encompass the complete compensation filter impulse response, q m . In general this will be somewhat longer than the g and h responses. Making N too small will limit the degrees of freedom needed to produce a good calibration response.
- Equation 16 can be manipulated to solve for the frequency response of the desired calibration filter, as in Equation 17.
- the transformed matrix elements are complex, so the indicated multiplication requires complex operations.
- the transformed matrices have conjugate symmetry with respect to the k index modulo N. This fact can be utilized to reduce the variable storage and computation time.
- Q k G k H k ⁇ 1 (17)
- Equation 18 To get the impulse response now requires taking the inverse Fourier transform, as in Equation 18.
- the output, q m is a sequence of N 2 ⁇ 2 matrices that is cycled through continuously by FIR filter 130 .
- Each of the individual matrices is a filter tap to be used by FIR filter 130 to correct for the mismatch of ADCs 104 and 105 .
- q m will hold for other signals that do not exceed the Nyquist frequency, 1/T.
- FIG. 2 is a flowchart embodiment showing method 200 for correcting for ADC mismatch.
- Process 201 determines h 1 (t) and h 2 (t).
- a well-controlled, known test input may be used as the analog baseband signal input for circuit 110 ( FIG. 1 ).
- the outputs of ADCs 104 and 105 are sampled and recorded at intervals of T/2. Substituting these values into Equation 2 above will yield a relation that may be manipulated to solve for discrete values of h 1 (t) and h 2 (t).
- Impulse responses h 1 (t) and h 2 (t) represent not only the impulse response of circuit 110 , but also the time offset error between ADCs 104 and 105 .
- Process 202 selects a desired frequency response, g(t).
- the desired frequency response is one wherein the ADCs have little or no frequency response mismatch, and it may even be mathematically ideal, theoretically eliminating mismatch totally.
- Process 203 samples and records the desired frequency response at intervals of T/2. This step puts the frequency response into a discrete form that can be used in Equations 4-18 above.
- Process 204 forms the array of matrices defined in Equations 9 and 10, using the sampled, recorded responses from blocks 201 and 203 .
- Process 205 performs the Fourier Transforms of Equation 13 on the matrices of Equations 9 and 10, wherein the array of individual matrix elements is treated as a real data sequence. This yields the frequency domain matrices of Equation 16.
- Process 206 inverts each H matrix array in the array to perform the multiplication of Equation 17. This step is performed matrix-by-matrix across the entire array of matrices.
- Process 207 performs the inverse Fourier Transform of Equation 18 on the results of the step of block 206 .
- the array of individual matrix elements is treated as a complex data sequence for the inverse Fourier Transform. This step yields the array of vectors, q m .
- Process 208 implements q m in FIR filter 130 to correct for frequency response mismatches between ADCs 104 and 105 (all of FIG. 1 ). Accordingly, any analog baseband input signal 120 , which does not exceed the Nyquist frequency of 1/T, may be input into circuit 110 , conditioned by filter 130 , and output as an accurate digital representation 107 of that original analog input signal 120 .
- FIG. 3 is one embodiment of system 300 for performing sample rate doubling using alternating ADCs. It is similar to system 100 , but instead of employing a delay element (such as element 102 of FIG. 1 ), system 300 uses advanced (or, alternatively, delayed) clock 301 . The result is the same as in system 100 —even and odd digital representation components 106 are produced at the outputs of ADCs 104 and 105 .
- the invention is not limited to any particular process of producing even and odd digital representation components of an input analog baseband signal, and other alternative embodiments are within the scope of the invention.
- Even and odd digital representation components are one example of a more general complementary relationship between sampled digital components when exactly two sampled components exist. As explained below, the complementary relationship may be generalized to encompass embodiments that include more than two sampled digital components.
- the above example embodiments utilize an FIR filter with 2 ⁇ 2 matrix taps.
- the present invention may be expanded to cover embodiments wherein the filter employs larger matrix taps.
- FIG. 4 is one embodiment of system 400 for performing sample rate tripling using three ADCs 401 - 403 .
- the rate of sampling may be tripled by employing three ADCs in the arrangement shown.
- ADC 401 has zero delay at its input, while ADC 402 has T/3 delay 405 to its input, and ADC 403 has 2T/ 3 delay 405 to its input.
- ADCs 401 - 403 are conceptually cyclic, so that, in a given clock cycle, together they produce a set of samples that includes a sample delayed by zero, a sample delayed by T/3, and a sample delayed by 2T/ 3 .
- system 400 uses three complementary components 406 that are delayed in a manner analogous to the delay in the two-ADC embodiments above.
- FIR filter 407 in this case, is a 3 ⁇ 3 filter.
- the computation of the matrix filter taps is similar to that of the 2 ⁇ 2 matrix taps, such that Equations 3, 11, and 16-18 hold true, however the intermediate calculation equations must be adapted for use of 3-element vectors and 3 ⁇ 3 matrices.
- N is not necessarily the same as that used in Equation 14, above
- the FIR filter applies N ⁇ N matrix taps to complementary digital representation components to correct for mismatch of the ADCs.
- ADCs 104 and 105 may be seen as taking samples at alternating times during time periods, T, with filter 130 (of FIG. 1 ) applying coefficients to even and odd samples at alternating times.
- This can be represented as time-varying, piecemeal equations, wherein filter 130 applies one set of coefficients during certain times to the even components and other sets of coefficients at other times to the odd components.
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Abstract
Description
- In the filed of signal receivers, converting both broadband and baseband analog signals to digital signals involves an inherent trade-off between Analog to Digital Converter (ADC) sample rate and accuracy. Designers are faced with the choice of using a faster ADC that may lack a high degree of accuracy or using a lower sample rate ADC that has more accuracy. Oftentimes, the choice is made for the designer because the frequency of the received signal, Fsignal, dictates the minimum sample rate, Fsample, that must be used to avoid aliasing. Typically this would be 2Fsignal=Fsample.
- One approach that has seen some success in the conversion of Intermediate Frequency (IF) signals is to use alternating ADCs that each sample at half of the desired sample rate (assuming that the bandwidth of the IF signal is less than or equal to double the first Nyquist intervals of each of the ADCs). First, the IF signal is converted into one In-Phase (I) and one Quadrature (Q) signal (i.e., I/Q baseband signals). The I and Q signals are then each digitized by one of a pair of alternating ADCs that sample at one half Fsample. Distortion is added to the signals because of non-ideal and non-matching frequency responses of the two ADCs. In fact, the frequency response mismatch of the two ADCs can eliminate much of the advantage of a two ADC system over a single ADC system.
- In one solution, the I and Q signals are then processed by local oscillators that multiply the I digitized signal by a sequence of [1, −1, 1 . . . ] and multiply the Q digitized signal by a sequence of [j, −j, . . . ]. This results in a clean, conceptual separation of I and Q samples between the real and imaginary paths for subsequent processing. The frequency response corruption of each ADC can then be associated with the real or imaginary data streams. A single Finite Impulse Response (FIR) filter is used to eliminate the corruption of the data paths, with the output of the filter being reassembled into one digital signal that includes all of the information of the original analog signal.
- The conceptual separation of distortion into real and imaginary components provides the key to understanding that a single FIR filter can be implemented to correct for the frequency response mismatch of the two ADCs. However, the IF signal solution does not necessarily lead to a solution for correcting for frequency response mismatch between two ADCs in a system that digitizes a single analog baseband input signal. This is because a single analog baseband input signal cannot be separated into real and imaginary components.
- One embodiment of the invention includes a system comprising an analog baseband signal input, a conversion circuit with N Analog to Digital Converters (ADCs) operable to receive the analog baseband signal, and a Finite Impulse Response (FIR) filter operable to receive outputs of the N ADCs and to produce a digital representation of the analog baseband signal corrected for a mismatch in the N ADCs.
- In another embodiment of the invention, correcting for frequency response mismatch in a dual-ADC system is accomplished by splitting the signal into even and odd paths, wherein the odd path signal is subjected to a time delay. The two paths are digitized by separate ADCs to produce even and odd digital representation components of the original analog baseband input signal. The even and odd components contain distortion from the frequency response mismatch between the two ADCs. To correct for the mismatch, the components are then input into a single FIR filter that applies 2×2 matrix filter taps. The result is corrected even and odd components that can be reassembled into a single digital signal that includes all of the information of the original analog baseband input signal.
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FIG. 1 is an illustration of one embodiment of the invention for performing sample rate doubling using alternating ADCs; -
FIG. 2 is a flowchart of one embodiment of the invention for correcting for ADC mismatch; -
FIG. 3 is an illustration of one embodiment of the invention for performing sample rate doubling using alternating ADCs; and -
FIG. 4 is an illustration of one embodiment of the invention for performing sample rate tripling using three ADCs. -
FIG. 1 is an illustration of one embodiment of the invention in whichsystem 100 is shown for performing sample rate doubling using alternating Analog to Digital Converters (ADCs). In this example,input 120 is an analog baseband signal that is provided tocircuit 101 for digital conversion. As with any circuit,circuit 110 includes an impulse response, illustrated by h(t) 101.Impulse response 101 is the response forADCs delay 102, and additional components of the circuit that are not shown. Althoughimpulse response 101 is determined by the characteristics of the various components ofcircuit 110, it is illustrated as a separate component ofcircuit 110 for simplicity. -
Input 120 is provided tocircuit 110 and split into two paths. The top path leads to ADC 104. The bottom path leads todelay 102 andADC 105. In this embodiment, ADCs 104 and 105 are both run byclock 103. Accordingly, while both paths convertsignal 120 into a digital signal, the lower path subjects input 120 to a time delay. Conceptually,ADCs ADCs digital representation components 106 ofanalog input signal 120. Neither component by itself represents all of the information contained in analogbaseband signal input 120 becauseADCs components 106 will represent all of the information in analogbaseband signal input 120 as long as eachADC - Ideally, ADCs 104 and 105 sample analog
baseband signal input 120 at exactly the same time and operate with exactly the same parameters. Practical embodiments, however, show some degree of frequency response mismatch. The result of frequency response mismatch is that whencomponents 106 are assembled into a single digital signal, there will be some amount of information distortion. Therefore, the accuracy of the digital representation will be degraded. -
Impulse response 101 includes the frequency response mismatch betweenADCs impulse response 101 to designfilter 130 to effectively correct for the mismatch.System 100 includes Finite Impulse Response (FIR)filter 130 operable to receiveoutputs 106 ofADCs digital representation 107 of analogbaseband signal input 120 corrected for the mismatch betweenADCs - A problem encountered in correcting for the frequency response mismatch between alternating ADCs is how to design a filter, such as
FIR filter 130, that can account for the fact that each of thedigital representation components 106 are not complete representations of analogbaseband signal input 120. It is not as simple as putting a single filter behind eachADC FIR filter 130 provides such a solution by incorporating a sequence of 2×2 matrix filter taps that are each computed using even and odd components ofsystem impulse response 101 and are each applied to even and odd components ofrepresentation 106. - The process of calculating the correct FIR filter taps will now be explored. The following equations treat each pair of even and odd
digital representation components 106 as a two-element vector. Performing the calculations with vectors and matrices is done for the convenience of the notation, sincesystem 100 uses alternatingADCs ADCs - The desired signal processing of analog baseband
signal input signal 120, x(t), is given in Equation 1.
where T is the sampling period of eachADC signal input signal 120, and it is usually chosen by the user. - However, the
actual output signal 106 from circuit 110 (a dual-ADC front end) is represented by Equation 2:
where h1(t) is the impulse response from the input connector through even-sample ADC 104, and h2(t) is the impulse response from the input connector through odd-sample ADC 105. Splittingimpulse response 101 into h1(t) and h2(t) is a way of adaptingresponse 101 to the vector notation used herein. It also expresses that each of the two paths have individual impulse responses. It should be noted that, similar to Equation 1, the right hand side represents an array of discrete sample values. Further, the bandwidth of h1(t) and h2(t) is assumed to be less than 1/T. - The goal is to determine the appropriate calibration filter response, qn, of
filter 130.Equation 3 represents the relationship of qn, yn, and xn. As shown below,Equation 3 can be manipulated to calculate qn.
y n =q n {circle around (×)}x n (3) -
Equation 3 can be rewritten as Equation 4 by explicitly writing out the convolution integrals:
where the new dummy integration variable τ=τ′+½. This does not change the integration result because of the infinite bounds. Similarly, the discrete sample data convolution summation can be written out explicitly, as in Equation 5. - The integration and summation can now be reordered. Also, since the dummy integration variable is the same for both elements of each vector, the integration can be performed with the integrand being a scalar multiplied by a vector, as in Equation 6.
- It is desirable to enforce Equation 6 to hold true for any arbitrary input signal x(t) and for all values of n and t. Accordingly, this is relationship is expressed as Equation
- Because of the bandwidth limits on the filters, the impulse responses g, h1, and h2, are all fully specified with time samples spaced at intervals of T/2. Thus, the constraint above need only be evaluated at discrete time points t=0 and t=T/2. The constraint at both of these time points can be written into a single matrix equation, as in Equation 8.
- It is now useful to define the following matrices in
Equations - The desired set of coefficient matrices, qm, is found by solving a matrix convolution equation, as in Equation 11.
- This solution can be approached by transforming the matrices to the frequency domain in order to avoid performing convolution. The length of the transform, N, should be long enough to encompass the complete impulse responses g, h1, and h2.
- Substitute p=n−m. This changes the limits on the rightmost summation.
- The limits on the rightmost summation may be adjusted to be independent of m if the value being summed is periodic in N. This is accomplished by replacing h with h′ which is a cyclic version of the finite duration impulse response, as expressed in Equation 14.
h′p=hp mod N (14) - Making this substitution and limiting the number of filter taps gives Equation 15. Note that the filter taps are non-zero only in the range 0 through N−1, such that the non-zero range is implemented cyclically in Equation 15. Thus, N must be chosen to be large enough to encompass the complete compensation filter impulse response, qm. In general this will be somewhat longer than the g and h responses. Making N too small will limit the degrees of freedom needed to produce a good calibration response.
- Each of the summations in Equation 15 represents a Fourier transform. Using capitals letters to denote the transforms yields Equation 16.
G k =Q k H k (16) - Equation 16 can be manipulated to solve for the frequency response of the desired calibration filter, as in
Equation 17. Note that the transformed matrix elements are complex, so the indicated multiplication requires complex operations. Also, note that since the original time domain matrices are real, the transformed matrices have conjugate symmetry with respect to the k index modulo N. This fact can be utilized to reduce the variable storage and computation time.
Q k =G k H k −1 (17) - To get the impulse response now requires taking the inverse Fourier transform, as in
Equation 18. - The output, qm, is a sequence of
N 2×2 matrices that is cycled through continuously byFIR filter 130. Each of the individual matrices is a filter tap to be used byFIR filter 130 to correct for the mismatch ofADCs -
FIG. 2 is a flowchartembodiment showing method 200 for correcting for ADC mismatch.Process 201 determines h1(t) and h2(t). Various ways exist to determine h1(t) and h2(t). For example, a well-controlled, known test input may be used as the analog baseband signal input for circuit 110 (FIG. 1 ). The outputs ofADCs Equation 2 above will yield a relation that may be manipulated to solve for discrete values of h1(t) and h2(t). Impulse responses h1(t) and h2(t) represent not only the impulse response ofcircuit 110, but also the time offset error betweenADCs -
Process 202 selects a desired frequency response, g(t). The desired frequency response is one wherein the ADCs have little or no frequency response mismatch, and it may even be mathematically ideal, theoretically eliminating mismatch totally. - Process 203 samples and records the desired frequency response at intervals of T/2. This step puts the frequency response into a discrete form that can be used in Equations 4-18 above.
- Process 204 forms the array of matrices defined in
Equations blocks -
Process 205 performs the Fourier Transforms ofEquation 13 on the matrices ofEquations -
Process 206 inverts each H matrix array in the array to perform the multiplication ofEquation 17. This step is performed matrix-by-matrix across the entire array of matrices. -
Process 207, performs the inverse Fourier Transform ofEquation 18 on the results of the step ofblock 206. The array of individual matrix elements is treated as a complex data sequence for the inverse Fourier Transform. This step yields the array of vectors, qm. -
Process 208 implements qm inFIR filter 130 to correct for frequency response mismatches betweenADCs 104 and 105 (all ofFIG. 1 ). Accordingly, any analogbaseband input signal 120, which does not exceed the Nyquist frequency of 1/T, may be input intocircuit 110, conditioned byfilter 130, and output as an accuratedigital representation 107 of that originalanalog input signal 120. -
FIG. 3 is one embodiment ofsystem 300 for performing sample rate doubling using alternating ADCs. It is similar tosystem 100, but instead of employing a delay element (such aselement 102 ofFIG. 1 ),system 300 uses advanced (or, alternatively, delayed)clock 301. The result is the same as insystem 100—even and odddigital representation components 106 are produced at the outputs ofADCs - The above example embodiments utilize an FIR filter with 2×2 matrix taps. The present invention, however, may be expanded to cover embodiments wherein the filter employs larger matrix taps.
-
FIG. 4 is one embodiment ofsystem 400 for performing sample rate tripling using three ADCs 401-403. Just as in the last examples, wherein the rate of sampling of a circuit is doubled by using two ADCs, the rate of sampling may be tripled by employing three ADCs in the arrangement shown.ADC 401 has zero delay at its input, whileADC 402 has T/3delay 405 to its input, andADC 403 has 2T/3delay 405 to its input. ADCs 401-403 are conceptually cyclic, so that, in a given clock cycle, together they produce a set of samples that includes a sample delayed by zero, a sample delayed by T/3, and a sample delayed by 2T/3. - It can be seen that, rather than using even and odd digital representation components (such as
components 106 ofFIG. 1 ),system 400 uses threecomplementary components 406 that are delayed in a manner analogous to the delay in the two-ADC embodiments above.FIR filter 407, in this case, is a 3×3 filter. The computation of the matrix filter taps is similar to that of the 2×2 matrix taps, such thatEquations 3, 11, and 16-18 hold true, however the intermediate calculation equations must be adapted for use of 3-element vectors and 3×3 matrices. - Other multiple-ADC embodiments are possible and are within the scope of the invention. In fact, the number of ADCs may be increased to N (“N” is not necessarily the same as that used in Equation 14, above), wherein the FIR filter applies N×N matrix taps to complementary digital representation components to correct for mismatch of the ADCs.
- It should be noted that the computation of the taps of
filter 130 is performed using matrices and vectors, effectively representing the even and odd samples as pairs that have been taken simultaneously and the filter coefficients as sets of four coefficients that are applied simultaneously. From another point of view,ADCs 104 and 105 (ofFIG. 1 ) may be seen as taking samples at alternating times during time periods, T, with filter 130 (ofFIG. 1 ) applying coefficients to even and odd samples at alternating times. This can be represented as time-varying, piecemeal equations, whereinfilter 130 applies one set of coefficients during certain times to the even components and other sets of coefficients at other times to the odd components. Applications using either view are within the scope of the various embodiments, and those of skill in the art will understand that the two approaches are mathematically equivalent. - Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the invention as defined by the appended claims. Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one will readily appreciate from the disclosure, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.
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US10/977,833 US7049992B1 (en) | 2004-10-29 | 2004-10-29 | Sample rate doubling using alternating ADCs |
DE102005039684A DE102005039684A1 (en) | 2004-10-29 | 2005-08-22 | Sample rate doubling using alternating ADCS |
GB0521294A GB2419482A (en) | 2004-10-29 | 2005-10-19 | Analog to digital signal conversion circuit and method |
JP2005316280A JP2006129499A (en) | 2004-10-29 | 2005-10-31 | Method and system for doubling sample rate using alternating adc |
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WO2010044838A2 (en) * | 2008-10-13 | 2010-04-22 | National Semiconductor Coropration | Continuous synchronization for multiple adcs |
US20120206285A1 (en) * | 2010-08-13 | 2012-08-16 | Rf Micro Devices, Inc. | Half-bandwidth based quadrature analog-to-digital converter |
US20150003221A1 (en) * | 2013-06-28 | 2015-01-01 | Seagate Technology Llc | Time-multiplexed single input single output (siso) data recovery channel |
US9281832B1 (en) * | 2014-12-31 | 2016-03-08 | Texas Instruments Incorporated | Circuits and methods for bandwidth estimation optimization of analog to digital converters |
CN110352561A (en) * | 2017-02-28 | 2019-10-18 | 索尼半导体解决方案公司 | Analog-digital converter, solid-state imaging element and electronic equipment |
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Also Published As
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DE102005039684A1 (en) | 2006-05-24 |
GB2419482A (en) | 2006-04-26 |
US7049992B1 (en) | 2006-05-23 |
JP2006129499A (en) | 2006-05-18 |
GB0521294D0 (en) | 2005-11-30 |
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