Entropy encoder/decoder including a context extractor

Abstract: In entropy, e.g., arithmetic or adaptive Huffman, encoding/decoding a context based on prior symbols is needed to provide accurate predictions of symbols to be encoded/decoded. Encoding/decoding efficiency is improved by employing an adaptive context extractor (105). The adaptive context extractor (105) automatically adjusts the configuration of the lag intervals used to define the context. This is realized by adaptively incorporating into the context configuration at least one lag interval found to have a "good" predictive value relative to the particular symbol stream being encoded/decoded. The context configuration adjustment is such that the at least one found lag interval is exchanged with the lag interval currently in an at least one so-called floating predictor position.

Description: Technical Field This invention relates to the coding of signals and, more particularly, to a context extractor for entropy encoding/decoding. Background of the Invention It is known that in an entropy encoder/decoder, e.g., arithmetic or adaptive Huffman, a probability estimate is required of the current symbol to be encoded/decoded. The probability estimate is usually conditional in the sense that it is dependent on values of the signal at prior symbol times. The particular choice of the positions of prior symbols to be used in predicting the current symbol is called the "context configuration" in entropy encoding/decoding. In general, a large context configuration referencing many prior symbols will provide a more accurate prediction of the current symbol. A problem with using such a large context configuration is that it is complex to implement since it requires a large memory. Additionally, it will cause a probability estimator to take a significantly longer time to reach "good" estimates of probability. Indeed, during intervals of changing signal statistics the probability estimator may be unable to track the changes with a consequent reduction in encoding/decoding efficiency. Prior known entropy encoders/decoders have heretofore employed fixed context configurations. A problem with such arrangements is that if a particular symbol positioned prior to the current symbol by a particular number of symbol intervals, i.e., a particular "lag" interval, happened to be an excellent predictor of the current symbol but its lag interval was not in the fixed context configuration, its predictive value would not be exploited. Consequently, this limited the efficiency of the encoders/decoders. An arithmetic encoder/decoder arrangement for compressing data for transmission is disclosed in WO-A-86/00479. An entropy encoder/decoder arrangement employing content extraction and probability estimates as set out in the preamble of claims 1 and 10 and carrying out the method set out in the preamble of claim 9 is described in an ISO standard by R.P. Arps and R.C. Pasco entitled 'Progressive Binary Image Compressor (PBIC) Proposal', ISO International Organisation for Standardisation, ISO/IEC/JTC1/SC2/WG8 JBIG No. 33, Rev 6, 28th June 1989, pages 1-37. Summary of the Invention The problems and other limitations of prior known entropy encoders/decoders are overcome, in accordance with an aspect of the invention, by employing an adaptive context extractor. More specifically, an adaptive context extractor is employed which automatically adjusts the configuration of lag intervals used to define the context. This is realized by adaptively incorporating into the context configuration at least one prior symbol at a lag interval found to have a good predictive value relative to the particular symbol stream being currently encoded/decoded. The context configuration adjustment is such that the at least one found lag interval is exchanged with the lag interval currently in an at least one so-called floating predictor position. In an embodiment of the invention, an adaptive context extractor is used in which so-called running measures are obtained and retained of the correlation between signal values separated by fixed lag intervals. If a "high" degree of correlation, either positive or negative, is found at some particular lag interval, the prior symbol preceding the current symbol being encoded/decoded by that particular lag interval is incorporated into the context configuration. Brief Description of the Drawing In the Drawing: FIG. 1 shows details of an arrangement employing an encoder and remote decoder employing an embodiment of the invention; FIG. 2 is a graphic illustration of symbols used in adaptively obtaining a context; FIG. 3 is a graphic illustration useful in describing the adaptive incorporation of at least one prior lag interval into the context configuration; FIG. 4 depicts a flow chart illustrating the operation of elements of the adaptive context extractor employed in the encoder and decoder shown in FIG. 1; and FIG. 5 shows a flowchart of the context configuration changer employed in the flowchart of FIG. 4. Detailed Description FIG. 1 shows details of encoder 101 in simplified block diagram form, including aspects of the invention, which receives data symbols s(k), encodes them into a compressed data stream a(i) and interfaces them to a transmission media 102 for transmission to remote decoder 103. Decoder 103, also including aspects of the invention, interfaces to transmission media 102 to obtain the received data stream and decodes it to obtain reconstructed replicas of the original symbols s(k). Symbols s(k) are chosen from the integers [0,...,S-1]. Thus, the symbols may be multi-level (S>2) or bi-level (S=2) as desired. The assumption that the symbol values are positive integers is for clarity of exposition. Generalizations allowing symbols to take on other than integer values will be obvious to those skilled in the art. Accordingly, encoder 101 includes, in this example, entropy encoder unit 104, adaptive context extractor 105, probability estimator 106 and line interface 107. Context c(k) is provided, in accordance with an aspect of the invention, and is supplied to probability estimator 106. Symbols s(k) and probability estimates (k) are supplied to entropy encoder unit 104 and employed therein in known fashion to generate an encoded data stream a(i). Such entropy encoder units are known in the art and may be, for example, an arithmetic encoder or an adaptive Huffman encoder. See, for example, an article entitled "Compression of Black-White Image with Arithmetic Coding", IEEE Transactions On Communications, VOL. COM.-29, No. 6, June 1981, pages 858-867, and U.S. patent 4,663,490 issued December 30, 1986 for arithmetic encoders/decoders used to encode and decode symbols having binary elements. Also see an article entitled, Arithmetic Coding For Data Compression", Communications of the ACM, Volume 30, No. 6, June 1987, pages 520-540, for an arithmetic encoder/decoder used to encode/decode symbols having multi-level elements. For Huffman type encoders/decoders see an article entitled "Compression of Text and Binary Files Using Adaptive Huffman Coding Techniques", IEEE Southeast Conference, April 11-13, 1988, Knoxville, Tenn., pages 660-663. Line interface 107 interfaces the encoded data stream a(i) to transmission media 102 which, in turn, supplies the data stream to remote decoder 103. To this end, line interface 107 includes appropriate apparatus for formatting the data stream into the signal format employed in transmission media 102. Some well known examples of possible transmission media 102 are T-carrier trunks, ISDN basic subscriber lines, local area networks and the like. Such line interface apparatus is known in the art. Probability estimator 106 is advantageously employed to generate probability estimates (k)=(p and₀ (k),..., p and S-1 (k)) for incoming symbol s(k)ε [0,...,S-1] and associated context c(k)ε [0,...,C-1] from adaptive context extractor 105. Any of a number of known probability estimators may be used for probability estimator 106. Adaptive context extractor 105 provides, in accordance with an aspect of the invention, the context c(k), where c(k)ε[0,...,C-1], of received symbol s(k). That is to say, adaptive context extractor 105 generates a unique context for the current symbol s(k) being encoded dependent on prior supplied symbols. Adaptive context extractor 105 can be readily implemented by appropriately programming a computer or digital signal processor. It is envisioned, however, that a superior mode of implementation is in a very large scale integrated (VLSI) circuit configuration on a semiconductor chip. For brevity and clarity of description, a specific embodiment of the invention will be described relating to images (two dimensional data) in which pixels, i.e., picture elements, are represented by bi-level signals. It will be apparent to those skilled in the art how to apply the invention to multi-level signals or how to apply the invention to signals that are not of dimensionality two. Speech is an example of a one dimensional, multi-level signal and video is an example of a three dimensional, multi-level signal. Accordingly, shown in FIG. 2 are a number of pixel positions, where position X indicates the current pixel to be encoded corresponding to a current symbol s(k), the lag intervals ℓ * / 0 through ℓ * / 6 point to positions of prior pixels (symbols) in a so-called fixed portion of a context configuration used in providing context c(k) for predicting X, the pixel position at lag interval ℓ * / 7 is a candidate position and is designated a so-called floating predictor position that is initially included in the context configuration along with the fixed portion and pixel positions at lag intervals ℓ * / 8 through ℓ * / 16 also point to candidate pixels. That is to say, the context configuration includes a fixed portion and a so-called floating portion including at least one floating predictor position. In this example, the pixel positions at lag intervals ℓ * / 0, ℓ * / 1 and ℓ * / 7 through ℓ * / 16 are in the same row of an image as the current pixel position X, while the pixel positions at lag intervals ℓ * / 2 through ℓ * / 6 are in a prior row and in a prescribed relationship to current pixel position X. A pixel in at least one of the positions at lag intervals ℓ * / 7 through ℓ * / 16 is controllably selected, in accordance with an aspect of the invention, to be included in the floating predictor position ℓ₇ in the context configuration. Accordingly, in this example, the initial context configuration includes the prior pixels in the positions at lag intervals ℓ * / 0 through ℓ * / 6 and floating predictor position ℓ * / 7. FIG. 3 is a graphic illustration of an aspect of the operation of the invention in adaptively incorporating pixels (symbols) at particular lag intervals from the candidate set into the context configuration. Although the example being described assumes that only one lag interval from the candidate set is to be incorporated into the context configuration, it will be apparent to those skilled in the art that more than one lag interval could be incorporated, if desired. In this example, the number of pixels (symbols) in a row is is denoted by R and a so-called fixed portion of the context configuration includes pixels in positions at lag intervals ℓ * / 0 through ℓ * / 6, where ℓ * / 0=1, ℓ * / 1=2, ℓ * / 2=R-2 (prior row and two to the right), ℓ * / 3=R-1, ℓ * / 4=R, ℓ * / 5=R+1 and ℓ * / 6=R+2. The current floating predictor position is at lag interval ℓ₇=ℓ * / 7=3. The remaining candidate positions are at lag intervals ℓ₈= ℓ * / 8=4, ℓ₉ = ℓ * / 9=5, ℓ₁₀ = ℓ * / 10=6, ℓ₁₁ = ℓ * / 11=7, ℓ₁₂ = ℓ * / 12=8, ℓ₁₃ = ℓ * / 13=9, ℓ₁₄ = ℓ * / 14=10, ℓ₁₅ = ℓ * / 15=11 and ℓ₁₆ = ℓ * / 16=12. If at a later time it is determined that a pixel at a lag interval in another of the candidate positions is a significantly better predictor for X than the pixel at lag interval ℓ₇=3, then that lag interval is adaptively exchanged, in accordance with an aspect of the invention, with the lag interval currently in the floating predictor position of the context configuration, i.e., ℓ₇, and thereby incorporated into the context configuration. For example, as shown in FIG. 3, if at some later time the pixel referenced by ℓ₁₀ (that is, six (6) positions to the left of the current pixel X) is determined to be a significantly better predictor for the current pixel X than is the pixel referenced by ℓ₇ (that is, three (3) positions to the left of the current pixel X), then ℓ₇ is changed to ℓ * / 10 while ℓ₁₀ is changed to ℓ * / 7. Since the pixel referenced by ℓ₇ is the pixel incorporated into the context configuration, the pixel at lag interval ℓ * / 10 will now be in the context configuration. That is to say, the pixel six (6) positions to the left of the current pixel X is adaptively exchanged for the pixel three (3) positions to the left of the current pixel X. Continuing, if at some still later time it is determined that a pixel located at a different lag interval is now a significantly better predictor for current pixel X, that lag interval will be adaptively exchanged for ℓ₇ (now ℓ * / 10). Thus, in the example of FIG. 3, the pixel at lag internal ℓ₁₂ (eight (8) positions to the left of current pixel X) is determined to be a significantly better predictor and the lag interval ℓ₁₂ is adaptively exchanged for ℓ₇ = ℓ * / 10=6. The context configuration remains fixed until the next adaptive exchange, i.e., adjustment, is made. In this manner the context configuration is adaptively adjusted, in accordance with an aspect of the invention. It is to be noted that any new lag interval being considered for movement to the at least one floating predictor position must reference a significantly better predictor than is referenced by the current floating predictor lag interval because it is undesirable to change the context configuration too often. The reason for this is that once the context configuration is changed, it takes some time for probability estimator 106 to stabilize and learn the new probability values. During this time the performance of the entropy encoder is suboptimal. Consequently, in considering changing the predictors in the context, possible improvement in the prediction quality must be balanced against the time required to learn the new probability estimates. The flow chart shown in FIG. 4 depicts the operation of elements of adaptive context extractor 105. Adaptive context extractor 105 provides a context c(k), in accordance with an aspect of the invention, in such a way as to cause prediction to be more certain so that the probabilities being estimated by probability estimator 106 are closer either to zero (0) or one (1). Accordingly, operation of adaptive context extractor 105 is begun via start step 401. Thereafter, operational block 402 initializes k=0, ℓ i =ℓ * / i for all iε[0,...,L+M-1] where "L" is the number of lag intervals in the fixed portion of the context configuration (in the above example L=7) and where "M" is the number of candidate lag intervals in a set from which a floating predictor will be selected (in the above example M=10). Operational block 402 also initializes s(k)=0 for all k < 0 and n m (k)=0 for all mε[L,...,L+M-1]. The n m (k) are running counts to be explained below. Operational block 403 causes the current symbol s(k) to be read. Operational block 404 causes the context c(k) to be calculated in accordance with Context c(k) is then supplied as an output to probability estimator 106 (FIG. 1). Operational block 405 causes the running counts n m (k) to be updated. It is to be noted that counts n m (k) provide an efficient and fast measure of predictive value. To this end, n m (k) are running counts of polarity coincidences, i.e., running counts of the number of times that s(k) and s(k-ℓ m ) are the same. Thus, step 405 causes the updating of n m (k) for all mε[L,...,L+M-1] in accordance with Conditional branch point 406 tests to determine if current time k is an allowed time for changing the context configuration. There is no need to allow possible changes in the context configuration at every time k and, consequently, processing overhead can be reduced by only periodically allowing context configuration changes. To this end step 406 tests to determine if k modulo K = 0 , where k is the symbol index and K is a predetermined parameter representative of the interval at which changes in the context configuration are to be allowed. If the test result in step 406 is NO, no change is to be made in the context configuration and operational block 407 increments the symbol index, namely, sets k = k+1. Thereafter, control is returned to step 403. If the test result in step 406 is YES, operational block 408 causes the context configuration changer to be called. Once the context configuration changer has run, operational block 407 increments the symbol index k and control is returned to step 403. FIG. 5 is a flow chart of the context configuration changer used in the main adaptive context extractor of FIG. 4. Accordingly, the context configuration changer is entered via step 501. Thereafter, operational block 502 causes ℓ MAX to be found in accordance with and causes i MAX to be found which equals the smallest m in [L,...,L+M-1] such that n m (k) = ℓ MAX , Thus, i MAX is an index of the predictor for the current symbol offering the maximum correlation. Operational block 503 causes ℓ MIN to be found in accordance with Conditional branch points 504 and 507 through 509 are employed to assure that the context configuration is not changed unless a significantly better prediction of the current symbol s(k) will result. Accordingly, conditional branch point 504 tests to determine if ℓ MAX is greater than a fraction of its maximum possible value K, namely, whether ℓ MAX > A×K , where A is a predetermined fraction. In one example, A is selected to be 7/8. If ℓ MAX is not greater than a significant fraction of its maximum possible value K, none of the candidates for the at least one floating predictor in the context configuration are particularly good predictors and there is no need to change the context configuration. If the test result in step 504 is NO, the context configuration is not to be changed and operational block 505 sets the running counts to zero, namely, n m (k) = 0 for all mε[L,...,L+m-1]. Thereafter, control is returned to the main routine via step 506. If the test result in step 504 is YES, conditional branch point 507 tests to determine if ℓ MAX - ℓ MIN > B×K , where B is a predetermined fraction. In one example, B is selected to be 1/4. When the condition of equation (9) is not satisfied all of the candidate lag intervals are approximately equally good predictors for the current symbol and, consequently, there is no need to change the context configuration. If the test result in step 507 is NO, the context configuration is not to be changed and steps 505 and 506 are iterated, as described above. If the test result in step 507 is YES, conditional branch point 508 tests to determine whether ℓ MAX - n L (k) > K - ℓ MAX . If the condition of equation (10) is not met, the improvement in prediction offered by changing the context configuration is not significant enough to warrant changing it. Thus, if the test result in step 508 is NO, the context configuration is not to be changed and steps 505 and 506 are iterated, as described above. If the test result in step 508 is YES, conditional branch point 509 tests to determine whether ℓ MAX - n L (k) > K/C , where C is a predetermined integer value. In one example, C is selected to be 64. If the condition of equation (11) is not met, the improvement in prediction offered by changing the context configuration is again not significant enough to warrant changing it. Thus, if the test result in step 509 is NO, the context configuration is not to be changed and steps 505 and 506 are iterated, as described above. If the test result in step 509 is YES, operational block 510 causes a change in the context configuration to occur by exchanging the more desirable lag interval with the lag interval currently in the floating predictor position. This is realized by setting ℓ TEMP = ℓ L ℓ L = ℓ i MAX ℓ i MAX =ℓ TEMP . Thereafter, steps 505 and 506 are iterated, as described above and control is returned to the main routine. It is noted that an adjustment in the context configuration is enabled, i.e., allowed, only if the prescribed criteria of steps 504 and 507 through 509 are met. The running counts n m (k) of polarity coincidences are measures of predictive value. Although this embodiment of the invention has been described assuming a bi-level signal, counting polarity coincidences would also provide a measure of predictive value for multi-level signals. Another possible measure of predictive value is correlation. A technique that could be advantageously used for obtaining correlations for multi-level and other signals is low-pass filtering. To this end, the products of the symbol value at a given time and the symbol value at some prior time are low-pass filtered to obtain the desired correlations. Such low-pass filtering techniques are known in the art. Decoder 103 includes, in this example, line interface 108, entropy decoder unit 109, adaptive context extractor 110 and probability estimator 111. Line interface 108 performs the inverse function of line interface 107 and de-formats the incoming signal, in a known manner, to obtain the data stream a(i). Entropy decoder unit 109 performs the inverse function of entropy encoder unit 104. To this end, the received data stream a(i) and probability estimates (k) from probability estimator 110 are supplied to entropy decoder unit 109 and used therein in known fashion to reconstruct the symbols s(k). Symbols s(k) are supplied to adaptive context extractor 110 which, in turn, provides context c(k) and supplies it to probability estimator 111. Again, such entropy decoder units are known in the art. See again the article entitled "Compression of Black-White Image with Arithmetic Coding" and U.S. patent 4,633,490, cited above, regarding binary applications and the article entitled "Arithmetic Coding For Data Compression", also cited above, for multilevel applications. Also see the article cited above regarding Huffman encoders/decoders entitled "Compression of Text and Binary Files Using Adaptive Huffman Coding Techniques". Adaptive context extractor 110 is identical to adaptive context extractor 105 in structure and operation and is not described again. Similarly, probability estimator 111 is identical to probability estimator 106 in structure and operation and is not described again.

Claims: An encoder (101) for encoding a supplied signal (s(k)) having a plurality of symbol values including, means (105) for extracting a context (c(k)) dependent on a configuration of prior symbols of said supplied signal, probability estimator means (106) being responsive to said supplied signal and said context for generating probability estimates ( (k)) of said supplied signal, entropy encoder means (104) being responsive to said supplied signal and said probability estimated for generating an encoded version of said supplied signal, means (107) for interfacing said entropy encoder means to a transmission medium or storage, CHARACTERIZED IN THAT a plurality of said prior symbols are at prescribed individual lag intervals relative to a current symbol being encoded, and said means for extracting a context includes means (401-408, 501-510) responsive to said supplied signal for adaptively adjusting said configuration. An encoder as defined in claim 1 wherein said means for adaptively adjusting includes means (406) for enabling adjustment of said configuration only at time when prescribed criteria based on correlation between signal values at said lag intervals are met. An encoder as defined in claim 1 wherein said configuration includes a predetermined portion comprised of at least one of said lag intervals and an adjustable portion comprised of at least one floating lag interval determined in response to said supplied signal. An encoder as defined in claim 3 wherein said means for adaptively adjusting includes means (501-510) for selecting said at least one floating lag interval from a predetermined set of candidate lag intervals. An encoder as defined in claim 4 wherein said means for selecting includes means (502, 503) for obtaining a measure of predictive value of each prior symbol at said lag intervals in said predetermined set of candidate lag intervals and means (504, 507-510) for selecting from said set of candidate lag intervals at least one of said lag intervals referencing a symbol having the greatest predictive value to be included as said floating lag interval in said configuration. An encoder as defined in claim 5 wherein said means for obtaining a measure of predictive value includes means (502, 503) for obtaining a measure of correlation at each of said candidate lag intervals and wherein said means for selecting includes means (504, 507-510) for determining which at least one of said lag intervals in said set is to be included in said configuration based on said correlations. An encoder as defined in claim 6 wherein said means for determining identifies an at least one lag interval of said set of candidate lag intervals having the maximum correlation (via 502) and further including means (510) for incorporating said identified at least one lag interval into said configuration. An encoder as defined in claim 5 wherein said means for obtaining a measure of predictive value includes means (405) for counting polarity coincidences between said current symbol and symbols at said candidate lag intervals and wherein said means (502-510) for selecting is responsive to counts of said polarity coincidences to select as said at least one lag interval to be included in said configuration at least one of said candidate lag intervals having the maximum count of said polarity coincidences. A method of encoding a supplied signal having a plurality of symbol values including the steps of, extracting a context (via 105) from said supplied signal dependent on a configuration of prior symbols of said supplied signal, generating probability estimates (via 106) of said supplied signal in response to said supplied signal and said context, entropy encoding (via 104) said supplied signal in response to said supplied signal and said probability estimates to generate an encoded version of said supplied signal, interfacing (via 107) said encoded version to a transmission medium or storage, CHARACTERIZED IN THAT a plurality of said prior symbols are at prescribed individual lag intervals relative to a current symbol being encoded, and said step of extracting a context includes adaptively adjusting (via 401-408, 501-510) said configuration in response to said supplied signal. A decoder (103) for reconstructing an original signal (s(k)) having a plurality of symbol values from a compressed data signal (a(i)) including, means (108) for interfacing to a transmission medium or storage (102) to obtain a compressed data signal, means (110) for extracting a context dependent on a configuration of prior symbols of a reconstructed signal, probability estimator means (111) being responsive to said reconstructed signal and said context for generating probability estimates ( (k)) of said reconstructed signal, entropy decoder means (109) being responsive to said obtained compressed data signal and said probability estimates for generating a reconstructed version of the original signal, CHARACTERIZED IN THAT a plurality of said prior symbols are at prescribed individual lag intervals relative to a current symbol being decoded, and said means for extracting a context include means (401-407, 501-510) responsive to said reconstructed signal for adaptively adjusting said configuration. A decoder as defined in claim 10 wherein said means for adaptively adjusting includes means (406) for enabling adjustment of said configuration only at times when prescribed criteria are met. A decoder as defined in claim 10 wherein said configuration includes a predetermined portion comprised of at least one of said lag intervals and an adjustable portion comprised of at least one floating lag interval determined in response to said applied signal. A decoder as defined in claim 12 wherein said means for adaptively adjusting includes means for selecting (501-510) said at least one floating lag interval from a predetermined set of candidate lag intervals. A decoder as defined in claim 13 wherein said means for selecting includes means (502, 503)for obtaining a measure of predictive value of each prior symbol at said lag intervals in said predetermined set of candidate lag intervals and means (504, 507-510) for selecting from said set of candidate lag intervals at least one of said lag intervals referencing a symbol having the greatest predictive value to be included as said floating lag interval in said configuration. A decoder as defined in claim 14 wherein said means for obtaining a measure of predictive value includes means (502, 503) for obtaining a measure of correlation at each of said candidate lag intervals and wherein said means for selecting includes means (504, 502-510) for determining which at least one of said lag intervals in said set is to be included in said configuration based on said correlations. A decoder as defined in claim 15 wherein said means for determining identifies means at least one lag interval of said set of candidate lag intervals having the maximum correlation (via 502) and further including means (510) for incorporating said identified at least one lag interval into said configuration. A decoder as defined in claim 14 wherein said means (405) for obtaining a measure of predictive value includes means for counting polarity coincidences between said current symbol and symbols at said candidate lag intervals and wherein said means (502-510) for selecting is responsive to counts of said polarity coincidences to select as said at least one lag interval to be included in said configuration at least one of said candidate lag intervals having the maximum count. A method of decoding a compressed data signal representative of an encoded version of an original supplied signal to obtain a reconstructed signal having a plurality of symbol values including the steps of, interfacing (via 108) to a transmission medium or storage to obtain a compressed data signal, extracting a context (via 110) from a reconstructed signal dependent on a configuration of prior symbols of said reconstructed signal, generating probability estimates (via 111) of said reconstructed signal in response to said reconstructed signal and said context, entropy decoding (via 109) said compressed data signal in response to said obtained compressed data signal and said probability estimates to generate said reconstructed signal version of the original signal, CHARACTERIZED IN THAT a plurality of said prior symbols are at prescribed individual lag intervals relative to a current symbol being decoded, and said step of extracting a context includes adaptively adjusting (via 401-408, 501-510) said configuration in response to said reconstructed signal.

Inventors: CHAMZAS CHRISTODOULOS, DUTTWEILER DONALD L, CHAMZAS, CHRISTODOULOS, DUTTWEILER, DONALD L.
Applicants: AT & T CORP, AT&T CORP.
Application year: 1989
Main classification: H03M7
IPC codes: H03M7, G06T9