Abstract: A characteristic thumbprint is extracted from a data signal, the thumbprint based on statistics relating to the data signal. The data signal can be compared indirectly by matching this thumbprint against one or more reference thumbprints. The data signal may be any type of signal, including streaming digitized audio or obtained from static files. A database may contain a number of these characteristic thumbprints, and the database can be searched for a particular thumbprint.

Abstract: Disclosed are systems, methods, and computer readable media for performing speech recognition. The method embodiment comprises selecting a codebook from a plurality of codebooks with a minimal acoustic distance to a received speech sample, the plurality of codebooks generated by a process of (a) computing a vocal tract length for a each of a plurality of speakers, (b) for each of the plurality of speakers, clustering speech vectors, and (c) creating a codebook for each speaker, the codebook containing entries for the respective speaker's vocal tract length, speech vectors, and an optional vector weight for each speech vector, (2) applying the respective vocal tract length associated with the selected codebook to normalize the received speech sample for use in speech recognition, and (3) recognizing the received speech sample based on the respective vocal tract length associated with the selected codebook.

Abstract: The invention relates to a speech recognition system and method with cepstral noise subtraction. The speech recognition system and method utilize a first scalar coefficient, a second scalar coefficient, and a determining condition to limit the process for the cepstral feature vector, so as to avoid excessive enhancement or subtraction in the cepstral feature vector, so that the operation of the cepstral feature vector is performed properly to improve the anti-noise ability in speech recognition. Furthermore, the speech recognition system and method can be applied in any environment, and have a low complexity and can be easily integrated into other systems, so as to provide the user with a more reliable and stable speech recognition result.

Abstract: A method of encoding/decoding a digital signal using linear quantization by sections, and an apparatus for the same are provided. The method of encoding includes: converting a digital input signal, and removing redundant information from the digital signal; allocating a number of bits allocated to each predetermined quantized unit considering the importance of the digital signal; dividing the distribution of signal values into predetermined sections based on the predetermined quantized units, and linear quantizing data converted pin the operation of converting the digital input signal by sections; and generating a bit stream from the linear quantized data and predetermined side information. Therefore, a sound quality is improved compared to a sound quality produced by conventional linear quantizing devices and a complexity of a non-linear quantizing device is reduced.

Abstract: An enhancement system extracts pitch from a processed speech signal. The system estimates the pitch of voiced speech by deriving filter coefficients of an adaptive filter and using the obtained filter coefficients to derive pitch. The pitch estimation may be enhanced by using various techniques to condition the input speech signal, such as spectral modification of the background noise and the speech signal, and/or reduction of the tonal noise from the speech signal.

Abstract: A method and apparatus for a voice transcoder that converts a bitstream representing frames of data encoded according to a first voice compression standard to a bitstream representing frames of data according to a second voice compression standard using perceptual weighting that uses tuned weighting factors, such that the bitstream of a second voice compression standard to produce a higher quality decoded voice signal than a comparable tandem transcoding solution.

Abstract: A method and an apparatus for generating a lattice vector quantizer codebook are disclosed. The method includes: storing an eigenvector set that includes amplitude vectors and/or length vectors, where the amplitude vectors and/or length vectors are different from each other and correspond to a root leader of a lattice vector quantizer; storing storage addresses of the amplitude vectors and length vectors, where the amplitude vectors and length vectors correspond to the root leader and are in the eigenvector set; and generating a lattice vector quantizer codebook according to the eigenvector set and the storage addresses.

Abstract: According to the invention, an excitation signal is generated as a result of sampled excitation values in order to excite an audio synthesis filter, the generated sampled excitation values being continuously stored in an adaptive codebook. A noise generator is provided which continuously generates random sampled values. A sequence of the stored sampled excitation values is selected from the adaptive codebook based on a fed audio fundamental frequency parameter by means of which a time gap between the sequence that is to be selected and the actual time reference is predefined. The excitation signal is generated by mixing the selected sequence with a random sequence encompassing actual random sampled valued of the noise generator.

Abstract: Methods, encoders, and digital systems are provided for predictive encoding of speech parameters in which an input frame is encoded by quantizing a parameter vector of the input frame with a strongly-predictive codebook and a weakly-predictive codebook to obtain a strongly-predictive distortion and a weakly-predictive distortion, adjusting a correlation indicator based on a relative correlation of the input frame to a previous frame, wherein the correlation indicator is indicative of the strength of the correlation of previously encoded frames, and encoding the input frame with the weakly-predictive codebook unless the correlation indicator has reached a correlation threshold.

Abstract: Provided are a method and apparatus for encoding and decoding a high frequency signal by using a low frequency signal. The high frequency signal can be encoded by extracting a coefficient by linear predicting a high frequency signal, and encoding the coefficient, generating a signal by using the extracted coefficient and a low frequency signal, and encoding the high frequency signal by calculating a ratio between the high frequency signal and an energy value of the generated signal. Also, the high frequency signal can be decoded by decoding a coefficient, which is extracted by linear predicting a high frequency signal, and a low frequency signal, and generating a signal by using the decoded coefficient and the decoded low frequency signal, and adjusting the generated signal by decoding a ratio between the generated signal and an energy value of the high frequency signal.

Abstract: In one embodiment, at least one channel in a frame of the audio signal is subdivided into a plurality of blocks such that at least two of the blocks having different lengths. A length of the frame is a user defined value and is determined within a predetermined value. Furthermore, information indicating the subdivision of the channel into the blocks is generated.

Abstract: In one embodiment, at least one channel in a frame of the audio signal is subdivided into a plurality of blocks such that at least two of the blocks having different lengths, and information indicating the subdivision of the channel into the blocks is generated.

Abstract: An encoding device (200) includes an MDCT unit (202) that transforms an input signal in a time domain into a frequency spectrum including a lower frequency spectrum, a BWE encoding unit (204) that generates extension data which specifies a higher frequency spectrum at a higher frequency than the lower frequency spectrum, and an encoded data stream generating unit (205) that encodes to output the lower frequency spectrum obtained by the MDCT unit (202) and the extension data obtained by the BWE encoding unit (204). The BWE encoding unit (204) generates as the extension data (i) a first parameter which specifies a lower subband which is to be copied as the higher frequency spectrum from among a plurality of the lower subbands which form the lower frequency spectrum obtained by the MDCT unit (202) and (ii) a second parameter which specifies a gain of the lower subband after being copied.

Abstract: There is provided a method of post-processing a speech signal. The method comprises applying a time-domain post-processing to the speech signal, using LPC coefficients, for a low-band frequency range and applying a frequency-domain post-processing to the speech signal, using MDCT coefficients, for the high-band frequency range. Applying the frequency-domain post-processing includes decoding an encoded speech signal to obtain MDCT coefficients representative of the speech signal divided into a plurality of sub-bands, generating an envelope for each sub-band of the plurality of sub-bands as an average magnitude of the MDCT coefficients of the sub-band, generating an envelope modification factor for each sub-band of the plurality of sub-band using the MDCT coefficients of the sub-band, modifying the envelope by the envelope modification factor for each sub-band of the plurality of sub-bands to provide a modified envelope, and generating the post-processed speech signal using the modified envelope.

Abstract: A quantizer according to an embodiment is configured to quantize a smoothed value of an input value (e.g., a vector of line spectral frequencies) to produce a corresponding output value, where the smoothed value is based on a scale factor and a quantization error of a previous output value.

Abstract: A signal processing apparatus includes a decoding unit, an analyzing unit, a synthesizing unit, and a selecting unit. The decoding unit decodes an input encoded audio signal and outputs a playback audio signal. When loss of the encoded audio signal occurs, the analyzing unit analyzes the playback audio signal output before the loss occurs and generates a linear predictive residual signal. The synthesizing unit synthesizes a synthesized audio signal on the basis of the linear predictive residual signal. The selecting unit selects one of the synthesized audio signal and the playback audio signal and outputs the selected audio signal as a continuous output audio signal.

Abstract: A method of mitigating errors in a distributed speech recognition process. The method comprises the steps of identifying a group comprising one or more vectors which have undergone a transmission error, and replacing one or more speech recognition parameters in the identified group of vectors. In one embodiment all the speech recognition parameters of each vector of the group are replaced by replacing the whole vectors, and each respective replaced whole vector is replaced by a copy of whichever of the preceding or following vector without error is closest in receipt order to the vector being replaced.

Abstract: A method and apparatus for implementing fixed codebooks as a common module are provided. In the method of implementing fixed codebooks of a plurality of speech codecs as a common module, it is possible to include only a part excluding fixed codebooks in a communication terminal or communication system, support various speech codecs without using a chip with high price and high performance, and reduce a memory space that is occupied by the speech codecs by generating a track of a fixed codebook corresponding to a speech codec based on information on the speech codec among the plurality of speech codecs and selecting a codebook vector corresponding to a target signal among codebook vectors constructed with combinations of pulses represented by the generated track. In addition, it is possible to reduce processing complexity as compared with a case of embodying the common fixed codebook module in software by embodying the common fixed codebook module in hardware.

Abstract: The present invention provides a method, a computer-software-product and an apparatus for enabling a determination of speech related audio data within a record of digital audio data. The method comprises steps for extracting audio features from the record of digital audio data, for classifying one or more subsections of the record of digital audio data, and for marking at least a part of the record of digital audio data classified as speech. The classification of the digital audio data record is performed on the basis of the extracted audio features and with respect to at least one predetermined audio class.

Abstract: A method comprises identifying a component k of a codevector from a codebook C having one or more codevectors, the component k introducing highest variance for an input vector; allowing ordering of codevectors in the codebook C; and searching for a best match vector for the input vector using ordered codevectors.

Abstract: There is provided a scalable encoding device capable of realizing a bandwidth scalable LSP encoding with high performance by improving the conversion performance from narrow band LSPs to wide band LSPs.

Abstract: In one embodiment, the method includes receiving an audio data frame having at least first and second channels. The first and second channels are synchronously subdivided into blocks such that the lengths of the blocks into which the second channel is subdivided correspond to the lengths of the blocks into which the first channel is subdivided if the first and second channels are correlated with each other and difference coding is used. The first and second channels are decoded and the subdivided blocks of the first and second channels are interleaved if the first and second channels are synchronously subdivided.

Abstract: Information about excitation signals of a first signal encoded by CELP is used to derive a limited set of candidate excitation signals for a second correlated second signal. Preferably, pulse locations of the excitation signals of the first encoded signal are used for determining the set of candidate excitation signals. More preferably, the pulse locations of the set of candidate excitation signals are positioned in the vicinity of the pulse locations of the excitation signals of the first encoded signal. The first and second signals may be multi-channel signals of a common speech or audio signal. However, the first and second signals may also be identical, whereby the coding of the second signal can be utilized for re-encoding at a lower bit rate.

Abstract: In one embodiment, at least first and second channels in a frame of the audio signal are independently subdivided into blocks if the first and second channels are not correlated with each other. At least two of the blocks have different block lengths. Furthermore, the first and second channels are correspondingly subdivided into blocks such that the lengths of the blocks into which the second channel is subdivided correspond to the lengths of the blocks into which the first channel is subdivided if the first and second channels are correlated with each other. At least two of the blocks have different block lengths.

Abstract: A hardware device for analyzing an audio signal comprises a calculator for calculating a neural activity pattern over time resulting at nerve fibers of an ear model based on the audio signal and a processor for processing the neural activity pattern to obtain a sequence of time information as an analysis representation describing a temporal position of consecutive trajectories, wherein a trajectory includes activity impulses on different nerve fibers based on the same event in the audio signal. A two-dimensional representation of the neural activity pattern is gradually distorted over time, and it is recognized when an approximately straight line is contained in the distorted two-dimensional representation of the neural activity pattern over time. Accordingly, a time information belonging to the trajectory is provided.

Abstract: A method of encoding/decoding a digital signal using linear quantization by sections, and an apparatus for the same are provided. The method of encoding includes: converting a digital input signal, and removing redundant information from the digital signal; allocating a number of bits allocated to each predetermined quantized unit considering the importance of the digital signal; dividing the distribution of signal values into predetermined sections based on the predetermined quantized units, and linear quantizing data converted pin the operation of converting the digital input signal by sections; and generating a bit stream from the linear quantized data and predetermined side information. Therefore, a sound quality is improved compared to a sound quality produced by conventional linear quantizing devices and a complexity of a non-linear quantizing device is reduced.

Abstract: A method for processing audio data includes determining a first common scalefactor value for representing quantized audio data in a frame. A second common scalefactor value is determined for representing the quantized audio data in the frame. A line equation common scalefactor value is determined from the first and second common scalefactor values.

Abstract: The invention is based on the idea of providing a method for high-resolution, waveform-preserving digitization of analog signals, wherein conventional scalar logarithmic quantization is transferred to multi-dimensional spherical coordinates, and the advantages resulting from this, e.g., a constant signal/noise ratio over an extremely high dynamic range with very low loss with respect to the rate-distortion theory. In order to make use of the statistical dependencies present in the source signal for an additional gain in the signal/noise ratio, the differential pulse code modulation (DPCM) is combined with spherical logarithmic quantization. The resulting method achieves an effective data reduction with a high long-term and short-term signal/noise ratio with an extremely small signal delay.

Abstract: The present invention provides a frame erasure concealment device and method that is based on reestimating gain parameters for a code excited linear prediction (CELP) coder. During operation, when a frame in a stream of received data is detected as being erased, the coding parameters, especially an adaptive codebook gain gp and a fixed codebook gain gc, of the erased and subsequent frames can be reestimated by a gain matching procedure. By using this technique with the IS-641 speech coder, it has been found that the present invention improves the speech quality under various channel conditions, compared with a conventional extrapolation-based concealment algorithm.

Abstract: Methods, devices, and systems for coding and decoding audio are disclosed. Digital samples of an audio signal are transformed from the time domain to the frequency domain. The resulting transform coefficients are coded with a fast lattice vector quantizer. The quantizer has a high rate quantizer and a low rate quantizer. The high rate quantizer includes a scheme to truncate the lattice. The low rate quantizer includes a table based searching method. The low rate quantizer may also include a table based indexing scheme. The high rate quantizer may further include Huffman coding for the quantization indices of transform coefficients to improve the quantizing/coding efficiency.

Abstract: In one embodiment, the method includes receiving an audio data frame having at least first and second channels. The first and second channels are independently subdivided into blocks if the first and second channels are not correlated with each other. The first and second channels are decoded, and the subdivided blocks of the first and second channels are not interleaved if the first and second channels are independently subdivided.

Abstract: The invention pertains to a method and apparatus of efficient encoding and decoding of vector quantized data. The method and system explores and implements sub-division of a quantization vector space comprising class-leader vectors and representation of the class-leader vectors by a set of class-leader root-vectors facilitating faster encoding and decoding, and reduced storage requirements.

Abstract: An audio encoder performs frequency extension coding that comprises determining one or more shape parameters using a displacement vector that corresponds to a displacement of an even number (e.g., an even number of sub-bands between a sub-band in a baseband frequency range and a sub-band in an extended-band frequency range). The shape parameters can be determined on a per-audio-block basis. Restricting a displacement to an even number (in frequency extension coding or in other signal modulation schemes) can improve the quality of reconstructed audio. An audio encoder also can perform frequency extension coding that comprises determining one or more scale parameters at one or more audio blocks, and determining one or more anchor points for interpolating the one or more scale parameters.

Abstract: A fixed codebook searching apparatus which slightly suppresses an increase in the operation amount, even if the filter applied to the excitation pulse has the characteristic that it cannot be represented by a lower triangular matrix and realizes a quasi-optimal fixed codebook search. This fixed codebook searching apparatus is provided with an algebraic codebook that generates a pulse excitation vector; a convolution operation section that convolutes an impulse response of auditory weighted synthesis filter into an impulse response vector that has a value at negative times, to generate a second impulse response vector that has a value at second negative times; a matrix generating section that generates a Toeplitz-type convolution matrix by means of the second impulse response vector; and a convolution operation section that convolutes the matrix generated by matrix generating section into the pulse excitation vector generated by algebraic codebook.

Abstract: Indexing methods are described that may be used by databases, search engines, query and retrieval systems, context sensitive data mining, context mapping, language identification, image recognition, and robotic systems. Raw baseline features from an input signal are aggregated, abstracted and indexed for later retrieval or manipulation. The feature index is the quantization number for the underlying features that are represented by an abstraction. Trajectories are used to signify how the features evolve over time. Features indexes are linked in an ordered sequence indicative of time quanta, where the sequence represents the underlying input signal. An example indexing system based on the described processes is an inverted index that creates a mapping from features or atoms to the underlying documents, files, or data. A highly optimized set of operations can be used to manipulate the quantized feature indexes, where the operations can be fine tuned independent from the base feature set.

Abstract: A fixed codebook search method includes: initializing a counter; searching for pulses and calculating the value of a cost function Qk; initializing the counter if the Qk value increases; increasing the value of the counter if the Qk value does not increase; judging whether the value of the counter is greater than the threshold value; continuing the search process if the value of the counter is not greater than the threshold value; and ending the whole search process if the value of the counter is greater than the threshold value. The present invention reduces the search count and improves the search efficiency.

Abstract: Provided are, among other things, systems, methods and techniques for decoding an audio signal from a frame-based bit stream. Each frame includes processing information pertaining to the frame and entropy-encoded quantization indexes representing audio data within the frame. The processing information includes: (i) code book indexes, (ii) code book application information specifying ranges of entropy-encoded quantization indexes to which the code books are to be applied, and (iii) window information. The entropy-encoded quantization indexes are decoded by applying the identified code books to the corresponding ranges of entropy-encoded quantization indexes. Subband samples are then generated by dequantizing the decoded quantization indexes, and a sequence of different window functions that were applied within a single frame of the audio data is identified based on the window information.

Abstract: A wideband audio coding concept is presented that provides good audio quality at bit rates below 3 bits per sample with an algorithmic delay of less than 10 ms. The concept is based on the principle of Linear Predictive Coding (LPC) in an analysis-by-synthesis framework. A spherical codebook is used for quantisation at bit rates which are higher in comparison to low bit rate speech coding for improved performance for audio signals. For superior audio quality, noise shaping is employed to mask the coding noise. In order to reduce the computational complexity of the encoder, the analysis-by synthesis framework has been adapted for the spherical codebook to enable a very efficient excitation vector search procedure. Furthermore, auxiliary information gathered in advance is employed to reduce a computational encoding and decoding complexity at run time significantly. This auxiliary information can be considered as the SCELP codebook.

Abstract: Provided is a signal processing method which can enhance the resolution of a spectrum round off by quantization and compensate energy of a spectrum truncated to zero by quantization so as to achieve reproduction without dissatisfaction or uncomfortable feeling. The selecting circuit selects a plurality of coefficients from coefficients of a frequency band of a dequantized acoustic signal. The computing circuit then computes an interpolation coefficient of a coefficient, which is not selected by the selecting circuit, by an interpolation method such as a Lagrange's interpolation method or a spline interpolation method which uses the plurality of coefficients selected by the selecting circuit.

Abstract: Speech is coded using an orthogonal search by calculating a search reference value. An adaptive codevector representing a pitch component is generated. A random codevector representing a random component is also generated. The orthogonal search further includes generating a synthetic speech signal by a synthesis filter being excited by the adaptive codevector and the random codevector. A distortion between the input speech signal and the synthetic speech signal is calculated. One random codevector that minimizes the distortion is selected.

Abstract: A fixed codebook search method includes initializing a counter, searching for pulses and calculating the value of a cost function Qk, initializing the counter if the Qk value increases, increasing the value of the counter if the Qk value does not increase, judging whether the value of the counter is greater than the threshold value, continuing the search process if the value of the counter is not greater than the threshold value, and ending the whole search process if the value of the counter is greater than the threshold value.

Abstract: Techniques and tools related to coding and decoding of audio information are described. For example, redundant coded information for decoding a current frame includes signal history information associated with only a portion of a previous frame. As another example, redundant coded information for decoding a coded unit includes parameters for a codebook stage to be used in decoding the current coded unit only if the previous coded unit is not available. As yet another example, coded audio units each include a field indicating whether the coded unit includes main encoded information representing a segment of an audio signal, and whether the coded unit includes redundant coded information for use in decoding main encoded information.

Abstract: A waveform interpolation speech coding apparatus and method for reducing complexity thereof are disclosed. The waveform interpolation speech coding apparatus includes: a waveform interpolation encoding unit for receiving a speech signal, calculating parameters for a waveform interpolation from the received speech signal, and quantizing the calculating parameters; and a realignment parameter calculating unit for restoring a characteristic waveform (CW) using the quantized parameter, calculating a realignment parameter that maximizes a cross-correlation among consecutive CWs for the restored CW.

Abstract: Provided are, among other things, systems, methods and techniques for encoding an audio signal, in which is obtained a sampled audio signal which has been divided into frames. The location of a transient within one of the frames is identified, and transform data samples are generated by performing multi-resolution filter bank analysis on the frame data, including filtering at different resolutions for different portions of the frame that includes the transient. Quantization data are generated by quantizing the transform data samples using variable numbers of bits based on a psychoacoustical model, and the quantization data are grouped into variable-length segments based on magnitudes of the quantization data. A code book is assigned to each of the variable-length segments, and the quantization data in each of the variable-length segments are encoded using the code book assigned to such variable-length segment.

Abstract: A scalable encoding apparatus, a scalable decoding apparatus and the like are disclosed which can achieve a band scalable LSP encoding that exhibits both a high quantization efficiency and a high performance. In these apparatuses, a narrow band-to-wide band converter receives and converts a quantized narrow band LSP to a wide band, and then outputs the quantized narrow band LSP as converted (i.e., a converted wide band LSP parameter) to an LSP-to-LPC converter. The LSP-to-LPC converter converts the quantized narrow band LSP as converted to a linear prediction coefficient and then outputs it to a pre-emphasizer. The pre-emphasizer calculates and outputs the pre-emphasized linear prediction coefficient to an LPC-to-LSP converter. The LPC-to-LSP converter converts the pre-emphasized linear prediction coefficient to a pre-emphasized quantized narrow band LSP as wide band converted, and then outputs it to a prediction quantizer.

Abstract: Included in the digital filtering equipment for extracting a feature quantity from a speech signal in order to execute a speech recognition based on an inputted speech signal are: a) an waveform determining section for obtaining an inputted speech signal and quantizing the speech signal waveform; b) a division value operating section for summing a quantized signal data in a prescribed adjoining region to divide the summation value by the number of summed data, with respect to a data quantized at each point by the waveform determining section, whereby a division value is obtained with the data being centered; c) a comparison section for comparing a division value calculated by the division value operating section and the quantized data calculated in the division value operating section to output logical truth of a comparison result, with respect to each data; and d) a conversion section for converting the quantized data into the selected data points based on an output from the comparison section.

Abstract: A method and apparatus is disclosed herein for a quantizing parameters using partial information on atypical subsequences. In one embodiment, the method comprises partially classifying a first plurality of subsequences in a target vector into a number of selected groups, creating a refined fidelity criterion for each subsequence of the first plurality of subsequences based on information derived from classification, dividing a target vector into a second plurality of subsequences, and encoding the second plurality of subsequences, including quantizing the second plurality of subsequences given the refined fidelity criterion.

Abstract: A method and apparatus is disclosed herein for quantizing data using a perceptually relevant search of multiple quantization patterns. In one embodiment, the method comprises performing a perceptually relevant search of multiple quantization patterns in which one of a plurality of prototype patterns and its associated permutation are selected to quantize the target vector, each prototype pattern in the plurality of prototype patterns being capable of directing quantization across the vector; converting the one prototype pattern, the associated permutation and quantization information resulting from both to a plurality of bits by an encoder; and transferring the bits as part of a bit stream.

Abstract: Even when a combination of the stegonography technique and prediction encoding is applied to sound encoding, a sound encoder does not cause deterioration in quality of decoded signals. In the device, an encoding section (102) outputs an encoding code (I) to a bit embedding section (104). A function extension encoding section (103) generates an encoding code (J) for information required for extending functions of the sound encoder (100) and outputs it to the bit embedding section (104). The bit embedding section (104) embeds information on the encoding code (J) into a part of bits of the encoding code (I) and outputs the resultant encoding code (I?). A synchronization information generating section (106) generates synchronization information according to the encoding code (I?) after the bit embedding and outputs the synchronization information to the encoding section (102).

Abstract: This invention relates to indexing an input vector contained in a set of vectors of a plurality of sets of vectors. The indexing comprises performing, in case that the input vector is contained in a set of vectors of a pre-defined group of one or more sets of vectors of the plurality of sets of vectors, a specific processing that is adapted to a characteristic of the sets of vectors in the pre-defined group of sets of vectors and is only applicable in case of input vectors contained in sets of vectors with the characteristic. The indexing further comprises performing, in case that the input vector is not contained in a set of vectors of the pre-defined group of sets of vectors, a general processing. The invention further relates to an according determining of a target vector contained in a set of vectors of a plurality of sets of vectors based on an index associated with said target vector.