Abstract: An electronic apparatus is provided. The electronic apparatus includes a microphone, a communication interface including circuitry and a processor configured to, based on identifying that a trigger word is included in a first sound signal received through the microphone, enter a voice recognition mode, identify a gain value for adjusting an intensity of the first sound signal to be in a predetermined intensity range based on the intensity of the first sound, adjust an intensity of a second sound signal received through the microphone in the voice recognition mode based on the identified gain value, and control the communication interface to transmit a user command obtained based on voice recognition regarding the adjusted second sound signal, to an external apparatus.

Abstract: An electronic apparatus is provided. The electronic apparatus includes a microphone, a communication interface including circuitry and a processor configured to, based on identifying that a trigger word is included in a first sound signal received through the microphone, enter a voice recognition mode, identify a gain value for adjusting an intensity of the first sound signal to be in a predetermined intensity range based on the intensity of the first sound, adjust an intensity of a second sound signal received through the microphone in the voice recognition mode based on the identified gain value, and control the communication interface to transmit a user command obtained based on voice recognition regarding the adjusted second sound signal, to an external apparatus.

Abstract: According to an aspect of the present invention an encoder for encoding an audio signal has an analyzer configured for deriving prediction coefficients and a residual signal from a frame of the audio signal. The encoder has a formant information calculator configured for calculating a speech related spectral shaping information from the prediction coefficients, a gain parameter calculator configured for calculating a gain parameter from an unvoiced residual signal and the spectral shaping information and a bitstream former configured for forming an output signal based on an information related to a voiced signal frame, the gain parameter or a quantized gain parameter and the prediction coefficients.

Abstract: The present invention identifies the cause of an anomaly, if any, in a signal input via a cable. A master device (13) comprises an acquisition unit (1321) which acquires the signal quality of a signal input via a cable, and a cause determination unit (1323) which performs cause determination for determining, from variations in the signal quality, whether the cause of noise included in the signal is due to a mechanical factor or is due to electrical noise.

Abstract: A voice processing method realized by a computer includes compressing forward a first steady period of a plurality of steady periods in a voice signal representing voice, and extending forward a transition period between the first steady period and a second steady period of the plurality of steady periods in the voice signal. Each of the plurality of steady periods is a period in which acoustic characteristics are temporally stable. The second steady period is a period immediately after the first steady period and has a pitch that is different from a pitch of the first steady period.

Abstract: There is provided a speech classification apparatus for hearing devices with electroencephalography, EEG, dependent sound processing, comprising a sound processing unit configured to capturing sound input signals from at least one external microphone and segmenting said captured sound input signals into segmented sound signals, a speech classification unit comprising a speech cepstrum calculation unit configured to calculate a speech cepstrum for each segmented sound signal, an EEG cepstrum calculation unit configured to calculate an EEG cepstrum for an EEG signal of a user's brain, a mapping unit configured to select a predetermined number of coefficients from each calculated sound cepstrum and from the calculated EEG cepstrum, and a correlation unit configured to calculate a correlation value for each captured sound input signal based on a correlation of the predetermined number of selected coefficients from the respective calculated sound cepstrum with the predetermined number of selected coefficients from

Abstract: The present disclosure provides a technical solution related to full duplex communication for voice conversation between chatbot and human beings. More particularly, by using such technique, the conventional conversation mode with message as center in the art is subverted so as to realize a conversation mode in full duplex mode. The entire expression that a user intents to express may be predicted when obtaining intermediate result of speech recognition, and response messages may be generated in advance based on the predicted whole expression so that the generated response message may be output immediately when a response condition is satisfied, e.g., it is determined that a user has finished a paragraph of talking. With such technical solution, the latency from the end of voice input of a user and the start of speech output of a chatbot may be minimized.

Abstract: Disclosed are a method and an apparatus for high frequency decoding for bandwidth extension. The method for high frequency decoding for bandwidth extension comprises the steps of: decoding an excitation class; transforming a decoded low frequency spectrum on the basis of the excitation class; and generating a high frequency excitation spectrum on the basis of the transformed low frequency spectrum. The method and apparatus for high frequency decoding for bandwidth extension according to an embodiment can transform a restored low frequency spectrum and generate a high frequency excitation spectrum, thereby improving the restored sound quality without an excessive increase in complexity.

Abstract: In general, techniques are described for determining quantization step sizes for compression of spatial components of a sound field. A device comprising one or more processors may be configured to perform the techniques. In other words, the one or more processors may be configured to determine a quantization step size to be used when compressing a spatial component of a sound field, where the spatial component generated by performing a vector based synthesis with respect to a plurality of spherical harmonic coefficients.

Abstract: A method performed in an audio decoder for reconstructing an original audio signal having a lowband portion and a highband portion is disclosed. The method includes receiving an encoded audio signal and extracting reconstruction parameters from the encoded audio signal. The method further includes decoding the encoded audio signal with a core audio decoder to obtain a decoded lowband portion and regenerating the highband portion based at least in part on a cross over frequency and the decoded lowband portion to obtain a regenerated highband portion. The method also includes creating a synthetic sinusoid with a level based at least in part on a spectral envelope value for the particular subband and a noise floor value for the particular subband and adding the synthetic sinusoid to the regenerated highband portion in the particular frequency band specified by the location information.

Abstract: A method performed in an audio decoder for reconstructing an original audio signal having a lowband portion and a highband portion is disclosed. The method includes receiving an encoded audio signal and extracting reconstruction parameters from the encoded audio signal. The method further includes decoding the encoded audio signal with a core audio decoder to obtain a decoded lowband portion and regenerating the highband portion based at least in part on a cross over frequency and the decoded lowband portion to obtain a regenerated highband portion. The method also includes creating a synthetic sinusoid with a level based at least in part on a spectral envelope value for the particular subband and a noise floor value for the particular subband and adding the synthetic sinusoid to the regenerated highband portion in the particular frequency band specified by the location information.

Abstract: A method performed in an audio decoder for reconstructing an original audio signal having a lowband portion and a highband portion is disclosed. The method includes receiving an encoded audio signal and extracting reconstruction parameters from the encoded audio signal. The method further includes decoding the encoded audio signal with a core audio decoder to obtain a decoded lowband portion and regenerating the highband portion based at least in part on a cross over frequency and the decoded lowband portion to obtain a regenerated highband portion. The method also includes creating a synthetic sinusoid with a level based at least in part on a spectral envelope value for the particular subband and a noise floor value for the particular subband and adding the synthetic sinusoid to the regenerated highband portion in the particular frequency band specified by the location information.

Abstract: A method and an apparatus for detecting correctness of a pitch period. The method for detecting correctness of a pitch period includes determining, according to an initial pitch period of an input signal in a time domain, a pitch frequency bin of the input signal, where the initial pitch period is obtained by performing open-loop detection on the input signal; determining, based on an amplitude spectrum of the input signal in a frequency domain, a pitch period correctness decision parameter, associated with the pitch frequency bin, of the input signal; and determining correctness of the initial pitch period according to the pitch period correctness decision parameter. The method and apparatus for detecting correctness of a pitch period according to the embodiments of the present invention can improve, based on a relatively less complex algorithm, accuracy of detecting correctness of a pitch period.

Abstract: A method for performing packet loss or Frame Erasure Concealment (FEC) for a speech coder receives encoded frames of compressed speech information transmitted from an encoder. The method determines whether an encoded frame has been lost, corrupted in transmission, or erased, synthesizes properly received frames, and decides on an overlap-add window to use in combining a portion of the synthesized speech signal with a subsequent speech signal resulting from a received and decoded packet, where the size of the overlap-add window is based on the unavailability of packets. If it is determined that an encoded frame has been lost, corrupted in transmission, or erased, the method performed an overlap-add operation on the portion of the synthesized speech signal and the subsequent speech signal, using the decided-on overlap-add window.

Abstract: Embodiments of the present invention provide a voice filtering method and apparatus and electronic equipment. The voice filtering method includes: determining a reference spectral characteristic to which a voice characteristic of a subscriber to be analyzed corresponds; and filtering an input sound signal according to the reference spectral characteristic. With the embodiments of the present invention, transmission effects of voices for different subscribers to be analyzed can be enhanced by using voice characteristics of the subscribers to be analyzed, so as to more efficiently transmit voice information.

Abstract: A storage system includes a storage medium operable to maintain a data set, a read/write head assembly operable to write the data set to the storage medium and to read the data set from the storage medium, a multi-level encoder operable to encode the data set at a plurality of different code rates before it is written to the storage medium, and a multi-level decoder operable to decode the data set retrieved from the storage medium and to apply decoded values encoded at a lower code rate when decoding values encoded at a higher code rate.

Abstract: A method includes determining, at a speech encoder, first gain shape parameters based on a harmonically extended signal and/or based on a high-band residual signal associated with a high-band portion of an audio signal. The method also includes determining second gain shape parameters based on a synthesized high-band signal and based on the high-band portion of the audio signal. The method further includes inserting the first gain parameters and the second gain shape parameters into an encoded version of the audio signal to enable gain adjustment during reproduction of the audio signal from the encoded version of the audio signal.

Abstract: Provided are a method, apparatus, and medium for encoding/decoding a high frequency band signal by using a low frequency band signal corresponding to an audio signal or a speech signal. Accordingly, since the high frequency band signal is encoded and decoded by using the low frequency band signal, encoding and decoding can be carried out with a small data size while avoiding deterioration of sound quality.

Abstract: Techniques disclosed herein include using a Maximum A Posteriori (MAP) adaptation process that imposes sparseness constraints to generate acoustic parameter adaptation data for specific users based on a relatively small set of training data. The resulting acoustic parameter adaptation data identifies changes for a relatively small fraction of acoustic parameters from a baseline acoustic speech model instead of changes to all acoustic parameters. This results in user-specific acoustic parameter adaptation data that is several orders of magnitude smaller than storage amounts otherwise required for a complete acoustic model. This provides customized acoustic speech models that increase recognition accuracy at a fraction of expected data storage requirements.

Abstract: Methods and systems for extracting speech from such packet streams. The methods and systems analyze the encoded speech in a given packet stream, and automatically identify the actual speech coding scheme that was used to produce it. These techniques may be used, for example, in interception systems where the identity of the actual speech coding scheme is sometimes unavailable or inaccessible. For instance, the identity of the actual speech coding scheme may be sent in a separate signaling stream that is not intercepted. As another example, the identity of the actual speech coding scheme may be sent in the same packet stream as the encoded speech, but in encrypted form.

Abstract: A vector joint encoding/decoding method and a vector joint encoder/decoder are provided, more than two vectors are jointly encoded, and an encoding index of at least one vector is split and then combined between different vectors, so that encoding idle spaces of different vectors can be recombined, thereby facilitating saving of encoding bits, and because an encoding index of a vector is split and then shorter split indexes are recombined, thereby facilitating reduction of requirements for the bit width of operating parts in encoding/decoding calculation.

Abstract: Unlike sound based pressure waves that go everywhere, air turbulence caused by wind is usually a fairly local event. Therefore, in a system that utilizes two or more spatially separated microphones to pick up sound signals (e.g., speech), wind noise picked up by one of the microphones often will not be picked up (or at least not to the same extent) by the other microphone(s). Embodiments of methods and apparatuses that utilize this fact and others to effectively detect and suppress wind noise using multiple microphones that are spatially separated are described.

Abstract: A method for decoding an audio signal having a bandwidth that extends beyond a bandwidth of a CELP excitation signal in an audio decoder including a CELP-based decoder element. The method includes obtaining a second excitation signal having an audio bandwidth extending beyond the audio bandwidth of the CELP excitation signal, obtaining a set of signals by filtering the second excitation signal with a set of bandpass filters, scaling the set of signals using a set of energy-based parameters, and obtaining a composite output signal by combining the scaled set of signals with a signal based on the audio signal decoded by the CELP-based decoder element.

Abstract: An electronic device for determining a set of pitch cycle energy parameters is described. The electronic device includes a processor and executable instructions stored in memory. The electronic device obtains a frame, a set of filter coefficients and a residual signal based on the frame and the set of filter coefficients. The electronic device determines a set of peak locations based on the residual signal and segments the residual signal such that each segment includes one peak. The electronic device determines a first set of pitch cycle energy parameters based on a frame region between two consecutive peak locations and maps regions between peaks in the residual signal to regions between peaks in a synthesized excitation signal to produce a mapping. The electronic device determines a second set of pitch cycle energy parameters based on the first set of pitch cycle energy parameters and the mapping.

Abstract: An signal processing apparatus, system and software product for audio modification/substitution of a background noise generated during an event including, but not be limited to, substituting or partially substituting a noise signal from one or more microphones by a pre-recorded noise, and/or selecting one or more noise signals from a plurality of microphones for further processing in real-time or near real-time broadcasting.

Abstract: A speech synthesis system can select recorded speech fragments, or acoustic units, from a very large database of acoustic units to produce artificial speech. When a pair of acoustic units in the database does not have an associated concatenation cost, the system assigns a default concatenation cost. The system then synthesizes speech, identifies the acoustic unit sequential pairs generated and their respective concatenation costs, and stores those concatenation costs likely to occur.

Abstract: A high quality speech is reproduced with a small data amount in speech coding and decoding for performing compression coding and decoding of a speech signal to a digital signal.

Abstract: Techniques disclosed herein include using a Maximum A Posteriori (MAP) adaptation process that imposes sparseness constraints to generate acoustic parameter adaptation data for specific users based on a relatively small set of training data. The resulting acoustic parameter adaptation data identifies changes for a relatively small fraction of acoustic parameters from a baseline acoustic speech model instead of changes to all acoustic parameters. This results in user-specific acoustic parameter adaptation data that is several orders of magnitude smaller than storage amounts otherwise required for a complete acoustic model. This provides customized acoustic speech models that increase recognition accuracy at a fraction of expected data storage requirements.

Abstract: A method and system for comparing and merging fault models which are derived from different data sources. Two or more fault models are first represented as bipartite weighted graphs, which define correlations between failure modes and symptoms. The nodes of the graphs are compared to find failure modes and symptoms which are the same even though the specific terminology may be different. A graph matching method is then used to compare the graphs and determine which failure mode and symptom correlations are common between them. Finally, smoothing techniques and domain expert knowledge are used to merge and update the fault models, producing an integrated fault model which can be used by onboard vehicle systems, service facilities, and others.

Abstract: System and method to improve intelligibility of coded speech, the method including: receiving an encoded speech signal from a network; extracting an encoded media data stream and one or more control data packets from the encoded speech signal; decoding the encoded media data stream to produce a decoded speech signal; boosting an upper spectral portion of the decoded speech signal to produce a boosted speech signal; and outputting the boosted speech signal. In another embodiment, the method may include: receiving an uncoded speech signal; processing the uncoded speech signal, wherein the processing comprises generating an unencoded data stream from the uncoded speech signal; boosting an upper spectral portion of the unencoded data stream to produce a boosted speech signal; encoding the boosted speech signal to produce an encoded speech signal; and outputting the boosted speech signal.

Abstract: A system and method may be configured to analyze audio information derived from an audio signal. The system and method may track sound pitch across the audio signal. The tracking of pitch across the audio signal may take into account change in pitch by determining at individual time sample windows in the signal duration an estimated pitch and a representation of harmonic envelope at the estimated pitch. The estimated pitch and the representation of harmonic envelope may then be implemented to determine an estimated pitch for another time sample window in the signal duration with an enhanced accuracy and/or precision.

Abstract: Systems and methods are described for performing packet loss concealment (PLC) to mitigate the effect of one or more lost frames within a series of frames that represent a speech signal. In accordance with the exemplary systems and methods, PLC is performed by searching a codebook of speech-related parameter profiles to identify content that is being spoken and by selecting a profile associated with the identified content for use in predicting or estimating speech-related parameter information associated with one or more lost frames of a speech signal. The predicted/estimated speech-related parameter information is then used to synthesize one or more frames to replace the lost frame(s) of the speech signal.

Abstract: A scalable decoder device (50) for signals representing audio comprises a primary decoder (21) connected to an input (40). The primary decoder (21) is arranged to provide a primary decoded signal (23) based on received parameters (4). A primary postfilter (31) is connected to the primary decoder (23) to provide a primary postfiltered signal (32). A secondary enhancement decoder (45) is connected to the input (40) and arranged to provide a secondary decoded enhancement signal (44). The device further comprises a combiner arrangement (55), arranged for combining the primary postfiltered signal (32) and a signal (53) based on the secondary decoded enhancement signal (44) into an output signal (6) to be provided at an output (6). The combining is made with an adaptable strength relation between contributions from the two signals. A method for decoding coded signals representing audio operates in analogy with the scalable decoder device (50).

Abstract: A method and device for searching an algebraic codebook during encoding of a sound signal, wherein the algebraic codebook comprises a set of codevectors formed of a number of pulse positions and a number of pulses distributed over the pulse positions. In the algebraic codebook searching method and device, a reference signal for use in searching the algebraic codebook is calculated. In a first stage, a position of a first pulse is determined in relation with the reference signal and among the number of pulse positions. In each of a number of stages subsequent to the first stage, (a) an algebraic codebook gain is recomputed, (b) the reference signal is updated using the recomputed algebraic codebook gain and (c) a position of another pulse is determined in relation with the updated reference signal and among the number of pulse positions.

Abstract: Spread level parameter correcting means 501 receives a contour parameter as information representing the contour of a feature sequence (a sequence of features of a signal considered as the object of generation) and a spread level parameter as information representing the level of a spread of the distribution of the features in the feature sequence. The spread level parameter correcting means 501 corrects the spread level parameter based on a variation of the contour parameter represented by a sequence of the contour parameters. Feature sequence generating means 502 generates the feature sequence based on the contour parameters and the corrected spread level parameters.

Abstract: Provided is a signal distortion elimination apparatus comprising: an inverse filter application means that outputs the signal obtained by applying an inverse filter to an observed signal as a restored signal when a predetermined iteration termination condition is met and outputs the signal obtained by applying the inverse filter to the observed signal as an ad-hoc signal when the predetermined iteration termination condition is not met; a prediction error filter calculation means that segments the ad-hoc signal into frames and outputs a prediction error filter of each frame obtained by performing linear prediction analysis of the ad-hoc signal of each frame; an inverse filter calculation means that calculates an inverse filter such that a concatenation of innovation estimates of the respective frames becomes mutually independent among their samples, where the innovation estimate of a single frame (an innovation estimate) is the signal obtained by applying the prediction error filter of the corresponding frame

Abstract: When a frame immediately preceding an encoding target frame to be encoded by a first encoding unit operating under a linear predictive coding scheme is encoded by a second encoding unit operating under a coding scheme different from the linear predictive coding scheme, the encoding target frame can be encoded under the linear predictive coding scheme by initializing the internal state of the first encoding unit. Therefore, encoding processing performed under a plurality of coding schemes including the linear predictive coding scheme and a coding scheme different from the linear predictive coding scheme can be realized.

Abstract: A method for decoding an audio signal includes: obtaining a lower-band signal component of an audio signal corresponding to a received code stream when the audio signal switches from a first bandwidth to a second bandwidth which is narrower than the first bandwidth; extending the lower-band signal component to obtain higher-band information; performing a time-varying fadeout process on the higher-band information to obtain a processed higher-band signal component; and synthesizing the processed higher-band signal component and the obtained lower-band signal component. With the methods provided in the embodiments of the invention, when an audio signal has a switch from broadband to narrowband, a series of processes such as bandwidth detection, artificial band extension, time-varying fadeout process, and bandwidth synthesis, may be performed to make the switch to have a smooth transition from a broadband signal to a narrowband signal so that a comfortable listening experience may be achieved.

Abstract: A voice encoding/decoding method and apparatus. A voice encoder includes: a quantization selection unit generating a quantization selection signal; and a quantization unit extracting a linear prediction coding (LPC) coefficient from an input signal, converting the extracted LPC coefficient into a line spectral frequency (LSF), quantizing the LSF with a first LSF quantization unit or a second LSF quantization unit based on the quantization selection signal, and converting the quantized LSF into a quantized LPC coefficient. The quantization selection signal selects the first LSF quantization unit or second LSF quantization unit based on characteristics of a synthesized voice signal in previous frames of the input signal.

Abstract: In a method of smoothing background noise in a telecommunication speech session; receiving and decoding S1O a signal representative of a speech session, the signal comprising both a speech component and a background noise component. Subsequently, determining LPC parameters S20 and an excitation signal S30 for the received signal. Thereafter, synthesizing and outputting (S40) an output signal based on the determined LPC parameters and excitation signal. In addition, modifying S35 the determined excitation signal by reducing power and spectral fluctuations of the excitation signal to provide a smoothed output signal.

Abstract: Systems and methods are described for performing packet loss concealment using an extrapolation of an excitation waveform in a sub-band predictive speech coder, such as an ITU-T Recommendation G.722 wideband speech coder. The systems and methods are useful for concealing the quality-degrading effects of packet loss in a sub-band predictive coder and address some sub-band architectural issues when applying excitation extrapolation techniques to such sub-band predictive coders.

Abstract: Provided are a method and apparatus for encoding or decoding an audio signal by adaptively interpolating a linear predictive coding (LPC) coefficient. In the method and apparatus of encoding or decoding an audio signal, LPC coefficient interpolation is selectively performed depending on whether a transient section is present in a current frame, thereby preventing noise from occurring when interpolating LPC coefficients in the transient section.

Abstract: A system including at least one storage node and at least one computation node connected by a switch is described herein. Each storage node has one or more storage units and one or more network interface components, the collective bandwidths of the storage units and the network interface components being proportioned to one another to enable communication to and from other nodes at the collective bandwidth of the storage units. Each computation node has logic configured to make requests of storage nodes, an input/output bus, and one or more network interface components, the bandwidth of the bus and the collective bandwidths of the network interface components being proportioned to one another to enable communication to and from other nodes at the bandwidth of the input/output bus.

Abstract: A voice conversion apparatus stores, in a parameter memory, target speech spectral parameters of target speech, stores, in a voice conversion rule memory, a voice conversion rule for converting voice quality of source speech into voice quality of the target speech, extracts, from an input source speech, a source speech spectral parameter of the input source speech, converts extracted source speech spectral parameter into a first conversion spectral parameter by using the voice conversion rule, selects target speech spectral parameter similar to the first conversion spectral parameter from the parameter memory, generates an aperiodic component spectral parameter representing from selected target speech spectral parameter, mixes a periodic component spectral parameter included in the first conversion spectral parameter with the aperiodic component spectral parameter, to obtain a second conversion spectral parameter, and generates a speech waveform from the second conversion spectral parameter.

Abstract: Provided are a new hybrid audio decoder and a new hybrid audio encoder having block switching for speech signals and audio signals. Currently, very low bitrate audio coding methods for speech and audio signal are proposed. These audio coding methods cause very long delay. Generally, in coding an audio signal, algorithm delay tends to be long to achieve higher frequency resolution. In coding a speech signal, the delay needs to be reduced because the speech signal is used for telecommunication. To balance fine coding quality for these two kinds of input signals with very low bitrate, this invention provides a combination of a low delay filter bank like AAC-ELD and a CELP coding method.

Abstract: A system for coding a hierarchical audio signal, comprising, at least, a core layer using parametric coding by analysis by synthesis in a first frequency band, a band extension layer for widening said first frequency band into a second frequency band, or wideband. The system also comprises a wideband audio coding quality enhancement layer based on transform coding using a spectral parameter obtained from said band extension layer. Application to transmitting speech and/or audio signals over packet networks.

Abstract: Provided is an audio encoding device which can detect an optimal pitch pulse when using pitch pulse information as redundant information.

Abstract: A high quality speech is reproduced with a small data amount in speech coding and decoding for performing compression coding and decoding of a speech signal to a digital signal.

Abstract: Methods, systems, and computer program products for silence insertion descriptor (SID) conversion are disclosed. According to one aspect, the subject matter described herein includes a method for silence insertion descriptor (SID) conversion. The method includes receiving a wireless frame, the frame identifying a first node as a frame source and a second node as a frame destination; determining whether tandem-free operation (TFO) is applicable; responsive to a determination that TFO is applicable, determining whether the frame is a SID frame; responsive to a determination that the frame is a SID frame, determining whether the SID format used by the first node is incompatible with the SID format used by the second node; and responsive to a determination that the SID format used by the first node is incompatible with the SID format used by the second node, converting the SID frame from the SID format used by the first node to the SID format used by the second node.

Abstract: A post filter and a decoder enabling improvement of the sound quality of a decoded signal even when the sound quality of the decoded signal is different from the bands are disclosed. A frequency converting section determines a decoded spectrum. A power spectrum computing section computes the power spectrum from the decoded spectrum. A correction band determining section determines the band in which the power spectrum is corrected according to layer information. A power spectrum correcting section corrects the power spectrum in the corrected band in such a way that the variation along the frequency axis is suppressed. An inverse converting section subjects the corrected power spectrum to inverse conversion to determine an autocorrelation function. An LPC analyzing section determines an LPC coefficient of the determined autocorrelation function.