Patent Application
20050080498
The invention relates to the field of wavetable based sound synthesis and more specifically to methods for use in a wavetable based sound synthesis, wherein a first processor stores wavetable data and wherein a second processor generates an output audio signal frame-by-frame based on samples of this wavetable data. The invention relates equally to corresponding processors, to a corresponding wavetable based sound synthesis system, to a corresponding device and to corresponding software program products.
Wavetable based sound synthesis is a popular sound synthesis for use in mobile telecommunication terminals. It has the advantage that a very high sound synthesis quality is achieved with a rather simple algorithm, which basically relies on processing and playing back previously recorded audio samples, called wavetables.
For the purpose of the music synthesis, the wavetables store the tones of real instruments that are recorded under different conditions, for instance using different pitches or musical notes, different note velocities, etc. Before the wavetables are actually included into the output audio sound, the raw wavetable data undergoes several signal processing operations, including decimation and interpolation for the purpose of pitch shifting the original note, amplitude modulation for the purpose of modeling the envelope of the output audio waveform, filtering, etc.
A signal processing operation that is extensively used in wavetable based sound synthesis is synchronous pitch-shifting. This operation is performed in order to modify the pitch of the recorded wavetable, which allows to synthesize higher or lower musical notes or tones. Basically, the operation is carried out by resampling the wavetable data by decimation and/or interpolation procedures, such that the pitch is increased or decreased without changing the output sampling rate. For instance, playing only every second sample from the wavetable data would caused a pitch increase by one octave and a reduction of the number of samples by half. In general, any pitch-shifting operation will alter the number of samples in the signal.
Modern mobile telecommunication terminals provide specific architectural features that should be exploited by any practical implementation of a wavetable sound synthesis. Often a terminal contains more than one processor. For instance, the terminal may comprise a micro controller unit (MCU) as main processor, as well as additionally one or more dedicated coprocessors. An example of such dedicated coprocessor is a digital signal processor (DSP) that is the preferred tool to perform computationally intensive operations characteristic to signal processing tasks.
In several hardware architectures, the size of the memory space addressable by different processors is different, and it might not always be possible to store the entire wavetable data in the memory space which is addressable by the very processor that is going to process it, for example the DSP. In such architectures, it might be necessary to store the wavetable data in a memory space which is addressable by some other processor, for example the MCU. The MCU then has to transfer the wavetable data to the DSP during playback. A technological solution for inter-processor communication consists in using a memory space addressable by both processors, called shared memory. Thus, taking care of avoiding conflicts, each processor can be allowed to access the shared memory at certain moments, in order to write data for the other processor, or to read data that was previously written for it by the other processor.
A known approach of implementing a wavetable based sound synthesis on such a multiprocessor architecture is to copy the entire wavetable data which is needed by all active voices from an MCU memory into a DSP memory for processing and playback.
Due to DSP memory limitations, such an approach can only be used for small polyphony synthesis, since the larger the number of active voices the higher the memory requirements for the DSP. In addition, very long wavetable data might also be difficult to utilize, since the size of a very long single wavetable might approach or even exceed the available DSP memory space. Summarized, the available DSP memory space might be insufficient to accommodate the entire wavetable data needed to produce a desired audio output.
The same problem may arise in any other wavetable based sound synthesis system having a first processor with sufficient memory space for storing the wavetable data and a second processor with sufficient computational power for processing the wavetable data.
In U.S. Pat. No. 6,100,461 A, a wavetable based sound synthesis system is described, in which wavetable data having a modified wavetable structure is transmitted in bursts from a memory to a wavetable audio synthesis device. In order to achieve an efficient transmission on a Peripheral Component Interconnect (PCI) bus, the data voice samples, that are 8 or 16 bits in length, are organized in units of 32-bits called frames. The group of samples transmitted in one burst comprises several such frames of data for a voice. It is assumed that the wavetable audio synthesis device has access to the main memory space where the entire wavetable data is stored, and that the data transfers between the main memory and the device can be carried out without involving the main processor of the host machine. As mentioned above, however, such a wavetable audio synthesis device is not always able to keep the entire wavetable data in the memory space that it is able to address, and hence an alternative solution is needed.
The invention provides an alternative to known approaches for wavetable sound synthesis. It provides in particular a possibility of implementing a wavetable sound synthesis making use of two processors, where a first processor is equipped with sufficient memory space to store the wavetable data, but insufficient computational power to process it, and where a second processor has the computational power to process the data for wavetable sound synthesis, but has insufficient memory space to store the raw wavetable data.
Two methods for use in a wavetable based sound synthesis are proposed, wherein a first processor stores wavetable data and wherein a second processor generates at least an output audio signal frame-by-frame based on samples of the wavetable data.
The first proposed method comprises at the first processor selecting those samples of the stored wavetable data, which are expected to be required at the most at the second processor for generating a respective next output audio frame. The selection is based on a given model of a pitch-shift evolution during a single frame and on the number of samples which have been used so far by the second processor during a generation of preceding audio frames. The first proposed method further comprises at the first processor making the selected samples available to the second processor.
The second proposed method comprises at the second processor receiving samples of the stored wavetable data for a kth output audio frame which is to be generated next, with k greater than 0, the samples being made available by the first processor. The second proposed method further comprises at the second processor determining an index Ik identifying a first sample among the received samples which has not been used for generating a (k−1)th output audio frame. The second proposed method further comprises at the second processor processing the received samples, beginning with the first sample identified by the determined index Ik, for generating the kth output audio frame. Finally, the second proposed method comprises at the second processor making the number Kk of samples required in generating the kth output audio frame available to the first processor. It is to be noted that for the first output audio frame, the index Ik is determined to be zero, as no preceding output audio frame exists, and thus no samples have been used for generating such a preceding frame.
In addition, a first processor providing wavetable data for a wavetable based sound synthesis to another processor is proposed, which processor comprises a memory for storing wavetable data and a processing component selecting those samples of the stored wavetable data, which are expected to be required at the most at the other processor for generating a respective next output audio frame. The selection is based on a given model of a pitch-shift evolution during a single frame and on the number of samples which have been used so far by the other processor during a generation of preceding audio frames. The processing component further makes the selected samples available to the other processor.
In addition, a wavetable based sound synthesis system and a device are proposed, either comprising the proposed first processor and a second processor. The second processor includes in both cases a memory for storing samples of wavetable data made available by the first processor and a processing component generating at least an output audio frame by processing samples from the memory of the second processor.
Moreover, a separate second processor for generating at least an output audio signal frame-by-frame based on samples of wavetable data is proposed. The second proposed processor comprises a processing component, which receives samples of the wavetable data for a kth output audio frame which is to be generated next, with k greater than 0, the samples being made available by a first processor. The processing component further determines an index Ik identifying a first sample among the received samples which has not been used for generating a (k−1)th output audio frame. The processing component further processes the received samples, beginning with the first sample identified by the determined index Ik, for generating the kth output audio frame. The processing component further makes the number Kk of samples required in generating the kth output audio frame available to the other processor.
Moreover, a first software program product is proposed, in which a software code for supporting a wavetable based sound synthesis is stored. When running in a processing component of a processor storing wavetable data, the software code selects samples of the stored wavetable data, which samples are expected to be required at the most at another processor for generating a respective next output audio frame. The selection is based on a given model of a pitch-shift evolution during a single frame and on the number of samples which have been used so far by the other processor during a generation of preceding audio frames. The software code further makes the selected samples available to the other processor.
Finally, a second software program product is proposed, in which a software code for supporting a wavetable based sound synthesis is stored. When running in a processing component of a processor for generating at least an output audio signal frame-by-frame based on received samples of wavetable data, the software code determines an index Ik identifying a first sample among received samples, which first sample has not been used for generating a (k−1)th output audio frame, wherein the received samples are samples of the wavetable data for a kth output audio frame which is to be generated next, with k greater than 0. The software code further processes the received samples, beginning with the first sample identified by the determined index Ik, for generating the kth output audio frame. The software code further makes the number Kk of samples required in generating the kth output audio frame available to another processor providing the received samples.
The invention proceeds from the idea that a real-time streaming of wavetable data between two processors can be enabled. It is therefore proposed that the entire wavetable data is stored in a first processor comprising a sufficiently large memory, and that basically only those data samples that are required at a time during the playback are transmitted to a second processor, in which the samples may undergo further processing and eventually contribute to the output generated sound. The wavetable data is thus stored in a memory space addressable only by the first processor and transferred to the second processor in short pieces, for real-time processing during playback.
The second processor will usually calculate and deliver to the audio output a certain number of audio samples at fixed time intervals. The audio samples delivered at each time interval form a frame. The second processor thus has to meet periodic deadlines at which it must deliver a frame of output audio samples for playback. The frames have a constant time duration and comprise therefore the same number of output audio samples each. On the one hand, a large frame duration would be preferable in order to reduce the effect of possible latencies in the first processor, to increase the efficiency by reducing the number of function calls in a software program for wavetable synthesis and to reduce the number of block data transfers per unit of time between the two processors. On the other hand, the frame size must be limited to an acceptable value such that the required data fits into the memory which is directly addressable by the second processor.
A difficulty arises from the fact that the number of raw wavetable samples required by the second processor to calculate the respective next output audio frame is not known in advance at the first processor. This is due to the fact that the amount of a pitch-shift, which has to be applied by the second processor to the raw wavetable samples for generating the desired audio signal, is calculated by the second processor only during the preparation of the output audio frame. The number of required samples is moreover often changing from one frame to another according to different real-time musical controls. The amount of pitch-shift does not even have to be constant for the duration of a single output audio frame. Often, its instantaneous value is changed during the frame duration due to musical effects, like vibrato, that are simulated by the second processor in real time. It is to be noted that it would be extremely inefficient to simulate the pitch-shift computations at the first processor beforehand, in order to determine how many samples the second processor will need for generating the next audio frame.
It is therefore proposed in addition that the first processor predicts the wavetable samples which the second processor will need to prepare the respective next audio frame, and sends a number of samples that is expected to cover the needs of the second processor.
If this number of samples is underestimated by the first processor, the raw wavetable data transferred to the second processor will turn out to be insufficient for calculating an entire output frame. On the other hand, if the number of wavetable samples needed by the second processor is overestimated, then it may happen for the first processor to advance too fast through the wavetable data in comparison to the second processor. In such a case, the second processor may be forced to jump over portions of the wavetable data for which it did not have time for processing.
It is therefore proposed more specifically that the first processor predicts the required samples for a respective next frame based on a given model of the pitch-shift evolution during one audio frame and on the number of samples the second processor needed for the preparation of preceding output audio frames.
The second processor should be able to synthesize output audio frames based on the wavetable samples provided by the first processor.
It is an advantage of the invention that it allows to reduce the memory requirements in the second processor significantly, since only an amount of samples somewhat larger than the amount required for one frame has to be stored at a time by the second processor. Alternatively or in addition, the invention allows for the same reason a much higher polyphony. Further, it allows the use of wavetable data of any size.
The invention can be easily adapted to a use with any model for the pitch-shift variation during one frame.
In an embodiment of the invention, the first and the second processor communicate through a shared memory space in which one processor allows to write data for the other processor and to read data previously written there by the other processor. In this case, the first processor provides the samples selected for the next frame to the second processor by writing them into the shared memory space, and the second processor reads the samples from the shared memory at an appropriate point of time. The second processor further records in this case the number Kk of samples required in generating the kth output audio frame into the shared memory for making it available to the first processor. The proposed software code copies in this case the selected samples directly into the shared memory, from where they can be fetched by the first processor at an appropriate moment.
The samples for one frame can be provided by the first processor in particular in one block per frame.
The data transfer from a shared memory to the memory addressable only by the second processor can be efficiently carried out as a single data block transfer per frame by taking advantage of a direct memory access (DMA) transfer, if available.
It is of importance to note that although the present invention describes in detail the problems related with streaming wavetable data for a single voice, it can be easily extrapolated to a plurality of voices. Thus, any block of data transferred from the first processor to the second processor may include the necessary wavetable data samples needed by all active voices rather than by a single voice, reducing thereby the number of such block data transfers to one per frame.
The invention can be implemented in software or in hardware. The invention can further be embedded into any wavetable based sound synthesizing system that is operating on a split processor architecture. The processors can be in particular, though not exclusively, an MCU storing the wavetable data and a DSP generating the output audio signal. The device can be in particular, though not exclusively, a mobile telecommunication terminal. The system can be, for example, equally a mobile telecommunication terminal or part of a mobile telecommunication terminal or an assembly of several components or devices.
Other objects and features of the present invention will become apparent from the following detailed description considered in conjunction with the accompanying drawings. It is to be understood, however, that the drawings are designed solely for purposes of illustration and not as a definition of the limits of the invention, for which reference should be made to the appended claims. It should be further understood that the drawings are not drawn to scale and that they are merely intended to conceptually illustrate the structures and procedures described herein.
The MCU 10 includes to this end a processing component 11 and a memory 12. The DSP 20 comprises equally a processing component 21 and a memory 22. The memory 12 of the MCU 10 is significantly larger than the memory 22 of the DSP 20, while the computational power of the processing component 21 of the DSP 20 is significantly larger than the computational power of the processing component 11 of the MCU 10, as known from conventional mobile telecommunication terminals.
The memory 12 of the MCU 10 stores raw wavetable data, and the processing component 11 of the MCU 10 runs a software 13 supporting the streaming of the raw wavetable data to the shared memory 30, from where it becomes available to the DSP 20 for transfer into memory 22. The software 13 is able to select samples of the stored raw wavetable data which can be expected to be required at the most at the DSP 20 for generating a next audio frame. The processing component 11 selects the samples according to the invention by means of a prediction based on a model for the most likely pitch evolution during one audio frame and on the numbers of raw data samples that the DSP 20 has used so far for producing output audio frames. The software 13 run by the processing component 11 of the MCU writes the selected samples directly into a data block 31 inside the shared memory 30, from where they are transferred at an appropriate time into the memory 22 of the DSP 20. In addition, the software 13 run by the processing component 11 of the MCU writes control information 32 on the provided data block into the shared memory 30. This information will be used at an appropriate time by the processing component 21 of the DSP 20 in order to handle a raw wavetable data block 31 copied from shared memory 30 into the memory 22.
The memory 22 of the DSP 20 stores only those samples at a time which are transferred to it, in a form of a data block 31, from the shared memory 30 by means of a data transfer initiated by the processing component 21 at the beginning of each frame. The software 23 is moreover able to synthesize output audio frames 40 from received raw wavetable data in a known manner. In addition, it is able to determine based on control information 32, received from the processing component 11 of the MCU 10, which samples in the DSP memory 22 are to be used for the respective next audio frame, and to provide feedback information 33 on the actually used number of samples for this next audio frame, into the shared memory 30. The feedback information 33 is read by the processing component 11 of the MCU 10 at the beginning of each frame and it is used to prepare a new data block 31.
The MCU 10 and the DSP 20 work independently from each other and communicate only once per frame. The temporal evolution of the communication between the MCU 10 and the DSP 20 is depicted in
The MCU 10 prepares directly into the shared memory 30 a first data block 31 with raw wavetable data together with the related control information 32 for the DSP 20. Thereafter, it prepares a second data block 31 together with the related control information 32 into the same shared memory 30 for the DSP 20, etc.
Upon receipt of a respective data block, the DSP 20 produces an output audio frame 40 and reports to the MCU how many raw data samples it needed for processing this specific audio frame. This report is done in the form of a feedback data 33 stored in the shared memory 30.
As can be seen in
The exact samples the MCU 10 should include into the next data block for enabling the DSP 20 to prepare the next audio frame is not known by the MCU 10. Hence it must be predicted as mentioned above with reference to
In case an insufficient number of raw data samples is transmitted from the MCU 10 to the DSP 20, the output frame would have to be completed with some neutral values, once the available raw data samples received from the MCU 10 have been consumed.
In order to prevent such an error, the MCU 10 must always submit to the DSP 20 a larger number of samples than the DSP 20 is expected to process for a specific audio frame. Consequently, the data blocks submitted by the MCU 10 to the DSP 20 will usually be overlapping to some degree. A corresponding block based streaming of a wavetable data array from the MCU 10 to the DSP 20 is illustrated in
A streaming mechanism will now be presented, which is suited to find a compromise between the requirements of a sufficiently large number of samples for the preparation of an audio frame and a sufficiently small number of samples for the storage in the shared memory 30 as well as in the memory 22 of the DSP 20.
Similarly as
In this diagram, Jk is the index of the first wavetable sample that shall be submitted to the DSP 20 in the kth data block. Ok is the number of wavetable samples common to the kth and the (k−1)th data block. Nk is the number of wavetable samples included into the kth data block provided by the MCU 10. And Kk is the number of wavetable samples used by the DSP 20 in order to produce the kth output audio frame.
Estimates for the number of wavetable samples needed by DSP 20 for audio frames k−1 and k are to be determined by the MCU 10 based on an underlying model of the pitch-shift during one frame and on the number of wavetable samples that has been used by the DSP 20 for each output audio frame until the frame k−2. Because any such estimate can be subject to errors, lower and upper bounds for the possible number of samples will be used to decide which wavetable samples should be sent to the DSP 20 in one data block.
For such upper and lower bounds, the following notations are employed: Lk-1 is the lower bound of the number of samples Kk-1 of the (k−1)th data block. Uk-1 is the upper bound of Kk-1. UUk is the upper bound of the number of samples Kk of the kth data block. All three bounds Lk-1, Uk-1 and UUk, are estimated based at least on the underlying model for pitch variation, and possibly in addition, depending on the selected model, on the DSP usage history until audio frame k-2.
In order to ensure that all raw data samples of the stored wavetable data are send to the DSP 20 in one of the data blocks and that there is no jumping over samples, the index Jk of the first data sample for each data block k should be as small as possible. The index can thus be calculated according to the following formula:
Jk=K1+K2+ . . . +Kk-2+Lk-1. (1)
The numbers K1 to Kk-2 may be summarized in a sum Sk.
In order to ensure that a sufficient number of samples is submitted in the kth data block to the DSP 20, the size Nk of the data block must be chosen as large as possible. The size can thus be calculated according to the following formula:
Nk=UUk+Uk-1−Lk-1. (2)
Finally, the number of overlapping samples between the kth and the (k-1)th data block can be determined according to the following formula:
Ok=Nk-1+Jk-1−Jk. (3)
Equations (1) to (3) result in three values which can be used by a streaming algorithm for each audio output frame k, where k>2.
The use of the formulas in a streaming mechanism is presented in a general form in the flow charts of
The operations carried out by the MCU processing component 11 are illustrated in
At the beginning of the data transfer, the MCU 10 has to prepare a first data block for the first output audio frame which is to be prepared by the DSP 20. It is assumed that the lower and upper bounds L1 and U1 for the first audio frame and the upper bounds UU2 for the second audio frame are known a priori at the MCU 10. Alternatively, they could be estimated by the MCU 10 based on an underlying model for pitch-shift variation.
For the first data block, the MCU 10 sets an auxiliary sum S1 and the index J1 to zero, the number of samples for the first data block N1 to the upper bound U1, and the number of overlapping samples O1 equally to zero. Then, the MCU 10 prepares the first data block for transmission. The data block includes N1 samples from the raw wavetable data stored in the MCU memory 12 beginning with the very first sample having the index J1=0. The prepared data block is then provided to the DSP 20 via the shared memory space 30 together with the number of samples N1 and the determined number of overlapping samples O1=0.
For the second data block comprising the samples for the second output audio frame which is to be prepared by the DSP 20, the MCU 10 sets the auxiliary sum S2 again to zero and the index J2 to L1. Further, the MCU 10 determines the number of samples for the second data block N2 and the number of overlapping samples O2 in accordance with above equations (2) and (3). Then, the MCU 10 prepares the second data block for transmission. The data block includes N2 samples from the raw wavetable data stored in the MCU memory 12 beginning with the sample having the index J2. The prepared data block is then provided to the DSP 20 via the shared memory space 30 together with the number of samples N2 and the determined number of overlapping samples O1.
For any further data block k, the MCU 10 first estimates bounds Lk-1, Uk-1 for the (k-1)th audio frame and bound UUk for the kth audio frame based on the underlying model for pitch-shift variation, and possibly in addition on the DSP history, that is on the values K1, K2 to Kk-2. The value Kk-2 is provided for each data block k by the DSP 20, as will be described below with reference to
Then, the auxiliary sum Sk=Sk-1+Kk-2 is calculated. The calculated sum Sk thus represents the sum K1+K2+ . . . +Kk-2. Thereupon, the index Jk is calculated according to above equation (1) making use of the auxiliary sum Sk. In addition, the MCU 10 determines the number of samples for the kth data block Nk and the number of overlapping samples Ok in accordance with above equations (2) and (3).
Now, the MCU 10 prepares the kth data block for transmission. The data block includes Nk samples from the raw wavetable data stored in the MCU memory 12 beginning with the sample having the index Jk. The prepared data block is provided to the DSP 20 via the shared memory space 30 together with the number of samples Nk and the determined number of overlapping samples Ok.
The operations carried out by the DSP processing component 21 are illustrated in
At the beginning, the DSP 20 receives the first data block k=1, the number of samples N1 and the determined number of overlapping samples O1 from the MCU 10 via the shared memory space 30. Further, it sets a local variable I1 to zero.
Then, the DSP 20 prepares the first output audio frame.
It processes to this end data samples from the received first data block beginning at index I1=0 in the data block, that is, with the very first sample. The actual preparation of the audio frame is carried out in a known manner by means of a wavetable sound synthesis, including for example pitch shifting operations. If the number of samples in the first data block is insufficient for preparing the first audio frame, a certain value, for example zero, might be used instead of each missing sample. The DSP 20 records the number K1 of samples that have been used in the preparation of the first output audio frame and provides this number K1 to the MCU 10 via the shared memory space 30.
Thereafter, the value of the variable I1 is increased by the number K1. If the new value I1 is larger than the total number of received samples N1 in the first data block, some samples have been missing for preparing the first audio frame, thus there is an error in the playback.
For any subsequent output audio frame k, the DSP 20 receives from the MCU 10 via the shared memory space 30 the kth data block, the number of samples Nk in this data block and the number Ok of overlapping samples. The DSP 10 first sets the local variable Ik according to the formula Ik=Ik-1−Nk-1+Ok. The resulting value indicates an index in the kth data block beginning from which samples are to be used for preparing the kth audio frame, since the samples at smaller indices have already been used for a preceding output audio frame. If the variable Ik has a value smaller than zero, this means that some samples are lost, which implies an error in the playback.
The DSP 20 then prepares the kth output audio frame. It processes to this end data samples from the received kth data block beginning at the determined index Ik in the data block. The actual preparation of the audio frame is carried out in a known manner by means of a wavetable sound synthesis. If the number of samples in the kth data block is insufficient for preparing the kth audio frame, a certain value, for example zero, might be used instead of each missing sample. The DSP 20 records the number Kk of samples that have to be used in the preparation of the kth output audio frame and provides this number Kk via the shared memory space 30 to the MCU 10.
Thereafter, the value of the variable Ik is increased by the number Kk. If the new value Ik is larger than the total number of received samples Nk in the kth data block, some samples have been missing for preparing the frame, thus there is an error in the playback.
Variations of the algorithm illustrated in
The model for pitch shift variation in
A beam at the top of
As can be seen, the DSP 20 receives enough wavetable samples with the (k-1)th data block for preparing the (k-1)th output audio frame. However, since the DSP reports are always two frames behind, as mentioned above with reference to
A beam at the top of
In this case, the wavetable samples of the kth data block start off with a sufficiently low index Jk. But the kth data block turns out to be too small such that, at some point, the DSP 20 will run out of samples during the preparation of the kth audio frame. The missing samples for frame k are indicated with a gray section. The DSP 20 might thus be forced to replace the missing samples with some neutral value, e.g. using a zero padding.
The two scenarios presented in
In the following, two simple examples of a model for pitch evolution are presented, which may be employed in the algorithm of
In a first example, the model for pitch evolution is selected such that the number of samples needed by the DSP 20 is assumed to lie always between two positive integer values m and M, where m<M. In this model, the bounds for the first two audio frames required by the MCU 10 for the first two data blocks are L1=m, U1=M, and UU2=M. Next, the estimates for the lower and upper bounds for the subsequent frames are L2=m, Lk-1=m, Uk-1=M, and UUk=M, where k>2.
In a second example, the model for pitch evolution imposes certain lower and upper bounds for the average amount of pitch-shift that may take place during a single audio frame. The average pitch-shift during one frame is assumed to be between −d and +d octaves. Denoting by F the number of samples in an output audio frame, the bounds for the first two audio frames are L1=floor(2−dF), U1=ceil(2dF), and UU2=ceil(22dF), where floor( ) and ceil( ) are well known functions that truncates their argument to the closest integer either towards minus or plus infinity, respectively. For audio frames k>2, the estimates for the lower and upper bounds are Lk-1=floor(2−dKk-2), Uk-1=ceil(2dKk-2), and UUk=ceil (22dKk-2), and the lower bound for the second audio frame is L2=floor(2−dF).
While there have been shown and described and pointed out fundamental novel features of the invention as applied to a preferred embodiment thereof, it will be understood that various omissions and substitutions and changes in the form and details of the devices and methods described may be made by those skilled in the art without departing from the spirit of the invention. For example, it is expressly intended that all combinations of those elements and/or method steps which perform substantially the same function in substantially the same way to achieve the same results are within the scope of the invention. Moreover, it should be recognized that structures and/or elements and/or method steps shown and/or described in connection with any disclosed form or embodiment of the invention may be incorporated in any other disclosed or described or suggested form or embodiment as a general matter of design choice. It is the intention, therefore, to be limited only as indicated by the scope of the claims appended hereto.
