Designing a Hybrid Codec with the help of Integer-MDCT and to estimate the audio quality by means of SPL and CR.
The MDCT can be taken as a critical sampled filterbank with 50% overlapped windows in the analysis of filterbank. This overlapping analysis windowing is very useful to audio coding since it helps to mitigate the blocking artifacts that deteriorate the reconstruction of transform audio coders with non-overlapped transforms. To achieve critical sampling, a sub-sampling operation is performed in the frequency domain; and the aliasing resulted from this sub-sampling operation is subsequently cancelled in the time domain by an "overlap and add" operation of two succeeding blocks in the synthesis filterbank .
The Discrete Cosine Transform (DCT) or MDCT for the purpose of lossless audio coding is ambivalent. While they provide a good decorrelation of the input signal, the number of possible output values increases considerably compared to the number of possible input values. Thus, a quantization operation is necessary in order to achieve a reduction of the data rate. This quantization either has to be fine enough to allow neglecting the resulting error after rounding to the target word length, or an additional residual error has to be coded in time domain  . The lifting scheme-based integer transform maps integers to integers and is reversible, and thus it has become a very useful tool for lossless coding applications. In addition, since the integer transform is an integer approximation of the original floating-point transform, the integer transform can be used for a lossy coding scheme .
This paper presents a design of hybrid codec which can bridge the gap between perceptual and lossless audio coding. The Integer Modified Discrete Cosine Transform (Int-MDCT) approximates the MDCT while producing integer output values. The development of hybrid codec is done by using Integer MDCT with long window. This method consists of paired codec of audio coding algorithm i.e. both the G. 722 andAAC. Certainly different audio codec's are most frequently used for encoding and decoding applications of audios. With the help of G.722 and AAC the audios are being encoded and decoded, providing better compression results and audio quality.
* Ravi K. Chivukula, Yuriy A. Reznik, Senior Member, IEEE, Yanyan Hu, Venkat Devarajan, Senior Member, IEEE, and Mythreya Jayendra-Lakshman , proposed a methodology known as the low delay spectral band replication in which the LD TDAC analysis and the synthesis filter banks are mapped which provides the faster implementation. It is designed by means of encoding and decoding methods, making the methodology to be difficult.
* Rongshan Yu, Susanto Rahardja, Lin Xiao, Chi Chung Ko,  proposes an algorithm known as Advanced Audio Zip which provides a lossless audio coding. It achieves an excellent compression ratio performance but introduces a marginal overhead when compared with the other methods and operates at the low bit range.
* X. Maitre,  the author describes the recommendation of CCITT standardized G.722 audio codec which is a wideband audio codec. It uses Adaptive Differential Pulse Code Modulation (ADPCM) for encoding and decoding with a bit rate 48/56/64 kbits/s. G.722 audio codec overcomes the bandwidth limitations, those are being faced by the G.711 audio codec. It consumes the low space for the storage, thereby providing the good audio quality.
* KARLHEINZ BRANDENBURG,  explains briefly about the successor of MP3. AAC has been designed to compress the music and also to overcome the disadvantage faced in the MPEG layer. The reconstructed audio sounds in the same manner as that of the original sound.
* Recommendation International Telecommunication Union BS.1187-1,  along with the moving picture experts group proposed the testing methodology for checking the audio quality of the perceived audio signal by means of two versions namely basic and advanced version. Basic version uses the FFT based model and the advanced version uses the filter bank used model.
* Rajesh Kumar,  describes subjective quality assessment and objective quality assessment for two different datasets and obtains the Mean Opinion Score (MOS) for subjective listening and objective listening.
* Communications Magazine,  proposed a audio codec G.711 to produde better compression by means of the companding techniques. It provides the huge bit conversion with less implementations. Though it is used for the wide communication applications, it provides the conversion with more complexity and delay.
The Integer Mdct:
The Integer Modified Discrete Cosine Transform has been employed in transform coding schemes as the analysis/synthesis stage based upon time domain aliasing cancellation(TDAC). It inherits most of the favourable properties of the MDCT, including the overlapping structure and critical sampling by means of TDAC. The integer MDCT is derived from its prototype Modified Discrete Cosine Transform. It is performed by means of the integer approximation of MDCT in the fonn of lifting steps or the rounding operations.
The number of Givens rotations needed for discrete trigonometric functions is [Nlog.sub.2]N, where N is the block size. Therefore, the total rounding number is also [Nlog.sub.2]N for the directly converted integer transforms. The approximation error increases with the number of rounding operations of [Nlog.sub.2]N. The fast algorithm has an immediate application in improving the performance of a lossless audio coding system. The total rounding number of this algorithm is only 2.5N times, while the approximation error appears to be less than that of the directly converted integer transforms. As a result, the lossless compression ratio of a lossless audio coding system employing the fast algorithm which refers to the Integer MDCT improves and at same time the computational complexity is greatly reduced. The rotations or the rounding operation can be done by means of the lifting scheme.
Definition And Basic Facts:
A. The Lifting Scheme or Rounding Operation:
Orthogonal block transforms are decomposed into given rotations,
[mathematical expression not reproducible] (1)
The inversion can in general not be done exactly within a limited precision of the input values and the coefficients. It can be solved by lifting scheme or ladder network. In lifting Scheme, decompositions of 2*2 matrices are utilized in the context of wavelet transforms. The basic building blocks of lifting scheme are called
[mathematical expression not reproducible] (2)
with a real value 'a' called "lifting coefficient ", or the transpose of this matrix. The lifting step [L.sub.a] maps two value ([x.sub.1], [x.sub.2]) to,
[L.sub.a]([x.sub.1], [x.sub.2]) = ([x.sub.1], [x.sub.2] + [ax.sub.1]) (3)
The inverse lifting step is given by,
[mathematical expression not reproducible] (4)
A rounding function [?] can be included into the lifting step and the resulting integer lifting step is given
[L.sub.a,[.]]([x.sub.1], [x.sub.2]) = ([x.sub.1], [x.sub.2] + [[ax.sub.1]]) (5)
The inverse integer lifting step is given as,
[L.sup.-1.sub.a,[.]]([x.sub.1], [x.sub.2]) = ([x.sub.1], [x.sub.2] + [[ax.sub.1]]) (6)
A lifting step decomposition for a 2 x 2 matrix [mathematical expression not reproducible] with b [not equal to] 0 and detenninant f is given by,
[mathematical expression not reproducible] (7)
Based on eqn (7), the following decomposition for Givens rotation can be obtained as,
[mathematical expression not reproducible] (8)
where, [mathematical expression not reproducible] (9)
[mathematical expression not reproducible] (10)
[mathematical expression not reproducible] (11)
B. Forward Transform:
The Integer MDCT is evolved by means of rounding operations or the lifting scheme. Rounding can be implemented by rotations, based on three lifting steps or rotations. To ensure the preservation of energy, the butterflies process of Int-MDCT have to be implemented as rounded given rotations with an angle of [pi]/4.
The forward transform of MDCT is,
[mathematical expression not reproducible] (12)
On multiplying the matrix (9) with eqn (12) and performing the rotation in the [pi] values, results in (13),
[mathematical expression not reproducible] (13)
On multiplying the matrix (10) with eqn (13) and performing the rotation in the [pi] values, results in (14),
[mathematical expression not reproducible] (14)
On multiplying the matrix (11) with eqn (14) and performing the rotation in the [pi] values, results in (15),
[mathematical expression not reproducible] (15)
Hence the Integer MDCT depends upon the Lifting Scheme or the rotations performed on MDCT.
C. Inverse Transform:
The integer approximation of lifting steps (or) rounding operation can be inverted without introducing any error. Applying this approximation to each of lifting steps, we get an integer approximation of the given rotations. If the rounding function 'r' is odd symmetric the inverse rounded rotation is identical to the rounded rotation with angle (-[theta]) and is given as,
[mathematical expression not reproducible] (16)
The whole process is invertible by applying the inverse rotation in reverse order. So we have an integer approximation of the MDCT known as Integer MDCT preserving perfect reconstruction.
Hence the inverse transform is given by,
[mathematical expression not reproducible] (17)
3. System Design:
The Figure 1 shown above has the following steps,
The input audio signal is taken in .wav format with a sampling frequency of 48 kHz. It is then fed to G.722 audio codec which consists of encoder and decoder. G.722 encoder consists of transmit quadrature mirror filter which splits the signal into subbands and encodes the signals using SB-ADPCM. The encoded signal is then multiplexed using a multiplexer and that signal is fed to the G.722 decoder.
The decoder performs inverse operation of encoder. First, the combined signal is demultiplexed and splitted into two bands. Then the signal is decoded using SB-ADPCM decoder. After decoding, the signal is combined using Receive Quadrature Mirror Filter (QMF). Finally, the reconstructed signal of G.722 is obtained in .wav format with some background noise and with less audibility. In order, to remove the noise created by G.722 Audio Codec, we go for RLS Algorithm and finally we obtain the adaptive audio signal with the removal of noise.
The adaptive audio signal of G.722 audio codec is then fed to AAC audio codec which consists of encoder and decoder. The signal is windowed with the help of the transform known as the Integer MDCT. The windowed signal is then transformed from time domain to frequency domain using Integer Modified Discrete Cosine Transform which is a modified form of MDCT. Finally, the encoder produces compressed signal with the help of Huffman coding in .AAC format. In order to reconstruct the signal, compressed signal is fed to the decoder, which is the reverse process of the encoder.
3. Proposed Work:
MATERIAL AND METHODS
In this study, dataset containing 30 audios with input sampling frequency 48kHZ and 16-bit mono audio format are taken. These audio signals are being processed by means of a hybrid codec such as G.722 and AAC, inorder to obtain the better compression results. Different Quality estimation algorithms are used to find the quality between original signal and reconstructed signal.
3.2 G. 722 Audio Codec:
It is an audio codec standardized by an International Telecommunication Union, which uses the Sub-band Adaptive Differential Pulse Code Modulation with the bitrate of 64 kbps.
The above figure 2 identifies the main functional blocks of G.722 Codec as follows:
* Transmit Quadrature Mirror Filters:
The transmit QMFs comprise two linear-phase non-recursive digital filters which split the frequency band 0 to8000 Hz into two sub-bands: the lower sub-band (0 to 4000 Hz) and the higher sub-band (4000 to 8000 Hz). The input to the transmit QMFs, [x.sub.in], is the output from the transmit audio part and is sampled at 16 kHz. The outputs, [x.sub.L] and [x.sub.H], for the lower and higher sub-bands respectively, are sampled at 8 kHz.
* Subband Encoder:
Encodes the data samples using adaptive differential pulse code modulation.
The multiplexer shown in G.722 is used to combine the signals, [I.sub.L] and [I.sub.H], from the lower and higher sub-band ADPCM encoders respectively
The Demultiplexer decomposes the received signal into two signals [I.sub.L] and [I.sub.H] which forms the codeword input to the lower sub band and higher sub band decoders.
* Sub-band Decoder:
Decodes the data samples using ADPCM.
* Receive Quadrature Mirror Filters:
The receive QMFs shown in G.722 are two linear-phase non-recursive digital filters which interpolate the outputs, [r.sub.L] and [r.sub.H], of the lower and higher sub-band ADPCM decoders from 8 kHz to 16 kHz and which then produce an output, [x.sub.out], sampled at 16 kHz which forms the input to the receive audio parts.
3.3 Adaptive Filtering Using RLS Algorithm:
3.3.1 Adaptive Filter:
It is the process by which it changes the filter parameters to adapt to the certain change in the audio signal characteristics. The RLS Algorithm is the closed loop adaptive process in which the weighting factors are being updated by means of the cost function.
3.3.2 Adaptive Filtering Methodology:
As the signal into the filter continues, the adaptive filter coefficients adjust themselves to achieve the desired result, such as identifying an unknown filter or cancelling noise in the input signal. In the figure 3, below, the shaded box represents the adaptive filter, comprising the adaptive filter and the adaptive recursive least squares (RLS) algorithm.
Choosing the adaptive filter for the removal of noise processes requires mainly the (i) Filter Consistency and the (ii) Filter Performance.
3.3.3 RLS Algorithm:
The Recursive least squares (RLS) is an adaptive filter which recursively finds the coefficients that minimize a weighted linear least squares cost function relating to the input signals. Least Mean Square is in contrast to RLS Algorithm, that aims to reduce the mean square error. The input signals are considered deterministic in the RLS, while for the LMS and similar algorithm they are considered stochastic.
The error signal and desired signal are defined in the negative feedback diagram shown in figure 4 below:
3.4 Aac Audio Codec:
For lossy digital audio compression, Advanced Audio Coding (AAC) is considered as an audio coding standard. AAC provides better sound quality at the same bit rates, which is designed to be the successor of MI format.
3.4.1 Proposed AAC:
The basic building blocks of AAC are represented using figure 5 and 6 respectively.
188.8.131.52 Steps in Encoding process of AAC:
* Provide Input in the form of samples in time domain.
* Use Integer-MDCT as a filter to find the frequency components.
* Find the envelope of the Integer-MDCT i.e. power coefficients.
* Based on the coefficients quantize using scale factor as step size.
* Then separate the coefficients based on codebooks.
* Code the coefficient as bit streams using Huffman Coding.
184.108.40.206 Steps in decoding process of AAC:
* The bit streams are coded back into coefficients using the Huffman decoding.
* The coefficients are merged together based on codebooks.
* Dequantize the coefficients using scale factor as step size.
* Use Inverse Integer-MDCT to convert the frequency components into time domain components.
* Reconstruct the output in the form of samples in time domain.
3.4.2 Functional Blocks of AAC:
220.127.116.11 Integer MDCT:
The AAC encoder transforms the audio samples into frequency coefficients by means of a Integer MDCT (Integer Modified Discrete Cosine Transform. The process is similar to that employed by the three layers of MPEG-1 and MPEG-2, but with higher resolution and with improvements. At any given time, the encoder transforms a set of consecutive audio samples referred to as a window. There are two types of windows, long and short. A long window consists of 2,048 consecutive samples and is transformed to produce 1,024 coefficients (a long transform). A short window is 256 samples long and results in 128 coefficients (a short transform). Once the coefficients of a window have been computed, the encoder shifts the audio samples in the buffer by half the window size. Thus the window overlaps by 50% of their size.
Long window produces many coefficients, so each coefficient corresponds to a narrow frequency band. This leads to precise quantization and thus to a more meaningful loss of data. The data lost in quanization corresponds to those parts of the audio that are not perceived by the ear/brain system. Thus, long windows make sense in those parts of the audio that are either tonal or low frequency. On the other hand, atonal or high-frequency audio varies rapidly, which is why such parts of the audio input lend themselves to better audio compression with short windows. It is upto the AAC encoder to analyze the input, identify its stationary and transient parts, and use this knowledge to decide when and how often to switch filtering windows.
Since the large coefficients can lose more bits with less effect on the reconstructed audio, the coarser quantization is applied. Every frequency coefficient is scaled, during quantization, by a quantity related to its scale factor. The scale factors are unsigned 8-bit integers. When the 1024 coefficients of long window are quantized, they are grouped into scale factor bands, where each band is a set of spectral coefficients that are scaled by one scale factor. The number of coefficients in a band is a multiple of 4 with a maximum of 32. This restriction makes it possible to Huffman-code sets of four consecutive coefficients.
18.104.22.168 Huffman Coding:
The quantized frequency coefficients are replaced by Huffman codes, which provides lossless compression and hence it is named as "noiseless". There are 12 Huffman codebooks, although one is a pseudo table, for coding runs of zero coefficients. A block of 1,024 quantized coefficients is divided into sections where each section contains one or several scale factor bands. The same Huffman codebook is used to code all the coefficients of a section, but different sections can use different code tables. The length of each section and index of the Huffman codebook used to code the section must be included in the output stream as side information for the decoder.
Huffman codebook 0 is special. It is an escape mechanism that's used for sections where all the quantized coefficients are zero. A long window produces 1,024 coefficients and a short window produces only 128 coefficients. However, short windows always come in sets of eight, so they produce 1,024 coefficients, organized as an 8x128 matrix. In order to further increase coding efficiency, the eight short windows can be grouped in such a way that coefficients within a group share scale factors. Finally using the codebook we obtain the bit stream.
Performance Measure gives the quantitative analysis between the original and the reconstructed audio signal. Two types of performance measure are taken. They are Compression Ratio (CR) and Sound Pressure Level (SPL) test.
4.1 Compression Ratio:
The ratio between the uncompressed size to the original size is known as Compression Ratio. Equation (18) represents the compression ratio,
compression ratio = uncompressed size/compressed size (18)
When a codec compresses an audio file from 10MB file to 2MB, it has a compression ratio of 10/2=5. It is notated as an explicit ratio, 5:1 or as an implicit ratio, 5/1. This formulation applies equally for all types of audio compression algorithm, where the uncompressed size is same as that of the original; and for decompression algorithm, where the uncompressed size is that of the reproduction.
4.2 Sound Pressure Level (SPL) Test:
Twenty times the logarithm to the base ten of the ratio of a given sound pressure to a reference sound pressure of 20 p Pa, expressed in decibels, dB. It is a logarithmic measure of the effective pressure of a sound relative to a Sound pressure level, denoted Lp and measured in dB, is defined by eqn (19),
SPL = 20log (p/Pref) (19)
p [right arrow] Sound pressure of the original/compressed signal
Pref [right arrow] Sound pressure of the reference signal.
The reference signal can be considered as air or water for air it is 20 [e.sup.06] and for water it is 10 [e.sup.06].
RESULTS AND DISCUSSIONS
A set of uncompressed audio files are chosen in order to perform audio coding. The audio dataset are shown in Table 3. The table describes the audio dataset for same sampling frequency of about 48 kHz with duration of 1 min and less than 1 min.
Based on the proposed work as shown in Figure 1, initially the audio files in .wav format are passed through G.722 audio codec that uses Subband Adaptive Differential Pulse Code Modulation technique. Here the audio files of 16 bit depth are converted to 8 bit depth files. G.722 works only for mono channel signal. The audio signal mostly has Sampling Frequency of about 32 kHz, 44.1 kHz, and 48 kHz. Hence the output at this stage is tabulated as shown in Table 4.
G.722 Codec reduces the file size to 472 KB with a Bit Rate 384 kbps. The representation of input audio signal and output audio signal obtained from G.722 Codec is shown in following Figures from 10 to 12.
Figures 7 represents input audio signal in .wav format with a Sampling Frequency of about 48 kHz.. The samples are of different length with different file sizes. Figure 8 represent the noisy output signal that is obtained from G.722 audio codec with a sampling frequency of 44 kHz and 16 bits format. Inorder, to enhance the audibility the weights are updated by means of RLS Algorithm which is represented by the figure 9 respectively and finally the adaptive audio signal has been obtained.
Table 5 shows the output of the audio signal obtained from AAC Codec. The Output Audio Signal obtained from G.722 codec is then sent to AAC Codec as per the block diagram shown in Figure 1.
After the enhancing the audibility process of G.722, the signal is again converted into 16 bit format with the sampling frequency of 44.1 kHz as shown in the figure 10 since the AAC codec accepts only of these formats. Figure 11 shows some of the audio samples obtained after AAC Codec. The Sampling Frequency of the output audio signal obtained from AAC codec is about 44 kHz. After sending the input through two audio codecs the file size of the signal is further reduced from MB to KB, which gives better compression of the audio signals.
6.1 PO.erformance Measure 1: Compression Ratio:
The Compression Ratio is calculated using the formula mentioned in the theory part and hence the compression ratio obtained from both the compressed and uncompressed audio for single codec and combining two codecs are tabulated. Table 6 gives the Compression Ratio between Original Input signal and Output Signal of G.722 audio codec. From the following table it is inferred that the Compression Ratio obtained from a single codec infers that a maximum compression is 2.5/1.
The Compression Ratio obtained from the combination of two audio codecs such as G.722 and AAC is better when compared with single codec as shown in Table 7. The maximum compression ratio obtained is 47/1.
6.2 Performance Measure 2: Sound Pressure Level (SPL) Test:
The Sound Pressure Level is calculated using the formula mentioned in the theory part and hence the SPL level in dB obtained for both the compressed and uncompressed audio for single codec and combination of two codecs are tabulated.
Table 8 represents the Sound Pressure Level of the Original Input Signal and G.722 Codec output signal. Table 9 Sound Pressure Level of Original and Compressed Signal obtained by combining two codecs. Sound Pressure Levels are represented in dB. The Tables 8 & 9 indicates SPL which helps us to visulaize that even though the bit depth of the audio file is decreased it does not affect the audible range of the sound file and it is maintained around 0 dB to 90 dB.
Integer Modified Discrete Cosine Transform is frequently used in audio compression, audio coding and audio signal analysis. It is used due to its perfect reconstruction and it also considers only real values of the samples. Hence, a hybrid audio codec that uses Integer MDCT was designed by combining two different audio codec's such as G.722 and AAC. The difference between the original and the compressed signal is analyzed by means of the performance measures such as the compression ratio and the Sound Pressure Level. The Compression Ratio obtained by a hybrid audio codec is better when compared with single audio codec. Combined Codec provides maximum compression of 47/1. Sound Pressure Level of combined codec is better when compared to the SPL of single codec.
From the entire test, it is concluded that combination of two codec's provide better quality and clarity when compared with single codec. Storage space or the memory space required for compressed signal is less when compared with original signal.
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(1) Mr. M. Davidson Kamala Dhas and (2) P. Maria Sheeba
(1) Assistant Professor, Department of Electronics and Communication Engineering, Mepco Schlenk Engineering College, Sivakasi, India.
(2) PG Student, Department of Electronics and Communication Engineering, Mepco Schlenk Engineering College, Sivakasi, India.
Received 14 September 2017; Accepted 15 October 2017; Available online 30 October 2017
Address For Correspondence:
Mr. M. Davidson Kamala Dhas, Department of ECE, Mepco Schlenk Engineering College, Sivakasi- 626005. Phone No.: 9443209306; E-mail: email@example.com
Caption: Fig. 1: System Design
Caption: Fig. 2: Block Diagram of G.722 Audio Coder
Caption: Fig. 3: Block Diagram That Defines the Inputs and Output of a Generic RLS Adaptive Filter
Caption: Fig. 4: Block Diagram of RLS Algorithm
Caption: Fig. 5: Block diagram of Encoding process of AAC
Caption: Fig. 6: Block diagram of decoding process of AAC
Caption: Fig. 7: Input Audio Signal (3.wav)
Caption: Fig. 8: Noise Signal of G.722 (3.wav)
Caption: Fig. 9: Adaptive Audio Signal of G.722 (3.wav)
Caption: Fig. 10: Input Audio Signal (Output of G.722)
Caption: Fig. 11: Output of encoded Audio Signal of AAC
Table 3: Audio Dataset with Same Sampling Frequency File Name Duration File Size 1.wav 1min 5.49 MB 2.wav 1min 5.49 MB 3.wav 1min 5.49 MB 4.wav 1min 5.49 MB 5.wav 1min 5.49 MB Table 4: Audio Dataset after G.722 Codec File Name Duration File Size 1.wav 1min 2.52 MB 2.wav 0m59s 2.52 MB 3.wav 0m59s 2.52 MB 4.wav 0m59s 2.52 MB 5.wav 0m56s 2.52 MB Table 5: Audio Dataset after AAC Codec File Name Duration File Size 1.wav 0m59s 121 KB 2.wav 0m56s 121 KB 3.wav 0m56s 121 KB 4.wav 0m59s 115 KB 5.wav 0m59s 121 KB Table 6: Compression Ratio of G.722 Codec File Name File Size of File Size of Compression Original Signal G.722 Codec Signal Ratio 1.wav 5.49 MB 2.52 MB 2/1 2.wav 5.49 MB 2.52 MB 2/1 3.wav 5.90 MB 2.52 MB 2.5/1 4.wav 5.49 MB 2.52 MB 2/1 5.wav 5.49 MB 2.52 MB 2/1 Table 7: Compression Ratio obtained by Combining Two Codecs File Name File Size of File Size of Compression Original Signal (G.722+AAC) Codec Signal Ratio 1.wav 5.49 MB 121 KB 45/1 2.wav 5.49 MB 121 KB 45/1 3.wav 5.49 MB 121 KB 45/1 4.wav 5.49 MB 115 KB 47/1 5.wav 5.49 MB 121 KB 45/1 Table 8: Sound Pressure Level of Single Codec Sound Pressure Level (dB) File Name Original Signal (.wav) G.722 Codec Signal(.wav) 1.wav 78.861 79.181 2.wav 77.192 77.568 3.wav 86.386 86.491 4.wav 82.712 83.819 5.wav 79.432 81.5691 Table 9: Sound Pressure Level obtained by Combining Two Codecs Sound Pressure Level (dB) File Name Original Signal (G.722+AAC) Codec (.wav) Signal(.wav) 1.wav 78.861 79.119 2.wav 77.192 76.842 3.wav 86.386 85.648 4.wav 82.712 84.092 5.wav 79.432 81.167
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|Title Annotation:||modified discrete cosine transform; sound pressure level; compression ratio|
|Author:||Dhas, M. Davidson Kamala; Sheeba, P. Maria|
|Publication:||Advances in Natural and Applied Sciences|
|Date:||Oct 1, 2017|
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