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TTT4130 : Overview Of Digital Communication

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Course Code: TTT4130
University: Norwegian University Of Science And Technology

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Country: Norway

Question: 

Digital audio has become an integral part of our lives. Nearly all of the transmission of speech signals over telephone channels is currently digital. Moreover, digital audio recording in the form of compact disks (CDs) has become very popular. This assignment exposes the student to real world applications of digital communication in digital audio transmission and recoding. Therefore, the student shall acquire skills to understand the real world requirements, critically review the existing techniques and write a technical report based on his or her investigation.
a) Requirement analysis: student is required to analyze the following for digital audio in telephone transmission systems:  
 Bandwidth of speech signals and the required sampling rates to avoid aliasing
b) In addition, student is also required to analyze the following for digital audio recording:     Bandwidth of high quality audio and the required sampling rates
2) Investigation of current methods: student is required to review and analyze waveform-coding techniques used in digital audio transmission and recording at present. At least PCM and DPCM methods need to be covered.

Answer:

Introduction:
The time elapse among certain repetitions determines the frequency which is known as the wavelength. While analyzing the recorded voice wave pattern we could see the wave pattern repetition that will not be accurate but it will be more precise. Wavelength is denoted by λ that is represented in the form of milliseconds or microseconds. The frequency is denoted as cycles per second which is said to be the reciprocal of λ, i.e. f = 1/ λ. The wave pattern obtained from the human speech or from musical instruments is composed of basic pattern with certain additional pattern [1]. These additional patterns is said to be known as the overtones that is imposed on the basic waves. These overtones are said to be the higher frequency waves that are the multiples of harmonics (the base wave). These necessarily provide the characteristic wave pattern of the human voice [2]. During the process of digitalization the rate of sampling depends on the overtones of the existing signal.
Necessary Sampling rate:
Analog signals will be in the continuous wave form, lessening in their amplitude. When these signals are stored in the computer it is necessarily converted in the form of digital pattern (0s and 1s). The wave form continues until the signals starts to diminish. Digital pattern is exactly the opposite of the analog wave pattern that is discontinuous in nature [3].  Since digital data are said to be in the form of 0 and 1 we have to only consider the approximate value of the analog signal. In order to store the digital data it is necessary to convert into the discontinuous wave form. Then again with the help of DAC we have to convert the system back to the analog form so that we could hear the voice signal. The work of the sound cards as well as the audio adapter helps in the two ways of conversion of signal.
Periodic Sampling:
This method is the typical method of conversion of analog signal to the digital form [4] [5]. x[n] is said to be the sequence of samples that is occurred from the continuous wave pattern xc(t) and it is denoted as
                                                                               
                                                       
From the above equation, T is determined to be the sampling time period, the sampling frequency is denoted by fs = 1/T that is said in terms of samples per second (Hertz).  Ideal continuous-to-discrete (C/D) converter is the representation of the system that operates by the above obtained equation [6]. Quantization is the very important process that takes up certain pre-scaled values from the continuous wave pattern for storing the values in the computer. This is what done in the ADC (sampling as well as quantization).  A sound card is composed of both Analog to digital and digital to analog converter that does the opposite operation [7].  Most sound cards store either 8 bits per sample and for the high quality sound it can store about 16 bits.
The Nyquist Sampling Theorem:
The concept behind the sampling theorem tells us to quickly sample the signal pattern so that there will be a good representation of the original signal. If the change in a signal is very fast then the sampling should also be done at a very fast rate, so that none of the variations will be left. Let’s see the concept behind the Nyquist Sampling Theorem regarding the action it takes quickly to define T [8].                                                                                
This concept was first introduced by Nyquist and he termed it as Nyquist sampling theorem where the sampling rate should exceed 2ωN which is said to be the sampling frequency, so this aliasing effect could be avoided.
Telephonic audio sampled signal:
Normally a single voice signal occupies 8 kHz of bandwidth. Each sample is quantized into 8 bits, yielding a rate of 64 kbps which is used universally. Lot of research has been done at the Bell Telephone for multiplexing voice signals. This research was conducted with several test groups with the bel audio unit and they also analyzed the sensitivity of human ear with the power distribution of voice signal. The signals were band passed lower than 300 Hz and took off above 3000 Hz. This had a better impact that produced a good human voice. These signals are said to be analog in nature [9]. With the help of Amplitude modulation it was further bought to 5 kHz that gave a better music at the background that made a better quality among folks. For the television, the system was designed to run at an approximate rate of 17.5 kHz that provided with the picture quality. But this lagged in the sound that the person could not hear the whine. The cutoff frequency was done sufficiently by the Single sideband radio that came became commercial at the year of 1960 [10] [11]. Audio band pass was improved to 20 KHZ or enhanced with Frequency modulation since the large carrier frequencies could be handled better with the sufficient music production.   
During the process of digital signaling the derived wave form, no matter how weird, it could be broken into several set of sine waves. This harmonic wave pattern produced spikey wave pattern of voice signals. At last, Nyquist was the one who produced the best concept of digital sampling at a particular frequency to produce sine waves. To produce sine wave it is required to take two samples. The high frequency produced will be half the value of the sample rate. For instance, if we require 10 kHz audio signal then we need 20 Hz of sample.
Quantization:
The process of representing the analog signals to a fixed number of bits for a sample and hold circuit is term as quantization [12]. The input analog signal is evaluated with the set of pre-defined level signal. During the sampling, each level is denoted in the form binary format and it is necessarily compared with the nearest analog value. This rounds off the nearby value of the analog voltage so that the digital value will be the approximation of the analog voltage value. There are several methods for the quantization sampling process and the popularly used method is the successive approximation and dual slope.
                                                                     
For the purpose of quantization, the numerical values are assigned from the samples that are taken from the digital circuits. We denote the bit resolution as the amount of bits obtained from the samples. These bit resolution will double by its available value at each sample. During the quantization, the instantaneous amplitude value has to be rounded off with the nearest digital value [13]. This process is termed as approximation. The rounded off distance of the analog values increases with the decrease in the amount of bits per sample. As shown in the above figure, quantization error is denoted in the form of difference among the digital and analog value.
The quantization noise could increase depending on the magnitude of the approximation errors. In order to reduce the digital noise is to implement large sampling word size that could communicate with the dynamic system, which could affect the signal to noise ratio. SNR is the necessary term that is to be measured in every digital system.  For each additional bit per sample it is require adding 6dB of dynamic range according to the thumb rule. Sony proposed a CD that originally used 14 bit sample size with the 84 dB dynamic range that was further increased to 16 bits. Sample size greatly affects the dynamic range of the system that is similar to the frequency response affected by the sample rate. This could provide a difference in the amplitude of the digital noise floor and the loudest possible sound before alteration.
Pulse Code Modulation:
Time discretization and amplitude discretization are the two basic operations in the conversion of analog to digital conversion. The earlier step is consummated with the sampling operation and finally by means of quantization. There is an additional process involved in the PCM which is other-wise called as code words [14]. In this process the quantized amplitudes is converted into a sequence of simple pulse pattern. This will be usually in the form of binary. This usually refers to the concept of quantizing each sample in the form of R -bit code word.
                                                               
m (t) is the message signal that bears the information, which is transmitted digitally. This message signal should be sampled and quantized. The output of the sample is obtained as
                                                                                     
Where,  
T s – sampling period
n – Appropriate integer.
 fs is denoted as sampling rate or sampling frequency. The quantizer converts each sample to the nearest value from the predefined set of discrete amplitudes. The representation of the R -bit code word with the samples quantized is done by the encoder [15]. This stream of bits travels and reached the receiver end. With the given sampling rate and the R -bit code word the PCM syatem could be represented in the form of
                                                                                                 
Next the decoder plays the process of converting the R -bit code word into its corresponding digital amplitudes. At last, reconstruction filter produces the analog signal by acting upon these discrete amplitudes that is indicated by m` (t). If there are no channel errors, then m` (t) = m(t).
Differential Pulse Code Modulation:
DPCM also does the same procedure of converting the analog signals into digital format where the sampling process is done and the sampling values of actual and predicted should be quantized. The estimated value of the actual samples depends on the value of the previous samples. The concept behind DPCM is purely based on the considerable correlation between the successive samples. This makes the quantizer to utilize the sample value redundancy that serves the minimum bit rate. The above figure shows the basic DPCM syatem with the adaptive scheme of Lloyd-Max’s quantizer. X[n] is said to be the input signal processed in the form of a frame manner. The sample passes through a buffer into a current frame that leads to the calculation of gain g. Lloyd-Max’s quantizer concept will be performed based on the adaptation. The feedback loop of the DPCM system is composed of a fixed predictor that serves as a predictive signal xˆ[n] to the output. d [n] that is denoted as the signal difference in the sampled values is the difference between the current input samples x [n] with their predicted value of xˆ[n]. This particular difference signal d[n] is a Lloyd-Max’s quantizer, considered for low bit rate that is functional in the adaptive scheme [16]. This scheme involves the normalization of samples of the signal difference d[n] by using quantized gain gˆ. The gain is calculated by means of taking the square root for the calculated variance with the signal difference σd2 that takes the frames individually. The variance of the input signal is denoted by σx2. The general representation is given as,
                               
                                                                                           Figure 4: DPCM system
Conclusion:
The sufficient topics regarding the communication theory has been discussed clearly in our paper. The Investigation regarding the current methods to analyze waveform-coding techniques used in digital audio transmission and recording at present has been discussed that covers the PCM and DPCM methods.
References:

Nikolic, Z. Peric, Lloyd–Max’s algorithm implementation in speech coding algorithm based on forward adaptive technique, Informatica, 19, 2, pp. 255–270, 2008.
Peric, J. Nikolic, An effective method for initialization of Lloyd–Max’s algorithm of optimal scalar quantization for Laplacian source, Informatica, 18, 2, pp. 279–288, 2007.
Despotovic, Z. Peric, L. Velimirovic, V. Delic, DPCM with forward gain-adaptive quantizer and switched first order predictor for high quality speech signals, Advances in Electrical and Computer Engineering, 10, 4, pp. 95–98, 2010.
Despotovic, Z. Peric, L. Velimirovic, Switched adaptive quantizer for speech compression based on optimal companding and correlation, IET Signal Processing, 5, 7, pp. 701–707, 2011.
J. P. De Figueiredo, A neural-network-based approach to speech signal prediction, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 55, 1, p. 42–48, 2010.
Robert Craig, Communication. Encyclopaedia of Rhetoric, OUP, London, 2002 (Print). Published Online 2009.
Meta, P. Hakkaart, F. V. der Zwan, P. Hoogeboom, and L. P. Ligthart, “First demonstration of an X-band airborne FMCW SAR,” in Proc. European Conf. on Synthetic Aperture Radar EUSAR’06, Dresden, Germany, May 2010.
Edrich, “Design Overview and Flight Test Results of the Miniaturised SAR Sensor MISAR,” in Proc. EuRAD’04, Amsterdam, The Netherlands, Oct. 2009, pp. 205–20
Meta, P. Hoogeboom, and L. P. Ligthart, “Range non-linearities correction in FMCW SAR,” in Proc. IEEE Int. Geoscience and Remote Sensing Symp. IGARSS’06, Denver, CO, USA, July 2008.

[10] M. C. W. van Buul,”Hybrid DPCM, a combination of PCM and DPCM,” IEEE Trans. Commun., vol. COM-26, pp.362-368, Mar. 2010
[11] K. N. Ngan and R. eele,”Enhancemnet of PCM and DPCM images corrupted by transmission error,” IEEE Trans. Commun., pp.257-265, Jan. 2010.
[12] R. Rivoir “Which Converter do you need for your application?” France ESD – MSD Cluster for Mixed-Signal Design Workshop on Embedded Data Converters, Stockholm Sweden, September 22, 2008.
[13] O. Machul, D. Hammerschidt, D. Weiler, B.J. Hosticka “Nonlinear Function Generation using Oversampled sigma-delta Modulators” ISCAS2000.
[14] B. Li, H. Tenhenen “A Structure of Cascasding Multi-bit Modulators without Dynamic Element Matching or Digital Correction”, March 2012
[15] Matthew R. Miller, Craig S. Petrie “A Multibit Sigma-Delta ADC for Multimode Receivers” IEEE Journal of Solid-State Circuits, 38, 3 March 2009
[16] B. Li , H. Tenhunen “A Design of Operational Amplifiers for Sigma Delta Modulators using 0.35um CMOS Process” Electronics System Design Laboratory, Royal Institute of Technology, Sweden, June 2008

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