Nonlinear quantizes µ-law and A-law compander in MATLAB
A-Low Compander:
This type of non-linear quantization is used in Europe and in which sample bit value is equal to 12 bit. It is defined by an equation which is given below in which A is a compression constant and for Europe value of A is equal to 87.7.
Where x- normalized integer value, and A- compression parameter
According to characteristics of this commander when the value of A=1, we investigated that there is no compression in the input waveform [2]. After that A-low has mid-riser at the value origin and it consists of non-zero value. This type of companding is used in the PCM digital audio system and we can use this technique to avoid the problem of aliasing into input data signals.
Figure: A-low compander characteristics
(Source: By Author)
MATLAB code
Data = 2:2:12;
Compressed = compand(data,255,max(data),’mu/compressor’)
Expanded = compand(compressed,255,max(data),’mu/expander’)
Compressed = 1×6
8.1644 9.6394 10.5084 11.1268 11.6071 12.0000
Expanded = 1×6
2.0000 4.0000 6.0000 8.0000 10.0000 12.0000
This type of technique is used by United State and Japan and data bit of this compander is equal to 13 bit. The value μ is given by 255 for US and Japan and it is defined by f(x) which is given below.
According to characteristics of this process at u=0, we detected that the characteristics are linear that shows a uniform quantization. At u= 255, it shows a non- uniform quantization which can be used in the PCM technique. Through this process, we can convert the analog signal into digital signals and we observed that the shape of waveform change according to the value of u.
Figure: Characteristics of Μ-Law Compander
(Source: by author)
Data = 1:5;
Compressed = compand(data,87.6,max(data),’a/compressor’)
Expanded = compand(compressed,87.6,max(data),’a/expander’)
Compressed = 1×5
3.5296 4.1629 4.5333 4.7961 5.0000
Expanded = 1×5
1.0000 2.0000 3.0000 4.0000 5.0000
Quantization is a process to convert the analog signal into digital signals and which is used in a digital communication system. The main difference between uniform and non-uniform quantization is that non-uniform quantization has unequal step size. This is an advanced version of uniform quantization which reduced the rate of quantization errors [4]. In any communication system signal or data transfer from a transmitter to a receiver in which input signals are in the form of analog that increases distortion and interference. Therefore, the quantization process is used to convert this signal into digital signals [5].
The first step of this process is to sample the data at given intervals and if the sampling time is Ts than sampling frequency is given by 1/Ts. Next step is that quantization in which signal converts into discrete signals and quantize output depends upon a number of quantization level [5].
Figure: Non-uniform quantization
(Source: Ouyang, Han, Fang and Liu, 2018)
In this process step size change with time which can reduce quantization error and after quantization technique encoding process starts in which signal convert into binary codes [6].
time = linspace(-1,1,1000);
Q=4;
Qu = round(time*2^Q)/2^Q;
S = @(x) sign(x).*sqrt(abs(x));
Sinv = @(x) sign(x).*(x.^2);
mu = 2^5-1;
S = @(x) sign(x).*log(1+mu*abs(x))/log(1+mu);
Sinv = @(x) sign(x).*((1+mu).^abs(x)-1)/mu;
Qnu = sign(time).*Sinv(round(S(abs(time))*2^Q)/2^Q);
subplot(2,2,1)
plot(time,S(time));
xlabel(‘Sigmoid function’)
subplot(2,2,2)
plot(time,Qu);
xlabel(‘Uniform quantization’)
subplot(2,2,3)
plot(time,Sinv(time));
xlabel(‘Inverse sigmoid function’)
subplot(2,2,4)
plot(time,Qnu);
xlabel(‘Non-uniform quantization’)
(Source: By Author)
|
Uniform Quantization |
Non-Uniform Quantization |
|
Step size is equals |
Step sizes are unequal |
|
It is divided into two parts such as mid-tread and mid-rise quantization |
Does not categorize |
|
Increase rate of quantization error |
Reduce quantization error |
(a) Digital Audio Systems
Digital audio is defined as a communication system which is used to communicate with another person through the digital communication system. In which electric signal converts into digital signal where the audio signal is encoded into binary code [6]. Generally, a compact disk is used as a digital audio system in which 16-bit data can be transmitted over 44.1 thousand SPS. In the digital audio system, ADC and DAC both technologies are used and pulse code modulation is a process which is used in digital audio signals. Digital to analog converter is used to convert the digital signal into an analog signal which is in form of the voice signal [6]. DAC is used to reduce distortion and energy losses from input signals and audio power amplifier is a part of the digital system which increases the strength of the input signal.
The bandwidth of speech signal is between 50 Hz and 10 KHz which is very sufficient to transmit the audio signal from transmitter to receiver. In digital communication, any analog signal converts into digital with the help of sampling and quantization process. In digital audio signal first analog signal converted into a digital signal by using analog to digital converter after that encoding process is done and signal transferred from transmitter to receiver [7].
Aliasing is a very big problem in a digital audio system which can be reduced by sampling rate and it is observed that 20 KHz sampling rate is enough to reduce the problem of aliasing into speech signals [7]. In digital audio when an analog signal transmitted from one location to another than many problems can occur like distortion, interference and signal losses and we can avoid this problem by adopting digital communication.
Around 8 bit per sample can be used to achieve voice quality in digital audio because 8-bit data can be easily transmitted in digital communication and bandwidth of speech signal is between 300 Hz and 3.4 KHz. Through which we can avoid many distortion and interferences in speech signals and we can reduce the problem of aliasing in telephone signals [7].
(b) Digital Audio Recording
In digital recording, audio information or data can be received by the transducer and any microphone system and the video signal can be received by camera or another signalling process [8]. In this digital system encoding and decoding processes are used and encoding is used to encode analog signal into digital and decode is used to convert the digital signal into analog.
The bandwidth of high-quality audio is between 20 Hz and 20 KHz in this we can produce a high-quality signal and the user can receive more effective data or information [9]. If we use quantization and amplifier process in the digital audio process then we can avoid the problem of aliasing and distortion losses.
The sampling rate of high-quality audio signals is around 44.1 KHz and it is observed that this sampling can be used to reduce the problem of aliasing in digital communication technology [8].
12 bit per sample is enough to produce a high-quality signal and we can use 8 bit per sample for the digital audio signal [9]. 12 bit means we send 12-bit data at a time through which people can increase the overall performance of communication systems.
It is a process which is used to convert one form of the data signal into another form of signal. Analog communication cannot produce an efficient output signal that produces many distortion and interferences [9]. Digital communication is a very popular process which can avoid the problem of analog communication. There are main two methods involve into waveform coding technique such as PCM and DPCM.
PCM is a pulse code modulation which is used to convert the analog waveform into binary code that is 0 and 1 [8]. This technique produces a binary output and it is used in digital communication to avoid the problem of distortion.
Figure: PCM quantization
(Source: Ouyang, Han, Fang and Liu, 2018)
In this method, the message signal is represented into the form of the analog waveform and in which sampler is used to convert the analog signal into digital waveform after that quantization converts the digital signal into samples.
Figure: PCM process
(Source: Ouyang, Han, Fang and Liu, 2018)
DPCM is a differential pulse code modulation which is an advanced version of PCM and it reduced the problem of aliasing and quantization error.
Figure: DPCM method
(Source: Ouyang, Han, Fang and Liu, 2018)
Figure: DPCM receiver
(Source: Ouyang, Han, Fang and Liu, 2018)
DPCM consist of quantizer and predictor circuit and quantizer is used to divide the digital signal into sample bits. Predictor circuit is used to predict the previous signal that avoids the problem of interference into output signals [10].
References
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