Techniques for Digitizing Voice and Channel MIC
ITEM 7: Techniques for Digitizing Voice and Obtaining the Channel MIC
7.1 Sampling
Nyquist Sampling Theorem: To transmit a signal of frequency f through a transmission line, it is not necessary to send the full signal. It is enough to send signal samples taken at a sampling rate (fm) that is at least twice the maximum frequency of the signal (fmax). For example, if we have a signal with a maximum frequency of 4 KHz, we would have to take samples at a sampling rate of at least 8 kHz.
Justification of the Theorem: To recover the original signal, it is only necessary to use a low-pass filter that only lets the range from fmin–fmax pass and blocks the rest. In telephone signals (band between 300 and 3400 Hz), we use an fm > 6800 Hz, although in practice, the signal is sampled with an fm > 8000 Hz.
Differences Between Ideal and Actual Sampling: In ideal sampling, the samples have a width of zero, while in actual sampling, the original signal samples are taken during a very short time compared to the time between two consecutive samples.
7.2 Quantification
Quantification: Quantification involves assigning specific values to our signal, which will be determined by the desired signal quality.
The samples obtained above cannot be transmitted directly because the range of amplitudes they can take is limited, not infinite. To overcome this drawback, the amplitude range (or operating range) is divided into a limited number of intervals called quantization intervals. Thus, all samples within the same range take the same value.
It is impossible to eliminate errors in this process because the effective sample size is replaced by an approximate range. This error is called quantization error.
Uniform Quantification: The operating range of 256 is divided into equal intervals. It is bounded by upper and lower virtual decision values, limiting the maximum amplitude of the signal that can be transmitted. The quantization error that occurs when approximating the true value of the signal will decrease as the number of quantization intervals increases.
This error could eventually be eliminated if the quantization intervals were infinite, which is not possible because:
- Each interval has its digital equivalent value. To represent all values, 8 bits are needed. If we increase the number of intervals, we need a larger number of bits, which would lead to excessive bandwidth.
In a uniform quantizer, the output signal only changes when the input voltage changes from one measurement interval to the next. The difference between the output voltage and input (Vs–Ve) represents the quantization error. This error distorts the reconstructed signal and leads to a distortion called quantization distortion or noise.
Non-Uniform Quantification: The problem with uniform quantification is that the quantization error is constant for any amplitude of the sample, resulting in a worse signal-to-noise ratio at low levels of the input signal, with critical values for signals of similar amplitude to the quantization intervals.
To maintain a stable signal-to-noise ratio, there are two alternatives:
- Increase the number of quantization intervals (not viable due to increased bandwidth).
- Use non-uniform quantization, which distributes a number of intervals unevenly, approximating the signal at low levels and separating them at higher levels.
Quantification in MIC Systems Used in Europe (A-law) and America (Mu-law): Non-uniform quantization always follows specific characteristics known as quantification characteristics or coding laws.
The coding law for voice frequency signals used in European systems is the A-law, and in American systems, it is the Mu-law.
The A-law uses 256 measurement intervals, 128 for positive signals and 128 for negative signals.
7.3 Consolidation
Consolidation: With this, quantified samples are represented by a sequence of binary ones and zeros.
Structure and Codes of the MIC Word: Since we use 256 quantization intervals, 8-bit binary sequences are necessary to represent each of the quantified samples. Thus, each MIC word is represented as:
- Group P: Indicates the polarity of the sample (1 if positive, 0 if negative).
- Group A: These 3 bits allow us to locate the sample within 23 = 8 line segments for each polarity, i.e., 16 segments.
- Group B: Consists of 4 bits that determine 16 possible intervals within each segment.
Thanks to the consolidation of MIC words, we can locate each of the ranges that define each segment of the potential value of the transmitted signal samples.
ITEM 8: MIC Channel Multiplexing and Transmission Hierarchies
8.1 Differences Between Time Division Multiplexing (TDM) and Frequency Division Multiplexing (FDM)
FDM is based on modulating different signals to be transmitted, making them occupy different frequency bands. They are then sent together through the same transmission channel without interference between signals.
TDM is used to multiplex different digital signals. The principle is to exploit the delay between signals to merge parts of other signals, sending the complete sequence through the same transmission line. At the receiving end, the different signals are separated in time. This is a basic process in digital telephony. At the sending end, samples are periodically taken from the three channels (tributary channels). Once coded, they are sent through a line, forming a grid pattern called an aggregate. At the receiving end, samples are assigned to their respective channels, so there must be perfect synchronization.
Time Frame: The time period between two consecutive samples of a channel.
Slot: Length of time occupied by a channel sample.