Pulse Code Modulation (PCM) in detail
In this article, I will explain Pulse Code Modulation (PCM) along with waveform and block diagram in detail. This article is easy to understand, clear and with all the information. Suitable for engineering and diploma students.
Modulation methods are the requirement of a common signal transmission in the same medium. Our senses can not grasp in its full continuity analog information signals. They perform only a finite number of intensity differences. Reduced to an analog information signal to the number of discernible steps, one is to continue to identify properly the location information. This approach resulted in 1938 a patent application on the sampling and quantization of speech signals, in order to transmit encoded. The new method was called pulse code modulation, PCM.Scanning with Sample and Hold
When PCM method, an analog signal is first converted by a discrete-time sampling in-PAM signal. The still ongoing in the amplitude of the signal charges a capacitor controlled sampling. Both processes work with the same carrier and carried out in a function block of sample-and-hold stage. The output signal is a time discrete and amplitude sections in the linearized PAM signal. The amplitudes of the stages are not discrete values, as it changes in proportion to the amplitude of the input signal.Quantization
The maximum amplitude of the sample and hold analog signal is adapted to the conversion characteristics of a digital converter, A / D converter. His work area is assumed to lie between ± 5 V.. If this range is converted to a linear 7-bit A / D conversion into binary data words, the 64 amplitude values are available for both positive and negative signal voltages 6 = 2. One bit is necessary for the change of sign at the zero crossing. Dividing the amplitude range of the defined voltage in stages is called quantization.Coding
Generated by the sample and hold means and adapted to quantizing PAM signal is finally converted into a digital signal. The A / D converter to read the pulse pauses of the sample & hold stage the processed value of voltage and encodes it into a parallel data word. The easiest A / D converter generates a binary code with a signal sequence of high and low signals. The output signals of the transducer can be read before the next serial clock.
From the analog signal has become the corresponding PCM signal via a PAM signal. The PCM signal is both time-and value-discrete. There are high and low with only two different amplitude values at a constant clock rate. Except for the necessary PAM signal adaptation to the A / D converter section can be regarded as a single operation, the quantization and digitization. The type of the quantization is determined by the method of A / D conversion. The diagram illustrated with block diagrams, the pulse code modulation.
The next picture shows the quantization and coding of bipolar PAM by a 4-bit A / D converter. The working range of the transducer comprises 2 4 = 16 levels. Each quantization interval is assigned a binary code. The most significant bit, MSB, most significant bit has all intervals that are both positive, the value 1 and for intervals in the negative range the value 0 The voltage value V 0 is uncoded in these examples.
The left Binary codes is called two's complement. Next to it is another opportunity for signed binary numbers to see identification. If the PAM sample the lower threshold of an interval, it receives the corresponding binary code of the interval. The probe signal reaches the upper threshold of this interval, the next higher code value is assigned to it.
If n is the number of binary digits in the code word, the range of values calculated for binary numbers with prefix -2 n-1 ... 2 n-1 - 1 and for unsigned binary numbers 0 to ... 2 n - 1 from the number of binary digits obtained with 2 n is the number of quantization levels or intervals.Quantization
Amplitude changes of the analog signal can not be detected within a quantization. A back-converted analog signal from the PCM signal is never perfectly match the original input signal. A quantization error for each interval can be determined from the difference between the two signals. In the working range of the A / D converter is the quantization error of ± DELTA.U / 2, where DELTA.U stands for the quantization. The difference between the reconverted PCM signal and the original signal is a new, independent signal quantization.
The quantization error depends on the number of bit positions. Based on the same operating area, and thus the intervals would halve the error a 5-bit A / D converter. For speech and music signals, the linear quantization is not ideal. In an assumed constant noise level of the signal / noise ratio is particularly large for small signal levels. This is counteracted by a compression method, in which the smaller amplitudes of more and larger amplitudes are amplified less.
The A / D conversion with companding usually operates with a logarithmic characteristic and is more quantization intervals are available for low signal amplitudes than high input amplitudes. The quantization error in the lower region is therefore smaller. On the receiver side is formed by the opposite process with an expander on the D / A conversion with an inverse characteristic of the dynamic range of the original signal again.Advantages and disadvantages of PCM
By a time-division multiplex method, the multiple use of the same transmission line is possible. The quality of the transmission is immune to interference, provided in sections regenerative amplifiers are used on long journeys. As the chart shows, they can be described by the rectangular bitmap regenerate, if the clock signal can be recovered. Occurring in the input signal amplitude fading and new noise components are not covered here. Only the quantization noise remains. The digital data of the PCM method can be easily and safely stored.
A disadvantage is the high electronic complexity in the transmitter and receiver for different methods such as PAM, multiplex, AD and DA conversion and steep-slope low pass filter. The bandwidth of transmission is very high. The quantization noise occurs as a new, permanent noise.
Parameters of digital modulation methods
The information unit
With a bit of the binary digit, the smallest unit of information in digital systems, are exactly two states can represent. The bit can be set to high or low = 1 = 0 can not be set. With 2 bits are used to measure 4 states and 3 bits there are 8 In general, the number of states z calculated from the number of bits n to z = 2 n.The bit rate
The bit duration within a PCM signal is the same. It determines the maximum transmission characters per second and is referred to as bit rate, bit rate and walking speed. The unit bits / second is called baud and abbreviated Bd.
f = v Bit Bit = 1 / T Bit [Bd]The amount of information
Quantizing an information signal determined by the number of quantization states z, and thus the number of the information units. N = log 2 (z) The two bit states 0 and 1 are counted as information unit. A limited bandwidth in the time function produced in compliance with the Shannon sampling theorem to exactly 2 · B · T values. They are encoded by the quantization n information units. The amount of information I is calculated from the product:
I = 2 · B · T · log 2 (z) [bit] with the transfer time T [s]The Nyquist bandwidth
In order to reconstruct the signal in the receiver, clearly at least the first harmonic of the highest frequency occurring in the signal to be transmitted. This frequency is called the Nyquist frequency or point. It is also the fundamental frequency of a periodic high-low-high change, are identical with the pulse time and pulse pause. The pulse repetition time T is thus P = 2 · T bits. B N is the Nyquist bandwidth provided by the following relationship:
B P = f N = 1 / (2 · T bit) = Bit f / 2 [Hz]The drawing speed
A complete data word usually begins with a start bit and ends with one or two stop bits. In between are the actual data bits, sometimes even followed by a parity bit. This unit is called a character frame and has the transmission duration T C. The duration of the individual bits in the frame should be the same, their total number is Z. The symbol rate is then defined as:
v = Z 1 / Z T [s -1] with Z = Z · T T BitThe baud rate
The baud rate is also called transmission speed. In binary code, it is identical to the bit rate or speed step. It is dependent not only on the bandwidth and the number n of the characteristic states of the data signal. The binary signal has two characteristic states. Ternary or quaternary Tarnary differ in the data signal between the states 3 and 4.
v u = v · lb bit (s) [Bd] v or u = z · z · v lb (s) with lb (n) = log 2 (n) = log (n) / log (2)Source of images
All the images are personally designed using CAD software
Mr. Vanitha K
According to Nyquist theorem, the basic VF of 4 khz must be sampled 8,000 times per second in order to convert the analog form into digital pulses that would carry the same information as the original analog signal. Those are the PAM signals you cited in the above article. Now, during the quantization process, only 254 discrete values were left, + 127 in the positive swing and - 127 in the negative. What happened to other bits/samples? Please explain.