PULSE CODE MODULATION (PCM) 1. PCM quantization Techniques 2. PCM Transmission Bandwidth 3. PCM Coding Techniques 4. PCM Integrated Circuits 5. Advantages of PCM 6. Delta Modulation 7. Adaptive Delta Modulation 8. Differential PCM ECE 416 DIGITAL COMMUNICATION Friday, 09 March 2018
SYLLABUS
KEY POINTS ABOUT PCM 1. While PCM is a pulse modulation technique much like PWM, PAM or PPM. 2. PCM is digital while the others are either analogue in time or amplitude, i.e PCM pulses are discrete in time and amplitude unlike PAM, PWM or PPM. 3. Essential aspects of a PCM transmitter are sampling, quantizing and encoding. 4. PCM is not a modulation in the conventional sense because it does not rely on varying a characteristic of a carrier (amplitude, frequency or phase).
PCM TRANSMITTER Analogue signal x(t) PAM Signal X(nT s ) Analogue to Digital Converter ADC Quantized PAM X q (nt s ) Low-pass Filter Sample and Hold q-level quantizer Binary encoder Timer Parallel to serial converter Sampling clock signal f s 2f m PCM out r = uf s
BINARY EQUIVALENTS AND PULSE CODE WAVEFORMS
PCM TRANSMISSION PATH PCM transmission path refers to the path the the signal travels between the transmitter and the receiver. From Transmitter Regenerative Repeater Regenerative Repeater To Receiver Distorted PCM Signal Clean PCM Pulse Distorted PCM Signal Clean PCM Pulse
PCM REPEATER Compensates for the effects of amplitude and phase distortions Makes a decision on whether the equalized PCM wave is a zero or one Amplitude and Phase Equalizer Decision Making Circuit Distorted PCM Signal Timing Circuit Clean PCM Pulse The timing clock is extracted from the PCM pulsestream
PCM RECEIVER Distorted PCM Pulse Trainl Clean PCM Pulse train Analogue Signal x(t) Regenerative Repeater Serial to Parallel converter Digital to Analogue Converter Sample and Hold circuit Low pass filter, f m Timer
TYPES OF QUANTIZERS Quantization Uniform Quantization Non-Uniform Quantization Midtread Quantization Midrise Quantization Step size is the same throughout the input signal range Step size varies according the input signal values
MIDTREAD QUANTIZER 1. A midtread quantizer assumes values of the form H i where is the step size and H i = 0, ±1, ±2, ±3,... 2. It is called mid-tread because the origin lies in the middle of a tread of a staircaselike graph.
MIDRISER QUANTIZER 1. A mid-riser quantizer has output levels are given by 2 H i, where is the step size and H i = ±1, ±2, ±3,... 2. The origin lies in the middle of the rising part of the staircase-like characteristic graph.
PCM TRANSMISSION BANDWIDTH 1. Assume the a PCM encoder has q levels which are encoded to υ bits. 2. We can infer q = 2 υ 3. The number of bits per second can be expressed as: f pcm = υf s where f s 2f m (Nyquist criterion) 4. It therefore follows that the bandwidth, BW of a PCM channel is bounded by: BW pcm 2υf m
EXAMPLE 1 1. A TV signal with a bandwidth of 4.2 MHz is transmitted using binary PCM system using 512 quantization levels. Determine (a) Code word-length (b) The PCM bandwidth/bit rate SOLUTION (a) f m = 4.2 MHz q = 2 υ = 512 υ = log 2 512 = 9 bits (b) Bandwidth, BW = 2υf m = 2 x9 4.2 = 75.6 Mb/s
WHY IT IS NECESSARY TO HAVE NON-UNIFORM QUANTIZATION? 1. Using linear quantization, the quantization error is given by: ε = 2 2. If q quantization levels of a bipolar signal are used, we can write: = 2x max q 3. Consider a PCM system with υ = 4 bits and x max = 16 Volt, then: q = 2 4 = 16 = 2 q = 2 16 = 1 8 The maximum quantization error is therefore ε max = 2 = 1 16 4. At maximum, the relative error is 1 volt out of 16 volts or 6.25% 5. At lower levels, e.g. 2 volts, the relative error is 1 volt out of 2 volts or 50%. 6. To reduce this high relative error at low levels, PCM systems use nonuniform quantization.
COMPANDING 1. With uniform sampling, the quantization step is fixed thus resulting in uniform quantization noise power. 2. However signal power is not constant, it is proportional to the square of the signal amplitude. This means Quantization Noise is very significant at low amplitudes. 3. To reduce quantization noise at lower amplitudes, we use commanding: Companding = Compressing + Expanding Input Compressor Uniform Quantizer Expander Output Provides High Gain to Weak Signals and Low Gain to strong Signals Provides Low Gain to Weak Signals and High Gain to strong Signals
COMPRESSING WITH MIDRIZER QUANTIZER
COMPANDING IN COMMUNICATION SYSTEMS 1. The loudest sound that can be tolerated (120 db SPL) is about one-million times the amplitude of the weakest sound that can be detected (0 db SPL). 2. If the quantization levels are equally spaced (uniform quantization), 12 bits must be used to obtain telephone quality speech. 3. However, only 8 bits are required if the quantization levels are made unequal (companding) to match the characteristics of human hearing.
THREE METHODS OF REALIZING COMPANDING IN COMMUNICATION SYSTEMS 1. Run the analog signal through a nonlinear circuit before reaching a linear 8 bit ADC, 2. Use an 8 bit ADC that internally has unequally spaced steps, or 3. Use a linear 12 bit ADC followed by a digital lookup table (12 bits in, 8 bits out). Each of these three options requires the same nonlinearity, just in a different place: at analog circuit, at the ADC, or a digital circuit after the ADC.
COMPANDING STANDARDS (1) μ255 law used in North America (2) "A" law, used in Europe. 19
"A" LAW COMPANDING Where A is the compression parameter 20
µ-law COMPANDING where µ is 255 for 8 bits. 21
BINARY ENCODING 1. Encoding converts the quantized samples into a form that is more convenient for the purpose of transmission. 2. It is a one-to-one mapping of the quantized samples by using code elements or symbols of the required length per sample.
FOLDED BINARY CODE The folded binary code (also called the signmagnitude representation) assigns the first (left most) digit to the sign and the remaining digits are used to code the magnitude. This code is superior to the natural code in masking transmission errors when encoding speech.
INVERTED FOLDED BINARY CODE 1. If only the amplitude digits of a folded binary code are complemented (1's changed to 0's and 0's to 1's), an inverted folded binary code results. 2. This code has the advantage of higher density of 1's for small amplitude signals, which are most probable for voice messages. 3. The higher density of 1's relieves some system timing errors.
GRAY CODE 1. With natural binary encoding, a number of codeword digits can change even when a change of only one quantization level occurs. For example, a change from level 7 to 8 entails every bit changing in the 4-bit code illustrated. 2. In some applications, this behavior is undesirable and a code is desired for which only one digit changes when any transition occurs between adjacent levels. 3. The Gray Code has this property
4-BIT PCM TRANSMITTER - CIRCUIT SCHEMATIC
PCM FOR BI-POLAR SIGNALS
PCM INTEGRATED CIRCUITS - MC14LC5480 1. The MC14LC5480 is a general purpose per channel PCM Codec Filter with pin selectable µ Law or A Law companding, and is offered in 20 pin DIP, SOG, and SSOP packages. 2. MC14LC5480 performs voice digitization and reconstruction as well as the band limiting and smoothing required for PCM systems. 3. MC14LC5480 designed to operate in both synchronous and asynchronous applications and contains an on chip precision reference voltage.
MC14LC5480 - BLOCK DIAGRAM μ/a Law Select (Pin 16) This pin controls the compression for the encoder and the expansion for the decoder. Mu Law companding is selected when this pin is connected to VDD A Law companding is selected when this pin is connected to VSS.
MC14LC5480 - TYPICAL CONNECTION
MC14LC5480 - COST KSH 700/=
ADVANTAGES OF PCM 1. PCM provides high noise immunity 2. Allows regeneration of clean signal by using repeaters placed between the transmitter and the receiver. 3. PCM signals can be stored for later use or retransmission with high fidelity 4. PCM signals can be encrypted more easily and to very high standards.
DISADVANTAGES OF PCM 1. PCM requires complex circuitry to sample, quantize, code and decode. 2. PCM requires large bandwidth compared with that of the original analog signal.
DELTA MODULATION ECE 416 Thursday, 08 March 2018
DELTA MODULATION 1. Delta modulation seeks to overcome the problem of high bandwidth requirement in conventional PCM. 2. Instead of generating and transmitting many bits per sample, only one bit is transmitted. 3. During coding, the present sample is compared with the previous and a 0 or 1 transmitted depending on whether the sample is higher or lower than the previous. PCM code for each sample
SIGNALS IN A DELTA MODULATION SYSTEM Amplitude Original Analog Signal Output from Encoder Output from the receiver (decoder) Time
DELTA MODULATION TRANSMITTER x(nt s ) + - x (nt s ) error e(nt s ) One-bit Quantizer b(nt s ) + + Output Delay T s u(nt s ) Accumulator
DELTA MODULATION RECEIVER + + Low-pass filter Demodulated Signal Delay T s Accumulator
ADVANTAGES OF DELTA MODULATION Delta Modulation: 1. Requires very small bandwidth since it transmits only one bit per sample 2. Has very simple transmitter and receiver circuitry.
DISADVANTAGES OF DELTA MODULATION Delta modulation has: a) Slope and overload distortion b) Granular and Idle noise
Slope-overload occurs when the step size is too small to follow a steep segment of the input waveform x(t ). SLOPE OVERLOAD
GRANULARITY Granularity refers to a situation where the staircase function x(t) hunts around a relatively flat segment of the input function, with a step size that is too large relative to the local slope characteristic of the input.
ADAPTIVE DELTA MODULATION ECE 416 Digital Communication Thursday, 08 March 2018
Amplitude THE PRINCIPLE OF ADAPATIVE DELTA MODULATION Adaptive Delta Modulation seeks to overcome quantization errors arising from slope overload and granular noise by varying the step size in accordance to the signal amplitude. n+1 n n 1 1 1 1 0 0 0 0 1 0 1 0 1 Time
ADAPTIVE DELTA MODULATION TRANSMITTER Logic for step control x(nt s ) + - x (nt s ) error e(nt s ) One-bit Quantizer + + Output Delay T s Accumulator
ADAPTIVE DELTA MODULATION RECEIVER Receiver Input + + + + Low-pass filter Receiver Output Logic for step-size control Delay T s Accumulator
DIFFERENTIAL PULSE CODE MODULATION (DPCM) ECE 416 Digital Communication Thursday, 08 March 2018
DIFFERENTIAL PULSE CODE MODULATION 1. Some signals such as speech have high correlation between adjacent samples. 2. When such highly correlated samples are encoded using basic PCM, the resulting code contains a lot of redundant information. 3. In such cases, basic PCM scheme is not the preferred coding method. 4. By removing this redundancy before encoding an efficient coded signal can be obtained. 5. One method of removing redundancy is by using the Differential PCM (DPCM) method. 6. DPCM is based on the principle that by knowing the past behaviour of a signal up to a certain point in time, it is possible to predict future values.
DPCM TRANSMITTER Analogue Signal X(t) x(nt s ) e nt s = x nt s x (nt s ) b nt s = coded form of x nt s x nt s x (nt s ) x (nt s ) Quantized value of e nt s = x nt s x (nt s ) u nt s = x^(nt s ) Predictor uses x^(nt s ) and previous values to predict x (nt s )
DPCM RECEIVER e nt s = x nt s x (nt s ) y nt s = x(nt s ) b nt s = coded form of e nt s x (nt s ) Predictor uses x^(nt s ) and previous values to predict x (nt s )
COMPARISON OF PCM, DELTA MODULATION AND ADAPTIVE PULSE CODE MODULATION N0 PARAMETER PULSE CODE MODULATION (PCM) DELTA MODULATION ADAPTIVE DELTA MODULATION 1 Levels and Step Size Number of levels depend on number of bits Level size is fixed Step size is fixed Step size varies according to the rate at which the signal is varying 2 Number of Bits Can take 4, 8 or 16 bits per sample 3 Quantization errors Quantization noise is and distortion present One bit per sample Has lope overload and granular noise 4 Bandwidth Highest bandwidth Low bandwidth required 5 Feedback in No feedback Feedback in transmitter or transmitter receiver 6 Complexity in implementation High Simple Simple One bit per sample Quantization noise is present Least bandwidth required Feedback in transmitter