PULSE CODE MODULATION

PCMPULSE CODE MODULATIONPCMPCM is adigitalscheme for transmittinganalogdata. The signals in PCM are binary; that is, there are only two possible states, represented by logic 1 (high) and logic 0 (low)PCMM=2nM number of Quantization levelsn number of bits per samplePCMSAMPLING, QUANTIZING, AND ENCODINGSAMPLINGgeneration of flat top PAM signal

PCMSAMPLING, QUANTIZING, AND ENCODINGQUANTIZINGconverting each sample value to a finite number of levels so that digital words with amplitude closest to the actual sampled value is usedWhen sampling at NYQUIST RATE(2B) or faster and there is negligible noise, there will still be QUANTIZING NOISEWill have an output called QUANTIZED PAM signalPCMSAMPLING, QUANTIZING, AND ENCODINGENCODINGPCM is obtained from quantized PAM signal by converting each sample value into digital wordGray code is used as binary code word PCM

PCM

PCMPRACTICAL PCM CIRCUIT

PCMPRACTICAL PCM CIRCUITa. Low-pass Filter limits analog input signal to standard frequency rangeb. Instantaneous sampler and hold periodically samples signals and converts them to a multilevel PAM signalc. Converts PAM to parallel PCM codes

PCMPRACTICAL PCM CIRCUITParallel PCM codes are converted to serial binary data and then outputted to the transmission line as digital pulsesTrans line repeaters are placed at a prescribed distances to regenerate digital pulses

PCMPRACTICAL PCM CIRCUIT- Converts serial pulses from transmission line to parallel PCM codes- Converts parallel PCM codes to multilevel PAM signals- Hold circuit is basically Low-Pass filter that converts PAM back to its original form

PCMThree popular techniques are used to implement the analog-to-digital converter (ADC) encoding operation: The counting or ramp, ( Maxim ICL7126 ADC)Serial or successive approximation, (AD 570)Parallel or flash encoders. ( CA3318)The objective of these circuits is to generate the PCM word.Parallel digital output obtained (from one of the above techniques) needs to be serialized before sending over a 2-wire channelThis is accomplished by parallel-to-serial converters [Serial Input-Output (SIO) chip]UART, USRT and USART are examples for SIOs

PRACTICAL PCM CIRCUITPCMBANDWIDTH OF PCM SIGNALSThe spectrum of the PCM signal is not directly related to the spectrum of the input signal.The bandwidth of (serial) binary PCM waveforms depends on the bit rate R and the waveform pulse shape used to represent the data.The Bit Rate R is R=nfs Wheren is the number of bits in the PCM word (M=2n)fs is the sampling rate

PCMBANDWIDTH OF PCM SIGNALSFor no aliasing case (fs 2B), the MINIMUM Bandwidth of PCM Bpcm(Min) is:Bpcm(Min) = R/2 = nfs/2

The Minimum Bandwidth of nfs/2 is obtained only when sin(x)/x pulse is used to generate the PCM waveform. PCMBANDWIDTH OF PCM SIGNALSFor PCM waveform generated by rectangular pulses, the First-null Bandwidth is:Bpcm = R = nfsPCM PCM Noise and CompandingQuantization NoiseSignal to Noise RatioPCM Telephone SystemNonuniform QuantizationCompandingPCMThe process of quantization can be interpreted as an additive noise process.

The signal to quantization noise ratio (SNR)Q=S/N is given as:

Quantization NoiseSignalXQuantized SignalXQQuantization NoisenQ

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Effects of Noise on PCMTwo main effects produce the noise or distortion in the PCM output: Quantizing noise that is caused by the M-step quantizer at the PCM transmitter. Bit errors in the recovered PCM signal, caused by channel noise and improper filtering.If the input analog signal is band limited and sampled fast enough so that the aliasing noise on the recovered signal is negligible, the ratio of the recovered analog peak signal power to the total average noise power is:

The ratio of the average signal power to the average noise power is

M is the number of quantized levels used in the PCM system. Pe is the probability of bit error in the recovered binary PCM signal at the receiver DAC before it is converted back into an analog signal.

PCMEffects of Quantizing NoiseIf Pe is negligible, there are no bit errors resulting from channel noise and no ISI, the Peak SNR resulting from only quantizing error is:

The Average SNR due to quantizing errors is:

Above equations can be expresses in decibels as,

Where, M = 2n = 4.77 for peak SNR = 0 for average SNR PCMDESIGN OF A PCM SIGNAL FOR TELEPHONE SYSTEMSAssume that an analog audio voice-frequency(VF) telephone signal occupies a band from 300 to 3,400Hz. The signal is to be converted to a PCM signal for transmission over a digital telephone system. The minimum sampling frequency is 2x3.4 = 6.8 ksample/sec.To be able to use of a low-cost low-pass antialiasing filter, the VF signal is oversampled with a sampling frequency of 8ksamples/sec. This is the standard adopted by the Unites States telephone industry.Assume that each sample values is represented by 8 bits; then the bit rate of the binary PCM signal is

This 64-kbit/s signal is called a DS-0 signal (digital signal, type zero). The minimum absolute bandwidth of the binary PCM signal is

8This B is for a sinx/x type pulse sampling

PCMDESIGN OF A PCM SIGNAL FOR TELEPHONE SYSTEMSWe require a bandwidth of 64kHz to transmit this digital voice PCM signal, whereas the bandwidth of the original analog voice signal was, at most, 4kHz.

We observe that the peak signal-to-quantizing noise power ratio is:

Note: Coding with parity bits does NOT affect the quantizing noise,However coding with parity bits will improve errors caused by channel or ISI, which will be included in Pe ( assumed to be 0).

If we use a rectangular pulse for sampling the first null bandwidth is given byPCMNonuniform QuantizationMany signals such as speech have a nonuniform distribution.The amplitude is more likely to be close to zero than to be at higher levels.Nonuniform quantizers have unequally spaced levelsThe spacing can be chosen to optimize the SNR for a particular type of signal.2468246-2-4-6Input sampleXOutput sampleXQ-2-4-6-8Example: Nonuniform 3 bit quantizerPCMCompandingNonuniform quantizers are difficult to make and expensive.An alternative is to first pass the speech signal through a nonlinearity before quantizing with a uniform quantizer.The nonlinearity causes the signal amplitude to be Compressed.The input to the quantizer will have a more uniform distribution.At the receiver, the signal is Expanded by an inverse to the nonlinearity.The process of compressing and expanding is called Companding.PCM-Law CompandingTelephones in the U.S., Canada and Japan use -law companding:

Where = 255 and |x(t)| < 1

Input |x(t)|Output |x(t)|PCMNon Uniform quantizing

Voice signals are more likely to have amplitudes near zero than at extreme peaks.For such signals with non-uniform amplitude distribution quantizing noise will be higher for amplitude values near zero.A technique to increase amplitudes near zero is called Companding.Effect of non linear quantizing can be can be obtained by first passing the analog signal through a compressor and then through a uniform quantizer.xQ(.)yUniform QuantizerC(.)xCompressorxPCM

Example: m-law Compandingx[n]=speech /song/y[n]=C(x[n])Companded SignalSegment of x[n]Segment of y[n]Companded SignalClose View of the SignalPCMA-law and m-law CompandingThese two are standard companding methods. u-Law is used in North America and JapanA-Law is used elsewhere to compress digital telephone signals

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SNR of Compander The output SNR is a function of input signal level for uniform quantizing. But it is relatively insensitive for input level for a companderPCMSNR Performance of Compander

The output SNR is a function of input signal level for uniform quantizing. But it is relatively insensitive for input level for a compander.

= 4.77 - 20 Log ( V/xrms) for Uniform Quantizer V is the peak signal level and xrms is the rms value

= 4.77 - 20 log[Ln(1 + )] for -law companding = 4.77 - 20 log[1 + Ln A] for A-law companding

PCMV.90 56-Kbps PCM Computer modemThe V.90 PC Modem transmits data at 56kb/s from a PC via an analog signal on a dial-up telephone line.A law compander is used in quantization with a value for of 255.The modem clock is synchronized to the 8-ksample/ sec clock of the telephone company.7 bits of the 8 bit PCM are used to get a data rate of 56kb/s ( Frequencies below 300Hz are omitted to get rid of the power line noise in harmonics of 60Hz). SNR of the line should be at least 52dB to operate on 56kbps.If SNR is below 52dB the modem will fallback to lower speeds ( 33.3 kbps, 28.8kbps or 24kbps).

PCMKEVIN CEAaljohn valdezjay angelo balanaRUSSEL FERNANDO jr.

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