Pulse Code Modulation Pulse Code Modulation (PCM) : method for conversion from analog to digital waveform Instantaneous samples of analog waveform represented by digital code words output in serial bit stream Digital Code Words n-bit binary digital word has M = 2n unique codes Each code word represents a specific discrete amplitude value of analog waveform Analog signal has infinite # of amplitude levels so discrete PCM amplitude introduces error Discrete value is closest value to actual amplitude “Quantizing” or “Roundoff” error ECE 4710: Lecture #8

Pulse Code Modulation Widely used for digital landline telephony Advantages Simple and inexpensive digital circuits can be used Multiple types of data (voice, video, internet, etc.) can be merged (interleaved) together into a single signal and transmitted over same channel Time Division Multi-plexing  TDM Clean PCM waveforms can be regenerated at repeater stations over long-distance communication links Noisy input PCM signal replaced with clean output PCM signal, perhaps with a few bit errors ECE 4710: Lecture #8

Pulse Code Modulation Advantages (continued) Primary Disadvantage S/N performance of digital signal can be much superior to analog signal Errors can be detected and corrected using channel codes Primary Disadvantage PCM signals typically have 10-20 times the bandwidth of the input analog signal Very inefficient use of spectrum Not used for most wireless applications ECE 4710: Lecture #8

PCM Generation Basic steps for generating PCM signal Bandlimit input analog signal to prevent aliasing (optional) Instantaneous sample and hold circuit to convert analog signal to flat-top PAM Quantize the PAM signal to produce discrete amplitude levels for analog PAM  “Quantized PAM” Quantize or roundoff error is irrevocably introduced PCM signal generated by taking discrete amplitude and generating a coded digital word to represent amplitude value Codes selected to minimize effect of bit errors ECE 4710: Lecture #8

PCM System PCM Signal ECE 4710: Lecture #8

PCM Quantization Uniform quantization divides signal amplitudes in to M = 2n equally spaced levels Approximation of analog amplitude with discrete value Error will be one-half of quantization step size Quantization error Even if No channel noise No system noise Sampling at fs  2 B  Quantization error cannot be fixed ECE 4710: Lecture #8

Quantization ECE 4710: Lecture #8 3-bit quantizer = 23 = 8 levels Step size = 16 V / 8 Levels = 2 V / Level Max Roundoff Error = 0.5 (2 V) = 1 V Discrete Continuous ECE 4710: Lecture #8

Quantization Error ECE 4710: Lecture #8

Encoding ECE 4710: Lecture #8 Encoding transforms quantized PAM signal into PCM signal Each discrete amplitude level represented by unique code word Codes selected to minimize impact of single bit errors or multiple sequential bit errors on signal quality Gray Code One-bit change between code words representing adjacent amplitude values (as much as possible) Single bit errors (excluding sign bit) have small impact Reed-Solomon Codes Correct sequential “burst” errors, e.g. errors that occur in sequential groups Used on CD’s to minimize impact of scratches or fingerprints ECE 4710: Lecture #8

Gray Coding ECE 4710: Lecture #8 Note that discrete voltage amplitude does not equal binary value  111  7 V!! Digital Word = Code Word ECE 4710: Lecture #8

Coded PCM Signal Coded word output in serial bit stream of n-bit digital words Many types of rectangular pulse shapes used to represent binary 1’s and 0’s Above example shows unipolar non-return to zero shape Unipolar NRZ (Fig. 3-15b, pg. 165) ECE 4710: Lecture #8

PCM Circuits PCM circuit combines functions on a single chip Sample & Hold + Quantizer + Encoder Analog-to-Digital Conversion = ADC Digital-to-Analog Conversion = DAC Decode PCM to produce analog signal Many chips are specialized for particular application Voice for telephony, audio for music, video, data, etc. Combination of Coder / Decoder = “Codec” Similar to Modulate / Demodulate = Modem ECE 4710: Lecture #8

PCM Signal BW Spectral shape of PCM signal is completely unrelated to spectral shape of input analog signal Spectral shape depends on type of digital pulse waveform used to represent serial PCM data PCM signal BW is indirectly related to input analog signal BW but it also depends on other factors Number of bits Sampling rate BW of serial pulse representing code words ECE 4710: Lecture #8

PCM Signal BW Bit rate of binary data  R = n fs (bits per sec = bps) e.g. 8-bit code words @ 5000 samples/sec = 40 kbps For no aliasing we require fs  2 B where B is the bandwidth of the input analog signal What kind of bandwidth measure is B? Absolute bandwidth for no aliasing Pre-filter usually done to obtain absolutely bandlimited input PCM signal bandwidth is bounded by Minimum BW only obtained for (sin x) / x pulse shape Not practical for most systems ECE 4710: Lecture #8

PCM Signal BW Rectangular-like pulse is usually used for PCM waveforms PCM signal BW will be larger than minimum: How much larger? Depends on type of line signals (RZ, NRZ) and pulse shapes (studied next) Typical BW for common line codes and pulse shapes Unipolar NRZ, Bipolar NRZ, Bipolar RZ  First-Null BW = R = 1 / Tb f PSD 1 / Tb = FNBW 1 Bit Period = Tb Signal BW = Bs  1 / Tb +V ECE 4710: Lecture #8

PCM Signal BW Typical rectangular pulses  PCM signal will have FNBW of Minimum BW was For Nyquist rate sampling fs = 2 B so minimum BW ECE 4710: Lecture #8

PCM Signal BW Typical FNBW For reasonable values of n, PCM signal BW will many times larger than input analog signal BW Primary disadvantage of PCM Example: Landline digital telephony Voice signal BW  300 Hz to 3,300 Hz fs  2 B = 2 • 3300 = 6.6 kHz but chosen to be fs = 8 kHz to allow inexpensive (non-ideal) LPF n = 8-bit code word  M = 256 level quantizer BPCM = n fs = 8 • 8000 = 64 kHz FNBW ~ 20  larger than 3.3 kHz input analog signal !!! Only for Nyquist rate sampling ECE 4710: Lecture #8

PCM Signal Filtering Filtering (LPF) of PCM rectangular pulse can be done to reduce signal BW by ~20-40% FNBW still many times larger than analog signal BW LPF will cause time smearing of rectangular pulses Care must be taken so that pulse smearing from LPF does not create too much ISI  BER  Even if no LPF is used to reduce PCM signal BW the frequency response of the transmission channel can also cause pulse smearing, ISI, and BER increase Mobile Radio Channel (wireless cellular) ECE 4710: Lecture #8