Formatting and Baseband Modulation Chapter Two Formatting and Baseband Modulation

Digital Communication Transformation

Formatting and Transmission of Baseband Signals

Message, Characters, and Symbols

Formatting Analog Information Formatting process Transform an analog waveform into a form that is compatible with a digital communication system Sampling theorem A bandlimited signal having no spectral components above hertz can be determined uniquely by values sampled at , where is also called the Nyquist rate

Impulse Sampling (Ideal Case)

Spectra for Various Sampling Rate Sampled spectrum (fs > 2fm) Sampled spectrum (fs < 2fm)

Natural Sampling

Comparison of Impulse Sampling and Natural Sampling Impulse sampling (Ideal case) Natural sampling (A practical way)

Sample-and-Hold Operation Transfer function where is the hold-operation and is the form of Two effects of hold-operation The significant attenuation of the higher frequency components The non-uniform spectral gain Post-filtering operation can compensate the effects of hold-operation

Aliasing for Sampling

Eliminate Aliasing for Higher Sampling

Aliasing Elimination Higher sampling rate Pre-filtering the original spectrum so that the new maximum frequency is reduced to fs/2 or less Post-filtering removes the aliased components Both the pre-filtering and the post-filtering will result a loss of signal information Trade-off is required between the sampling rate and cutoff bandwidth Engineer’s version of the Nyquist sampling rate is

Pre-filter Eliminates Alias

Post-filter Eliminates Alias

Alias Frequency by Sub-Nyquist Sampling Rate

Sampling Process (I) Without oversampling (sampling rate is the Nyquist rate) The analog signal passes through a high performance analog low-pass filter Sampling rate is the Nyquist rate for the band-limited signal The samples are mapped to a finite list of discrete output levels and processed by the following digital signal process

Sampling Process (II) With over-sampling (sampling rate is higher than the Nyquist rate) The analog signal passes through a low performance analog low-pass filter The pre-filtered signal is sampled at the higher Nyquist rate for the band-limited signal The samples are mapped to a finite list of discrete output levels and processed by a high performance digital filter to reduce the bandwidth of the digital samples

Analog Source Description

Source of Corruption Sampling and quantizing effects Channel effects Quantization noise due to round-off or truncation error Increase the number of levels employed in the quantization process Quantizer saturation AGC can be used to avoid the saturation Timing jitter Stable clock Channel effects Channel noise (thermal noise, interference from other users) Intersymbol interference (ISI)

Quantization Level

Signal to Noise Ratio for Quantized Pulse Assume the quantization error ,e, is uniformly distributed over a single interval q-wide, the quantizer error variance is The peak power is The ratio of signal peak power to average quantization error power

Quantization Samples

Pulse Code Modulation (PCM) Quantize PAM signal into a digital word Increase the number of levels Reduce the quantization noise Increase the number of bits per PCM sequence The data rate is thus increased, and the cost is a greater transmission bandwidth Some communication systems can be tolerable to the time delay so that the more quantization levels need not more bandwidth (ex: outer space communication)

Statistics of Speech Amplitudes

Uniform and Non-uniform Quantization

Quantizer Characteristics

Compression Characteristics Figure 2.20 Compression characteristics. (a) μ-law characteristic. (b) A-law characteristic.

Compression Functions m-law compression A-law

Baseband Transmission

Waveform Representation of Binary Digits Binary digits needs to be represented by physical waveform

PCM Waveform Considerations DC component Eliminate DC energy to enable the system to be ac coupled Self-clocking Some PCM coding schemes aid in the recovery of the clock signal Error detection Bandwidth compression Such as multi-level codes Differential encoding Noise immunity Some PCM schemes have better error performance

Spectral Densities of Various PCM Waveform

Bits per PCM Word and Bits per Symbol PCM word size Required number of bits per analog sample for the allowable quantization distortion For example, we specified the quantization error is specified not to exceed a fraction of the peak-to-peak analog voltage , Bits per symbol is decided by M-level signal transmission

Quantization Levels and Multi-level Signaling Example 2.3 The information in an analog waveform, with the maximum frequency fm=3 kHz, is to be transmitted over an M-ary PAM system, where the number of pulse levels is M=16. The quantization distortion is specified not to exceed of the peak-to-peak analog signal What is the minimum number of bits/sample, or bits/PCM word that should be used in digitizing the analog waveform? What is the minimum required sampling rate, and what is the resulting bit transmission rate? What is the PAM pulse or symbol transmission rate? If the transmission bandwidth equals 12 KHz, determine the bandwidth efficiency for this system

Correlative Coding Transmit 2W symbols/s with zero ISI, using the theoretical minimum bandwidth of W Hz, without infinitely sharp filters. Correlative coding (or duobinary signaling or partial response signaling) introduces some controlled amount of ISI into the data stream rather than trying to eliminate ISI completely Doubinary signaling

Duobinary Decoding Example Binary digit sequence xk: 0 0 1 0 1 1 0 Bipolar amplitudes xk : -1 -1 +1 -1 +1 +1 -1 Coding rule yk=xk+xk-1 -2 0 0 0 2 0 Decoding decision rule If , decide that If , decide opposite of the previous decision Error propagation could cause further errors

Precoded Doubinary Signaling

Duobinary Precoding Example Binary digit sequence 0 0 1 0 1 1 0 Precoded sequence 0 0 1 1 0 1 1 Bipolar sequence -1 -1 +1 +1 -1 +1 +1 Coding rule -2 0 +2 0 0 +2 Decoding decision rule If , decide that If , decide that Decoded binary sequence 0 1 0 1 1 0

Duobinary Equivalent Transfer Function

Duobinary Transfer Function

Comparison of Binary with Duobinary Signaling Binary signaling assumes the transmitted pulse amplitude are independent of one another Duobinary signaling introduces correlation between pulse amplitudes Duobinary technique achieve zero ISI signal transmission using a smaller system bandwidth Duobinary coding requires three levels, compared with the usual two levels for binary coding Duobinary signaling requires more power than binary signaling (~2.5 dB greater SNR than binary signaling)