Digital Transmission Principles Analog and Digital Communication Baseband channel Channel Analog source Analog destination Analog source Modulator (Tx)Demodulator (Rx) Analog destination Analog signal and baseband transmission Analog transmission using mod’n and demod’n Digital channel Analog channel Digital Coder Decoder Digital sink Digital Modem Modem Digital sink source source Digital signal transmitted on digital channel Digital signal transmitted by modem Digital channel Analog A/D Decoding & Digital sink Analog signal transmitted digitally source conversion D/A & coding conversion Analog channel Analog signal digitized Analog A/D Modem Modem Decoding & Digital sink and transmitted by source conversion D/A modem & coding conversion Spectrum of a Modulating Square Wave Spectrum contains an infinite number of odd harmonics plus its fundamental frequency. Assume a fundamental frequency of the modulating square wave to be 1 kHz and a carrier frequency of 1 MHz. When these signals heterodyne: 1. Two new frequencies will be produced: sum frequency of 1.001 MHz and difference frequency of 0.999 MHz. 2. The harmonics contained in the square wave heterodynes with the carrier frequency as well. Hence, the third harmonic of the square wave heterodynes with the carrier and produces sideband frequencies at 1.003 and 0.997 MHz. Another set will be produced by the fifth, seventh, ninth, eleventh, thirteenth, fifteenth, seventeenth, and nineteenth harmonics of the square wave, and so on to infinity.
Spectrum distribution when modulating with a square wave. The first set of sidebands is directly related to the amplitude of the square wave. The second set of sidebands is related to the third harmonic content of the square wave and is 1/3 the amplitude of the first set. The third set is related to the amplitude of the first set of sidebands and is 1/5 the amplitude of the first set. This relationship will apply to each additional set of sidebands. Various square‐wave modulation levels with frequency‐spectrum carrier and sidebands. Observations: (carrier modulated with a square wave) 1. As the amplitude of the modulating square wave is increased, the RF peaks increases in amplitude during the positive alternation of the square wave and decrease during the negative half of the square wave. 2. For the frequency spectrum, the carrier amplitude remains constant, but the sidebands increase in amplitude in accordance with the amplitude of the modulating square wave. 3. In view (C) the amplitude of the square wave of voltage is equal to the peak voltage of the unmodulated carrier wave. This is 100% modulation, just as in conventional AM. 4. In the frequency spectrum, the sideband distribution is also the same as in AM. The total sideband power is 1/2 of the total power when the modulator signal is a square wave. This is in contrast to 1/3 of the total power with sine‐wave modulation. 5. In view (D), the increase of the square‐wave modulating voltage is greater in amplitude than the unmodulated carrier. The sideband distribution does not
change; but, as the sidebands take on more of the transmitted power, so will the carrier. In pulse modulation, the same general rules apply as in AM. Pulse Timing Some pulse‐modulation systems modulate a carrier in the manner of increasing or decreasing the amplitude of the modulating square wave. Others produce no RF until pulsed; that is, RF occurs only during the actual pulse. If we allow oscillations to
occur for a given period of time only during selected intervals, as in view (B), we are PULSING the system. Pulse Transmission Note: The pulse transmitter is gated on and off instead of being modulated by a square wave. Varying pulse‐modulating waves Note: Carrier frequencies in pulse systems can vary. The carrier frequency is not the only frequency we must concern ourselves with in pulse systems. We must also note the frequency that is associated with the repetition rate of groups of pulses. Pulse‐repetition time (PRT) ‐ the total time of one complete pulse cycle of operation (rest time plus pulse width) Pulse‐repetition frequency (PRF) — the rate, in pulses per second, that the pulse occurs
Pulse‐repetition time (prt) and pulse‐repetition frequency (prf) Figure 2-34.—Pulse cycles.Pulse width — the duration of time RF frequency is transmitted Rest time — the time the transmitter is resting (not transmitting) . Pulse width and rest time The pulse width is the time that the transmitter produces RF oscillations and is the actual pulse transmission time. During the nonpulse time, the transmitter produces no oscillations and the oscillator is cut off. Power in a Pulse System Peak power ‐ the maximum value of the transmitted pulse Average power ‐ peak power value averaged over the pulse‐repetition time. Peak power is very easy to see in a pulse system.
Duty Cycle ‐ ratio of actual transmitting time to transmitting time plus rest time. To establish the duty cycle, divide the pulse width by the pulse repetition time of the system. Digital transmission – transmission of digital signals between two or more points in a communication system Advantages of Digital Transmission 1. Noise immunity, since it is not necessary to evaluate the precise amplitude, frequency or phase to ascertain logic condition. A simple determination is made whether the pulse is above or below a prescribed level. 2. Digital signals are better suited than analog signals for processing and multiplexing. It is easier to store digital signals and the transmission rate can be varied to adapt different environments and to interface with different types of equipment. 3. More resistant to analog systems to additive noise because they use signal regeneration rather than signal amplification. 4. Simpler to measure and evaluate than analog signals Advantages of Digital Transmission 1. Transmission of digitally encoded analog signals requires significantly more bandwidth than simply transmitting the original analog signal. 2. Analog signals must be converted to digital pulses prior to transmission and converted back to analog form at the receiver, thus requiring additional encoding and decoding circuitry 3. Requires precise time synchronization between the clocks in the transmitters and receivers 4. Some digital transmission systems are incompatible with older analog transmission systems. Communications Pulse Modulators To transmit intelligence using pulse modulation, one must provide a method to vary some characteristic of the pulse train in accordance with the modulating signal. The characteristics of these pulses that can be varied are amplitude, pulse width, pulse‐repetition time, and the pulse position as compared to a reference. In addition to these three characteristics, pulses may be transmitted according to a code to represent the different levels of the modulating signal. Pulse‐Amplitude Modulation
Pulse‐amplitude modulation (PAM) in which the amplitude of each pulse is controlled by the instantaneous amplitude of the modulating signal at the time of each pulse. • The simplest form of pulse modulation. • Generated in much the same manner as analog‐amplitude modulation. • The timing pulses are applied to a pulse amplifier in which the gain is controlled by the modulating waveform. • Since these variations in amplitude actually represent the signal, this type of modulation is basically a form of AM. The only difference is that the signal is now in the form of pulses. • Have the same built‐in weaknesses as any other AM signal ‐ high susceptibility to noise and interference. • The reason for susceptibility to noise is that any interference in the transmission path will either add to or subtract from any voltage already in the circuit (signal voltage). Thus, the amplitude of the signal will be changed. Since the amplitude of the voltage represents the signal, any unwanted change to the signal is considered a SIGNAL DISTORTION. For this reason, PAM is not often used. When PAM is used, the pulse train is used to frequency modulate a carrier for transmission. Demodulating PAM: Peak detection uses the amplitude of a PAM signal or the duration of a PWM signal to charge a holding capacitor and restore the original waveform. This demodulated waveform will contain some distortion because the output wave is not a pure sine wave. However, this distortion is not serious enough to prevent the use of peak detection.
Pulse‐Time Modulation Time characteristics of pulses may also be modulated with intelligence information. Two time characteristics may be affected: 1. the time duration of the pulses, referred to as pulse‐duration modulation (PDM) or pulse‐width modulation (PWM) 2. the time of occurrence of the pulses, referred to as pulse‐position modulation (PPM) A special type of pulse‐time modulation (PTM) referred to as pulse‐frequency modulation (PFM) may also be employed. Pulse‐time modulation (PTM) ‐ PDM.
Pulse‐time modulation (PTM) ‐ PPM Pulse‐time modulation (PTM) ‐ PPMPulse‐duration modulation (pulse‐width modulation) • The width of each pulse in a train is made proportional to the instantaneous value of the modulating signal at the instant of the pulse. Either the leading edges, the trailing edges, or both edges of the pulses may be modulated to produce the variation in pulse width. • PWM is often used because it is of a constant amplitude and is, therefore, less susceptible to noise. Generating PWM: Add the modulating signal to a repetitive sawtooth waveform. The resulting waveform is then applied to a one‐shot multivibrator circuit which changes state when the input signal exceeds a specific threshold level. The action produces pulses with widths that are determined by the length of time that the input waveform exceeds the threshold level. Demodulating PWM: The peak detector circuit may also be used for PWM. To detect PWM, modify the peak detector so that the time constant for charging C1 through CR1 is at least 10 times the maximum received pulse width. This may be done by adding a resistor in series with the cathode or anode circuit of CR1. The amplitude of the voltage to which C1 charges, before being discharged by the negative pulse, will be directly proportional to the input pulse width. A longer pulse width allows C1 to charge to a higher potential than a short pulse. This charge is held, because of the long time constant of R1 and C1, until the discharge pulse is applied to diodes CR2 and CR3 just prior to the next incoming pulse. These charges across C1 result in a wave shape similar to the output shown for PAM detection. Comparing PWM with PPM
Disadvantage: Varying pulse, width and therefore, of varying power content. This means that the transmitter must be powerful enough to handle the maximum‐width pulses, although the average power transmitted is much less than peak power. Advantage: PWM will still work if the synchronization between the transmitter and receiver fails; in PPM it will not, Pulse‐position modulation — The amplitude and width of the pulse is kept constant in the system. The position of each pulse, in relation to the position of a recurrent reference pulse, is varied by each instantaneous sampled value of the modulating wave. Generating PPM: Apply PWM pulses to a differentiating circuit. This provides positive‐ and negative‐polarity pulses that correspond to the leading and trailing edges of the PWM pulses. The position of the leading edge is fixed, whereas the trailing edge is not. After differentiation, the negative pulses are position‐modulated in accordance with the modulating waveform. Both the negative and positive pulses are then applied to a rectification circuit. This application eliminates the positive, non‐modulated pulses and develops a PPM pulse train Demodulating PPM: PPM, PFM and PCM are most easily demodulated by first converting them to either PWM or PAM. The trigger pulses must be synchronized with the unmodulated position of the PPM pulses, but with a fixed time delay from these pulses. As the position‐modulated pulse is applied to the flip‐flop, the output is driven positive. After a period of time, the trigger pulse is again generated and drives the flip‐flop output negative and the pulse ends. Because the PPM pulses are constantly varying in position with reference to the unmodulated pulses, the output of the flip‐ flop also varies in duration or width. This PWM signal can now be applied to either a peak detector or low‐pas filter for demodulation. Comparing PPM with PWM Advantage: requires constant transmitter power since the pulses are of constant amplitude and duration Disadvantage: depends on transmitter‐receiver synchronization Pulse‐frequency modulation (PFM) • PFM is a method of pulse modulation in which the modulating wave is used to frequency modulate a pulse‐generating circuit. For example, the pulse rate may be 8,000 pulses per second (pps) when the signal voltage is 0. The pulse rate may step up to 9,000 pps for maximum positive signal voltage, and down to 7,000 pps for maximum negative signal voltage.
• This method of modulation is not used extensively because of complicated PFM generation methods. It requires a stable oscillator that is frequency modulated to drive a pulse generator. Since the other forms of PTM are easier to achieve, they are commonly used. Pulse‐Code Modulation • Invented by Alec Reeves in 1937 • Most commonly used digital communications technique • Form of pulse modulation where samples of the analog input are converted to binary coded pulses Block Diagram of a PCM Transmission System Bandpass filter – limits the frequency of the analog signal to the voice band frequency range Sample‐and‐hold circuit – periodically samples the analog input signal and converts the samples to multilevel PAM signal ADC – converts the PAM samples to parallel PCM codes Parallel‐to‐serial converter – converts the parallel PCM codes to serial digital pulses
Forms of Sampling Natural sampling – tops of the sample pulses retain their original shape during the sample interval Flat‐top sampling – sampling of an analog signal using a sample‐and‐hold circuit, such that the sample has the same amplitude for its whole duration The sampling process alters the frequency spectrum and introduces aperture error, which is when the amplitude of the sampled signal changes during the sample time. Sampling Theorem For an analog receiver to be fully reconstructed at the receiver’s output, the rate at which an analog input signal should be sampled must at least be twice the highest audio frequency component present. fs ≥ 2fa Aliasing or foldover distortion – results when the signal is undersampled; distortion created by using too low a sampling rate when coding an analog signal for digital transmission falias = fs – fa Quantization – process of converting samples of the analog input as a number of discrete values. Quantization interval or quantum – magnitude difference between adjacent steps
Overload distortion or peak limiting – occurs if the magnitude of the sample exceeds the highest quantization interval Resolution – magnitude of a quantum; also equal to the voltage of the minimum step size Quantization range – (+) or (‐) one‐half the resolution Quantization noise or quantization error – results when the sampled analog signal is rounded off to the closest available code. Max Qe = ½ Resolution Dynamic Range – ratio of the largest possible magnitude to the smallest possible magnitude that can de decoded by the DAC at the receiver. V V DR = max = max = 2 n − 1 Vmin Resn Expressing DR in dB: Vmax V DR (dB) = 20 log = 20 log max = 20 log ( 2 n − 1) ≈ 6.02n Vmin Resn Coding Efficiency – a numerical indication of how efficiently a PCM code is utilized. min. no. of bits (inc. sign bit) Coding Eff = * 100 actual no. of bits (inc. sign bit) Signal‐to‐Quantization Noise Ratio for Linear PCM codes (or SNR) v2 / R SQR (dB) = 10 log 2 (q / 12) / Rwhere: R = resistance (ohms) v2/R = ave. signal power (watts) v = rms signal voltage (volts) (q2/12)/R = ave. quant. noise power (watts) q = quantization interval (volts) v2 vAssuming equal resistances: SQR (dB) = 10 log 2 = 10.8 + 20 log (q / 12) q Alternatively: SNRpk = 3M2 M = number of symbols or levels Noting that M = 2 n (n = number of bits), SNRpk in dB is also: SNRpk (dB) = 4.77 + 6.02n If the ratio of the peak to mean signal power v2peak/v2ave be denoted by α, then the average SNR is SNR = 3 (22n) (1/ α)
Expressing in dB: SNR (dB) = 4.77 + 6.02n – αdB Note: For sinusoidal signals, α = 2 (or 3 dB), for Gaussian random signals, α = 16 (or 12 dB), and for speech, α = 16 (or 12 dB) PCM Bit Rate = nfs Note: CD systems use a standard sampling rate of 44.1 KHz. Idle channel noise – random thermal noise quantized by the ADC when inputted at the PCM sampler. Nonlinear PCM With voice transmission, low‐amplitude signals are more likely to occur than large‐amplitude signals. As a result, there would be fewer codes available for higher amplitudes, thereby increasing quantization error for larger‐amplitude signals. This technique is called nonlinear encoding. Companding Techniques (compressing then expanding) With companded systems, higher‐amplitude signals are compressed (amplified less than the lower‐amplitude signals prior to transmission) and then expanded (amplified more than lower‐amplitude signals) in the receiver. Analog Companding I. μ‐law companding – North American standard for voice compression V ln (1 + μ in ) Vmax Vout = Vmax ln (1 + μ) where: Vmax = max. uncompressed analog input amplitude (V) Vin = amplitude of the input signal at a particular instant of time (V) μ = parameter used to define the amount of compression Vout = compressed output amplitude Indicators: The higher the μ value, the higher the compression. For μ = 0, the curve is linear (no compression). Most recent PCM systems use an 8‐bit code with μ = 255. II. A‐law companding AVin /Vmax V 1 Vout = Vmax 0 ≤ in ≤ 1 + ln A Vmax A 1 + ln (AVin /Vmax ) 1 Vin = ≤ ≤ 1 1 + ln A A Vmax
ITU Recommendation G.711 – recognizes A‐law and μ‐law as the international toll quality standard for digital coding of voice frequency signals; uses a sampling rate of 8 kHz and 8 encoding law of 8 binary digits per sample. Bandwidth Reduction Techniques 1. Differential Pulse Code Modulation ‐ the difference in the amplitude between two successive samples is transmitted rather than the actual samples. The adjacent samples derived from most naturally generated information signals are not usually independent but correlated. 2. Adaptive Differential Pulse Code Modulation – a more sophisticated version of DPCM; adopted by the ITU as the reduced bit rate standard. The ADPCM encoder takes a 64‐kbps companded PCM signal (G.711) and converts it to a 32‐ kbps ADPCM signal (G.721). Other specifications are defined by the ITU‐T, G.726 and G.727 for ADPCM with transmission rates of 16 kbps to 40 kbps. 3. Delta Modulation – uses a single‐bit PCM code to achieve digital transmission of analog signals. (Algorithm: If the current sample is smaller than the previous sample, a logic 0 is transmitted. If the current sample is larger than the previous sample, a logic 1 is transmitted) Problems Encountered on Delta Modulation • Slope overload – The slope of the analog signal is greater than what the delta modulator can maintain. To reduce slope overload, increase the magnitude of the minimum step size. • Granular noise – The reconstructed signal has variations that were not present in the original signal. It can be reduced by decreasing the step size. 4. Adaptive Delta Modulation – In conventional DM, the problem of keeping both quantization noise and slope overload acceptably low is solved by oversampling (keeping the DM size and sampling many times the Nyquist rate). The penalty incurred is loss of some bandwidth savings, which is expected of DM. An alternative strategy is to make the DM size variable, making it larger during periods when slope overload would otherwise dominate and smaller when granular noise might dominate. Such systems are called adaptive DM systems. Digital companding The analog signal is first sampled and converted to linear PCM code, after which the code will be digitally compressed. In the receiver, the compressed PCM code is expanded, then decoded (back to analog). Most recent PCM systems use a 12‐bit linear PCM code and an 8‐bit compressed PCM code. Problems:
1. For a sample rate of 20 kHz, determine the maximum analog input frequency. 2. Determine the alias frequency for a 14‐kHz sample rate and an analog input frequency of 8 kHz. 3. Find the Nyquist interval for a signal defined as 5 cos1000πt cos 4000πt 4. Determine the dynamic range for a 12‐bit sign‐magnitude PCM code 5. Determine the minimum number of bits required in a PCM code for a dynamic range of 80 dB. What is the coding efficiency? 6. For a resolution of 0.04 V, determine the voltages for the following linear seven‐ bit magnitude PCM codes: (a) 0110101; (b) 1000001 7. Determine the range of an 8‐bit sign magnitude PCM code given as 10111000 if its resolution is 0.1 V. 8. Determine the resolution and quantization error for an 8‐bit linear sign‐ magnitude PCM code for a maximum decoded voltage of 1.27 V. 9. Determine the SQR for a 2‐Vrms signal and a quantization interval of 0.2 V. 10. A digital communications system is to carry a single voice signal using linearly quantized PCM. What bit rate will be required if an ideal anti‐aliasing filter with a cut‐off frequency of 3.4 kHz is used at the transmitter at the SNR is to be kept above 50 dB? 11. Given μ = 255, Vmax = 1 V and Vin = 0.75 V, determine the compressor gain. 12. A 12‐bit linear sign‐magnitude PCM code is digitally compressed into 8 bits. For a resolution of 0.016 V, determine the following quantities for an input voltage of ‐6.592V (a) 12‐bit linear PCM code; (b) 8‐bit compressed PCM code; (c) decoded 12‐bit code; (d) decoded voltage; (e) percentage error Motion Pictures Experts Group (MPEG) Compression Standards MPEG‐1 – a lossy compression system, which is capable of achieving transparent, perceptually lossless compression of stereophonic audio signals at high sampling rates. Subjective listening tests performed by the MPEG Audio Committee, under very difficult listening conditions, have shown that even with a 6‐to‐1 compression ratio, the coded and original audio signals are perceptually identical. The MPEG‐1 coding standard exploits two psychoacoustic characteristic of the auditory systems: Critical Bands Human ear – responds to incoming acoustical waves. It has three main parts: Outer ear – aids in sound collection Middle ear – provides an acoustical impedance match between the air and the cochlea fluids, thereby conveying the vibrations of the tympanic membrane (eardrum) due to incoming sounds to the inner ear in an efficient manner Inner ear – converts the mechanical vibrations from the middle ear to an electrochemical or neural signal for transmission to the brain for processing
The inner ear represents the power spectra of incoming signals on a nonlinear scale in the form of limited frequency bands called the critical bands. The audible frequency band, extending up to 20 kHz, is covered by 25 critical bands, whose individual bandwidths increase with frequency. The auditory system may be viewed as a band‐pass filter bank, consisting of 25 overlapping band‐pass filters with bandwidths less than 100 Hz for the lowest audible frequencies and up to 5 kHz for the highest audible frequencies. Auditory Masking (noise masking) – frequency‐domain phenomenon that arises when a low‐level signal (the maskee) and a high‐level signal (masker) occur simultaneously and are close enough to each other in frequency. If the low‐level signal lies below a masking threshold, it is made inaudible (masked) by the stronger signal. The auditory masking is most pronounced when both signals lie in the same critical band, and less effective when they lie in neighboring bands. MPEG Audio Coding System Transmitter Digital (PCM) Encoded bit stream audio signal Time-to- frequency Quantizer Frame-packing mapping and coder unit network Psychoacoustic model Encoded bit stream Digital (PCM) Freq-sample Frequency-to- audio signal Frame reconstruction time mapping Unpacking unit network network Receiver
Encoder Functions Time‐to‐frequency mapping network – decompose the audio input signal into multiple subbands for coding The mapping is performed in three layers, labeled I, II and III, which are of increasing complexity, delay and subjective perceptual performance. Algorithm in Layer I – uses a band‐pass filter bank that divides the audio signal into 32 constant‐width subbands; this filter bank is also found in layers II and III. The design of this filter bank is a compromise between computational efficiency and perceptual performance. Algorithm in Layer II – a simple enhancement of Layer I; it improves the compression performance by coding the data in larger groups. Algorithm in Layer III – much more refined and is designed to achieve frequency resolutions closer to the partitions between the critical bands. Psychoacoustic model – analyzes the spectral content of the audio input signal and computes the signal‐to‐mask ratio for each subband in each of the three layers. The information is, in turn, used by the quantizer‐coder to decide how to apportion the available number of bits for the quantization of the subband signals. This dynamic allocation of bits is performed so as to minimize the audibility of the quantization noise. Frame packing unit‐ assembles the quantized audio samples into a decodable bit stream.