Module 14-pulse Code Modulation
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Have you ever wonder how signals travel in a telephone line?
1
MODULE 14
PULSE CODE MODULATION
Prepared by: Engr. Jo-Ann C. Viñas 2
OBJECTIVES:
1. 2. 3. 4.
Discuss the concept of digital transmission Review the Pulse Modulation Theory and the parameters of PCM Discuss the process of producing PCM Apply sampling theorem and quantization to the PCM process
3
DIGITAL TRANSMISSION
– is the transmission of digital signals between the transmitter and receivers and requires physical transmission medium such as cable, fiber optic , etc.
4
DIGITAL TRANSMISSION
Transmission Medium
Digital Information
Digital Information Transmitter Wire, cable, fiber optic, etc
Receiver
DAC
ADC
Analog Information
ADC – Analog to Digital Converter DAC – Digital to Analog Converter
Analog Information
DIGITAL TRANSMISSION ADVANTAGES
1. 2. 3. 4.
Noise immunity Better suited to processing and multiplexing Uses signal regeneration than signal amplification Simpler to measure and evaluate
6
DIGITAL TRANSMISSION DISADVANTAGES
1. 2. 3. 4.
Requires more bandwidth Need for additional encoding and decoding circuitry Requires precise time synchronization between transmitter and receiver Incompatible with existing analog facilities
7
PULSE MODULATION
- The process sampling an analog information signals and then converting those samples into discrete pulses and transporting the pulses from a source to a destination over a physical medium.
PULSE MODULATION
- The process of using some characteristic of a pulse (amplitude, width, position) to carry an analog signal.
1. PULSE AMPLITUDE MODULATION
- Amplitude of the modulating signal changes the amplitude of the pulses (information)
10
STEP 1: PAM PROCESS
Signals to be Mixed
pulse train
modulating signal
11
STEP 2: PAM PROCESS
Pulse Amplitude Modulation
pulse AM signal
modulating signal
12
2.
PULSE WIDTH MODULATION
- A process where the pulse width of a fixed amplitude pulse varies proportionally to the amplitude of the analog signal.
FIGURE 2: PWM SIGNAL
time
3.
PULSE POSITION MODULATION
- A form of pulse modulation where the position of a constant width pulse within a prescribed timeslot is varied according to the amplitude of the modulating signal
15
FIGURE 3: PPM SIGNAL
4.
PULSE CODE MODULATION
- The process of transmitting analog information in digital form, which involves sampling the analog signal and converting the sampled to a digital number
17
PULSE MODULATION
WHERE: • Analog Signal • Sample Pulse • PWM • PPM • PAM • PCM
18
SIMPLEX PCM TRANSMISSION
19
PCM TRANSMIT BLOCKS
20
PCM DECODER
STEPS TO PRODUCE PCM
1. 2. 3.
Sampling Quantizing Encoding
22
BANDLIMITING
- The anti-alias or bandpass filter limits the frequency of the input analog signal to the standard voice frequency band of 0 to 4 kHz. PURPOSE: is to eliminate any unwanted signal that will result to aliasing or fold over distortion at the receiver.
23
1. SAMPLING
- The act of periodically holding a value (sample) of the continually changing analog input signals.
24
TYPES OF SAMPLING
1. Natural Sampling (Gating) 2. Flat-Top Sampling
25
A.
NATURAL SAMPLING (Gating)
The natural sampling method retains the natural shape of the sample analog waveform
26
FIGURE 4: NATURAL SAMPLING
27
B.
FLAT-TOP SAMPLING
The most common method used for sampling voice signals in PCM where the sample-and-hold circuit convert those samples to a series of constant-amplitude PAM levels.
28
FIGURE 5: FLAT-TOP SAMPLING
29
FIGURE 6: SAMPLE AND HOLD CIRCUIT
30
FIGURE 7: INPUT AND OUTPUT WAVEFORMS OF SAMPLE AND HOLD CIRCUIT
31
EXAMPLE
For the sample and hold circuit, determine the largest value capacitor that can be used. Use an output impedance for Z1 of 10 Ω , an on resistance for Q1 of 10 Ω , an acquisition time of 10 µ sec, a maximum peak to peak input voltage of 10V, a maximum output current from Z1 of 10mA, and an accuracy of 1%.
32
NYQUIST SAMPLING THEOREM
- States that for a sample to be reproduced accurately at the receiver, the sampling frequency must be at least twice of the highest modulating signal.
fs ≥ 2 f m where: fm= highest modulating signal fs = sampling frequency 34
FIGURE 8: OUTPUT SPECTRUM OF SAMPLE AND HOLD CIRCUIT
35
3-BIT PCM CODE
36
SIGN MAGNITUDE CODES
The codes currently used for PCM, where MSB is the sign bit and the remaining bits are used for magnitude
37
FOLDED BINARY CODE
- The codes on the bottom half of the table are a mirror image of the codes in the top half, except for the sign bit.
38
3-BIT PCM CODE
39
QUANTIZATION INTERVAL
- the magnitude difference between steps
40
FIGURE 9
where: a.
Analog input signal
c.
PAM
b.
Sample pulse
d.
PCM
41
FIGURE 10
where: a.
Analog input signal
b.
Sample pulse
c.
PAM signal
42
EXAMPLE
For a sample rate of 20 kHz, determine the maximum analog input frequency.
43
EXAMPLE
Determine the alias frequency for a 14 kHz sample rate and an analog input frequency of 8 kHz.
44
2. QUANTIZATION
- The process of assigning discrete level to time-varying quantity in multiples of some fixed unit, at a specified instant or specified repetition rate. - Is the process of approximating sample levels into their closest fixed value
45
QUANTIZING BY USING SIGN AND MAGNITUDE
46
QUANTIZATION ERROR/NOISE
- The quantized levels are those fixed levels that are the nearest to f(s) at the point the sample is taken.
47
QUANTIZATION ERROR
Qe =
Vmin 2
Resolution Qe = 2
48
LINEAR INPUT VS.OUTPUT TRANSFER
49
RESOLUTION
- The magnitude of a quantum. - It is equal to the voltage of the least significant bit(Vlsb ) of the PCM code.
Resolution =
Vmax 2n
50
DYNAMIC RANGE
- The ratio of the largest possible magnitude to the smallest possible magnitude (other than 0V) that can be decoded by the digital-to-analog converter in the receiver.
DR = Vmax / Vmin DR = 2n -1 51
EXAMPLE
Determine the Dynamic range for a 10-bit sign-magnitude PCM code.
52
EXAMPLE
For a resolution of 0.04V, determine the voltages for the following linear seven-bit sign magnitude PCM codes: a) b) c) d) e)
0110101 0000011 1000001 0111111 1000000
53
EXAMPLE
For the following resolutions, determine the range of the eight-bitsign-magnitude PCM codes: Code 10111000 00111000 10011100 00011100 00110101 11100000 00000111
Resolution 0.1 0.1 0.05 0.05 0.02 0.02 0.02
54
EXAMPLE
Determine the minimum number of bits required for PCM codes with the following dynamic ranges and determine the coding efficiencies: a. DR = 24 dB b. DR = 48 dB c. DR = 72 dB
55
CODING EFFICIENCY
- A numerical indication of how efficiently a PCM code is utilized. -
The ratio of the minimum number of bits required to achieve a certain dynamic range to the actual number of PCM bits used.
η
β =
β
Where min
X 100 % max
β min = min # of bits (including the sign bit) β max = actual # of bits (including the sign bit) 56
EXAMPLE
Determine the number of bits required ina PCM code for a dynamic range of 80 dB. What is the coding efficiency?
57
3. ENCODING
- The process of converting the quantized discrete-signal (PAM samples) to parallel PCM codes.
58
FROM ANALOG SIGNAL TO PCM DIGITAL CODE
59
SIGNAL-TO-QUANTIZATION NOISE
SQR(dB)
2 V /R = 10 log (q2/12)/R
Where: R = resistance V = rms voltage q = quantization interval
60
EXAMPLE
Determine SQR for a 2Vrms signal and a quantization interval of 0.2V.
61
EXAMPLE
Determine the SQR for the following input signal and quantization noise magnitudes: Vs 1 Vrms 2 Vrms 3 Vrms 4 Vrms
Vn(V) 0.01 0.02 0.01 0.2 62
LINEAR PCM CODES
- the magnitude change between any two successive steps is uniform
63
FIGURE 11: LINEAR PCM CODES
64
NON LINEAR PCM CODES
-
the step size increases with the amplitude of the input signal
65
FIGURE 12: NONLINEAR PCM CODES
66
LINEAR VERSUS NON LINEAR PCM CODES
67
MIDTREAD QUANTIZATION
- the first quantization interval is made larger in amplitude than the rest of the steps.
68
MIDRISE QUANTIZATION
- the lowest-magnitude positive and negative have the same voltage range as all the other codes
69
IDLE CHANNEL NOISE
70
MASTERY EXERCISE
1. 2. 3. 4. 5. 6. 7.
What are the different types of pulse modulation? What is the significance of the Nyquist Sampling rate? What type of modulation is effectively used by sampling method? Describe the difference between natural and flat-top sampling. Why is the used of a sample-and-hold circuit desirable? Define the process of quantization. What is quantization noise?
71
MASTERY EXERCISE
8. 9.
What are the functional sections of a PCM modulator? What PCM functions does an analog-to-digital converter perform? 10. Why is a sample-and-hold circuit required in the PCM decoder?
72
SEATWORK
1. Determine the Nyquist sampling rate for the following maximum analog input frequencies: a) b) c) d)
2kHz 5kHz 12kHz 20kHz
73
SEATWORK
2. Determine the alias frequency for the following Nyquist sample rate: fa(kHz) 3 5 6 5
fs(kHz)
4 8 8 7 74
SEATWORK
3. For the sample and hold circuit, determine the largest value of the capacitor that can be used for the following parameters: Z1 output impedance = 15ohms, an on resistance of Q1 of 15 ohms, an acquisition time of 12 microseconds, a maximum output current from Z1 of 10mA, an accuracy of 0.1%, and a maximum change in voltage in dv = 10V.
75
SIMPLEX PCM TRANSMISSION
ANALOG INPUT SIGNAL
BANDPASS BANDPASS FILTER FILTER
SERIAL PCM CODE
SAMPLE SAMPLE AND AND HOLDCIRCUIT CIRCUIT HOLD
ANALOG-TOANALOG-TODIGITAL DIGITAL CONVERTER CONVERTER
PARALLEL-TOPARALLEL-TOSERIAL SERIAL CONVERTER CONVERTER
SAMPLE PULSE
CONVERSION CLOCK
LINE SPEED CLOCK
REGENERATIVE REGENERATIVE REPEATER REPEATER
REGENERATIVE REGENERATIVE REPEATER REPEATER
SERIAL PCM CODE
PARALLEL DATA SERIAL-TOSERIAL-TOPARALLEL PARALLEL CONVERTER CONVERTER
DIGITAL-TODIGITAL-TOANALOG ANALOG CONVERTER CONVERTER
LINE SPEED CLOCK
CONVERSION CLOCK
HOLDCIRCUIT CIRCUIT HOLD
LOWPASS LOWPASS FILTER FILTER
ANALOG OUTPUT SIGNAL
FIGURE 8: OUTPUT SPECTRUM OF SAMPLE AND HOLD CIRCUIT 2fs - fa fs + fa
fs - fa
3fs - fa 2fs + fa
3fs + fa
AUDIO fs
0
2fs
3fs
frequency
SHADED AREAS INDICATE SPECTRAL FOLDOVER fs - fa
0
fs + fa
2fs + fa
2fs - fa 3fs - fa fs 2fs 3fs
4fs - fa
3fs + fa
frequency
1
MODULE 14
PULSE CODE MODULATION
Prepared by: Engr. Jo-Ann C. Viñas 2
OBJECTIVES:
1. 2. 3. 4.
Discuss the concept of digital transmission Review the Pulse Modulation Theory and the parameters of PCM Discuss the process of producing PCM Apply sampling theorem and quantization to the PCM process
3
DIGITAL TRANSMISSION
– is the transmission of digital signals between the transmitter and receivers and requires physical transmission medium such as cable, fiber optic , etc.
4
DIGITAL TRANSMISSION
Transmission Medium
Digital Information
Digital Information Transmitter Wire, cable, fiber optic, etc
Receiver
DAC
ADC
Analog Information
ADC – Analog to Digital Converter DAC – Digital to Analog Converter
Analog Information
DIGITAL TRANSMISSION ADVANTAGES
1. 2. 3. 4.
Noise immunity Better suited to processing and multiplexing Uses signal regeneration than signal amplification Simpler to measure and evaluate
6
DIGITAL TRANSMISSION DISADVANTAGES
1. 2. 3. 4.
Requires more bandwidth Need for additional encoding and decoding circuitry Requires precise time synchronization between transmitter and receiver Incompatible with existing analog facilities
7
PULSE MODULATION
- The process sampling an analog information signals and then converting those samples into discrete pulses and transporting the pulses from a source to a destination over a physical medium.
PULSE MODULATION
- The process of using some characteristic of a pulse (amplitude, width, position) to carry an analog signal.
1. PULSE AMPLITUDE MODULATION
- Amplitude of the modulating signal changes the amplitude of the pulses (information)
10
STEP 1: PAM PROCESS
Signals to be Mixed
pulse train
modulating signal
11
STEP 2: PAM PROCESS
Pulse Amplitude Modulation
pulse AM signal
modulating signal
12
2.
PULSE WIDTH MODULATION
- A process where the pulse width of a fixed amplitude pulse varies proportionally to the amplitude of the analog signal.
FIGURE 2: PWM SIGNAL
time
3.
PULSE POSITION MODULATION
- A form of pulse modulation where the position of a constant width pulse within a prescribed timeslot is varied according to the amplitude of the modulating signal
15
FIGURE 3: PPM SIGNAL
4.
PULSE CODE MODULATION
- The process of transmitting analog information in digital form, which involves sampling the analog signal and converting the sampled to a digital number
17
PULSE MODULATION
WHERE: • Analog Signal • Sample Pulse • PWM • PPM • PAM • PCM
18
SIMPLEX PCM TRANSMISSION
19
PCM TRANSMIT BLOCKS
20
PCM DECODER
STEPS TO PRODUCE PCM
1. 2. 3.
Sampling Quantizing Encoding
22
BANDLIMITING
- The anti-alias or bandpass filter limits the frequency of the input analog signal to the standard voice frequency band of 0 to 4 kHz. PURPOSE: is to eliminate any unwanted signal that will result to aliasing or fold over distortion at the receiver.
23
1. SAMPLING
- The act of periodically holding a value (sample) of the continually changing analog input signals.
24
TYPES OF SAMPLING
1. Natural Sampling (Gating) 2. Flat-Top Sampling
25
A.
NATURAL SAMPLING (Gating)
The natural sampling method retains the natural shape of the sample analog waveform
26
FIGURE 4: NATURAL SAMPLING
27
B.
FLAT-TOP SAMPLING
The most common method used for sampling voice signals in PCM where the sample-and-hold circuit convert those samples to a series of constant-amplitude PAM levels.
28
FIGURE 5: FLAT-TOP SAMPLING
29
FIGURE 6: SAMPLE AND HOLD CIRCUIT
30
FIGURE 7: INPUT AND OUTPUT WAVEFORMS OF SAMPLE AND HOLD CIRCUIT
31
EXAMPLE
For the sample and hold circuit, determine the largest value capacitor that can be used. Use an output impedance for Z1 of 10 Ω , an on resistance for Q1 of 10 Ω , an acquisition time of 10 µ sec, a maximum peak to peak input voltage of 10V, a maximum output current from Z1 of 10mA, and an accuracy of 1%.
32
NYQUIST SAMPLING THEOREM
- States that for a sample to be reproduced accurately at the receiver, the sampling frequency must be at least twice of the highest modulating signal.
fs ≥ 2 f m where: fm= highest modulating signal fs = sampling frequency 34
FIGURE 8: OUTPUT SPECTRUM OF SAMPLE AND HOLD CIRCUIT
35
3-BIT PCM CODE
36
SIGN MAGNITUDE CODES
The codes currently used for PCM, where MSB is the sign bit and the remaining bits are used for magnitude
37
FOLDED BINARY CODE
- The codes on the bottom half of the table are a mirror image of the codes in the top half, except for the sign bit.
38
3-BIT PCM CODE
39
QUANTIZATION INTERVAL
- the magnitude difference between steps
40
FIGURE 9
where: a.
Analog input signal
c.
PAM
b.
Sample pulse
d.
PCM
41
FIGURE 10
where: a.
Analog input signal
b.
Sample pulse
c.
PAM signal
42
EXAMPLE
For a sample rate of 20 kHz, determine the maximum analog input frequency.
43
EXAMPLE
Determine the alias frequency for a 14 kHz sample rate and an analog input frequency of 8 kHz.
44
2. QUANTIZATION
- The process of assigning discrete level to time-varying quantity in multiples of some fixed unit, at a specified instant or specified repetition rate. - Is the process of approximating sample levels into their closest fixed value
45
QUANTIZING BY USING SIGN AND MAGNITUDE
46
QUANTIZATION ERROR/NOISE
- The quantized levels are those fixed levels that are the nearest to f(s) at the point the sample is taken.
47
QUANTIZATION ERROR
Qe =
Vmin 2
Resolution Qe = 2
48
LINEAR INPUT VS.OUTPUT TRANSFER
49
RESOLUTION
- The magnitude of a quantum. - It is equal to the voltage of the least significant bit(Vlsb ) of the PCM code.
Resolution =
Vmax 2n
50
DYNAMIC RANGE
- The ratio of the largest possible magnitude to the smallest possible magnitude (other than 0V) that can be decoded by the digital-to-analog converter in the receiver.
DR = Vmax / Vmin DR = 2n -1 51
EXAMPLE
Determine the Dynamic range for a 10-bit sign-magnitude PCM code.
52
EXAMPLE
For a resolution of 0.04V, determine the voltages for the following linear seven-bit sign magnitude PCM codes: a) b) c) d) e)
0110101 0000011 1000001 0111111 1000000
53
EXAMPLE
For the following resolutions, determine the range of the eight-bitsign-magnitude PCM codes: Code 10111000 00111000 10011100 00011100 00110101 11100000 00000111
Resolution 0.1 0.1 0.05 0.05 0.02 0.02 0.02
54
EXAMPLE
Determine the minimum number of bits required for PCM codes with the following dynamic ranges and determine the coding efficiencies: a. DR = 24 dB b. DR = 48 dB c. DR = 72 dB
55
CODING EFFICIENCY
- A numerical indication of how efficiently a PCM code is utilized. -
The ratio of the minimum number of bits required to achieve a certain dynamic range to the actual number of PCM bits used.
η
β =
β
Where min
X 100 % max
β min = min # of bits (including the sign bit) β max = actual # of bits (including the sign bit) 56
EXAMPLE
Determine the number of bits required ina PCM code for a dynamic range of 80 dB. What is the coding efficiency?
57
3. ENCODING
- The process of converting the quantized discrete-signal (PAM samples) to parallel PCM codes.
58
FROM ANALOG SIGNAL TO PCM DIGITAL CODE
59
SIGNAL-TO-QUANTIZATION NOISE
SQR(dB)
2 V /R = 10 log (q2/12)/R
Where: R = resistance V = rms voltage q = quantization interval
60
EXAMPLE
Determine SQR for a 2Vrms signal and a quantization interval of 0.2V.
61
EXAMPLE
Determine the SQR for the following input signal and quantization noise magnitudes: Vs 1 Vrms 2 Vrms 3 Vrms 4 Vrms
Vn(V) 0.01 0.02 0.01 0.2 62
LINEAR PCM CODES
- the magnitude change between any two successive steps is uniform
63
FIGURE 11: LINEAR PCM CODES
64
NON LINEAR PCM CODES
-
the step size increases with the amplitude of the input signal
65
FIGURE 12: NONLINEAR PCM CODES
66
LINEAR VERSUS NON LINEAR PCM CODES
67
MIDTREAD QUANTIZATION
- the first quantization interval is made larger in amplitude than the rest of the steps.
68
MIDRISE QUANTIZATION
- the lowest-magnitude positive and negative have the same voltage range as all the other codes
69
IDLE CHANNEL NOISE
70
MASTERY EXERCISE
1. 2. 3. 4. 5. 6. 7.
What are the different types of pulse modulation? What is the significance of the Nyquist Sampling rate? What type of modulation is effectively used by sampling method? Describe the difference between natural and flat-top sampling. Why is the used of a sample-and-hold circuit desirable? Define the process of quantization. What is quantization noise?
71
MASTERY EXERCISE
8. 9.
What are the functional sections of a PCM modulator? What PCM functions does an analog-to-digital converter perform? 10. Why is a sample-and-hold circuit required in the PCM decoder?
72
SEATWORK
1. Determine the Nyquist sampling rate for the following maximum analog input frequencies: a) b) c) d)
2kHz 5kHz 12kHz 20kHz
73
SEATWORK
2. Determine the alias frequency for the following Nyquist sample rate: fa(kHz) 3 5 6 5
fs(kHz)
4 8 8 7 74
SEATWORK
3. For the sample and hold circuit, determine the largest value of the capacitor that can be used for the following parameters: Z1 output impedance = 15ohms, an on resistance of Q1 of 15 ohms, an acquisition time of 12 microseconds, a maximum output current from Z1 of 10mA, an accuracy of 0.1%, and a maximum change in voltage in dv = 10V.
75
SIMPLEX PCM TRANSMISSION
ANALOG INPUT SIGNAL
BANDPASS BANDPASS FILTER FILTER
SERIAL PCM CODE
SAMPLE SAMPLE AND AND HOLDCIRCUIT CIRCUIT HOLD
ANALOG-TOANALOG-TODIGITAL DIGITAL CONVERTER CONVERTER
PARALLEL-TOPARALLEL-TOSERIAL SERIAL CONVERTER CONVERTER
SAMPLE PULSE
CONVERSION CLOCK
LINE SPEED CLOCK
REGENERATIVE REGENERATIVE REPEATER REPEATER
REGENERATIVE REGENERATIVE REPEATER REPEATER
SERIAL PCM CODE
PARALLEL DATA SERIAL-TOSERIAL-TOPARALLEL PARALLEL CONVERTER CONVERTER
DIGITAL-TODIGITAL-TOANALOG ANALOG CONVERTER CONVERTER
LINE SPEED CLOCK
CONVERSION CLOCK
HOLDCIRCUIT CIRCUIT HOLD
LOWPASS LOWPASS FILTER FILTER
ANALOG OUTPUT SIGNAL
FIGURE 8: OUTPUT SPECTRUM OF SAMPLE AND HOLD CIRCUIT 2fs - fa fs + fa
fs - fa
3fs - fa 2fs + fa
3fs + fa
AUDIO fs
0
2fs
3fs
frequency
SHADED AREAS INDICATE SPECTRAL FOLDOVER fs - fa
0
fs + fa
2fs + fa
2fs - fa 3fs - fa fs 2fs 3fs
4fs - fa
3fs + fa
frequency
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