Baseband Signals PDF

Wireless Communication (EC43107FP) Chapter Baseband Signals 2 Learning Objectives 1. Define & compute ‘Analogue’ signal parameters:...

Wireless Communication (EC43107FP) Chapter Baseband Signals 2 Learning Objectives 1. Define & compute ‘Analogue’ signal parameters: Amplitude/Frequency/Period/Wavelength/Bandwidth 2. Define and compute ‘Digital’ signal parameters: Voltage Level/Bit Rate/Baud Rate/Bandwidth 3. Describe the conversion steps in ‘Analogue-to-Digital Conversion’: Sampling/Quantization/Encoding 4. Describe ‘ASCII’ character encoding scheme. Chapter (2) Baseband Signals - Page 1 Wireless Communication (EC43107FP) 1.0 WAVES 1.1 A ‘wave’ is an oscillation accompanied by a transfer of energy that travels through a medium. 1.2 Wavelength, ‘λ’ is the distance travelled by a wave during the time of one cycle. The standard unit for wavelength is meter (m). FIG 1: Wavelength 1.3 The Frequency ‘f’ and Wavelength ‘λ’ of a wave are related to the velocity of the wave, ‘c’ by: c=fλ 1.4 The velocity of sound waves 343.21 m/s in air and 1,484 m/s in water. 1.5 Waves are found everywhere in the natural world. Examples of waves: Sound, Light and Microwave Wave, X-Ray and etc. FIG 2 – Types of Waves 1.6 The velocity of radio waves is 3 x 108 m/s. Chapter (2) Baseband Signals - Page 2 Wireless Communication (EC43107FP) 2.0 SOUND WAVES 2.1 Sound is produced when an object vibrates and causes the air around it to move. 2.2 The frequency of the sound wave produced is equal to the rate at which the source oscillates, and is measured in Hertz (Hz or cycles per second). 2.3 Sine waves have a pure sound because they consist of energy at only one frequency, and are often called pure tones. 2.4 In real situations, most sound sources do not vibrate in a simple manner. Most real sounds are made up of combination of vibration patterns which result in a complex waveform. FIG 3 – Sound Waves 2.5 No matter how complex, sound waveforms can be broken down into a series of frequency components known as harmonics. FIG 4– Harmonics of Square Wave Chapter (2) Baseband Signals - Page 3 Wireless Communication (EC43107FP) 3.0 SIGNAL REPRESENTATION 3.1 A ‘Signal is a function that conveys information about the behaviour or attributes of some phenomenon. Example: Sound 3.2 ‘Signals’ are typically provided by a Sensor, and often the original form of a signal is converted to another form of energy using a Transducer. For example, a Microphone converts sound waves into electrical signals. 3.3 An electrical signal is often represented in a voltage-time graph. In this representation, 1 cycle of the waveform corresponds to 1 period. 3.4 Period, ‘T’ of a signal is the time taken to complete one cycle, and is related to the frequency ‘f’ by: T = 1 / f seconds (s) 3.5 While Frequency, ‘f’ of a signal is the number of complete cycles per second. It is measured in ‘Hertz’ (Hz). 3.6 A signal can be made up of a range of frequencies. Its Bandwidth, ‘BW’ is determined by the difference between the upper and lower frequency limits of the signal. BW = f2 – f1 3.7 The Peak Amplitude, ‘Vp’ is the maximum value of voltage or current that occurs in a signal. The units can be ‘volts’ or ‘amperes’. 3.8 The Peak-to-Peak Amplitude, ‘Vpp’ is the change between peaks (highest amplitude value) and trough (lowest amplitude value). 3.9 A more meaningful reference has been developed to measure the average amplitude of a wave over time, called the Root-Mean-Squared. Vms = 0.707 x Vp OR Vp = 1.414 x Vrms FIG 5: Voltage-Time Representation of Signal Chapter (2) Baseband Signals - Page 4 Wireless Communication (EC43107FP) 3.10 Different frequencies in time are represented in Fig 6. Time FIG 6: Different Frequencies 4.0 DATA LINE ENCODING 4.1 Digital information in the form of 0s and 1s, must be encoded before transmission to facilitate its transmission on the physical medium. 4.2 The common types of ‘Line Encoding’ are: Unipolar Encoding Polar Encoding Bipolar Encoding Manchester Encoding 4.3 Unipolar Encoding 4.3.1 In ‘Unipolar Encoding’, a positive voltage represents a Binary 1, and zero volts indicates a Binary 0. It is the simplest form of ‘Line Encoding’, directly encoding the bit stream. FIG 7 – Unipolar Encoding 4.3.2 Works well when the signal path (cable) is short. However, due to the presence of stray capacitance in the transmission medium (cable), it may charge up leading to Residual DC problems. Hence, it is unsuitable for long distance transmission. 4.3.3 It can also face synchronization problems between the Transmitter and Receiver's Clock oscillator if there is a long series of logical 1s or 0s in a row. FIG 8 – Long Series of ‘1’ or ‘0’ Chapter (2) Baseband Signals - Page 5 Wireless Communication (EC43107FP) 4.4 Polar (NRZ) Encoding 4.4.1 The digital encoding is symmetrical around 0 Volts. The signal does not return to zero; it is either a positive voltage or a negative voltage. 4.4.2 Polar line encoding is also called ‘None Return To Zero’ (NRZ). FIG 9 – Polar Encoding 4.4.3 The ‘RS-232D’ interface uses ‘Polar’ line encoding. 4.4.4 ‘Polar’ line encoding is the simplest pattern that eliminates most of the Residual DC problem of ‘Unipolar’ encoding. 4.4.5 ‘Polar’ encoding has an added benefit in that it reduces the power required to transmit the signal by one-half. 4.4.6 ‘Polar’ and ‘Unipolar’ line encoding both share the same synchronization problem: if there is a long string of logical 1s or 0s, the receive oscillator may drift and become unsynchronized. 4.5 Bipolar (AMI) Encoding 4.5.1 ‘Bipolar’ line encoding has 3 voltage levels. A low or ‘0’ is represented by a 0 Volt level, and a high or ‘1’ is represented by alternating polarity pulses. 4.5.2 ‘Bipolar’ line encoding is also called Alternate Mark Inversion (AMI). 4.5.3 By alternating the polarity of the pulses for ‘1’s, the Residual DC component cancels. FIG 10 - Bipolar Line Encoding 4.5.4 Synchronization of receive and transmit clocks is greatly improved except if there is a long string of ‘0’s transmitted. Chapter (2) Baseband Signals - Page 6 Wireless Communication (EC43107FP) 4.6 Manchester Line Encoding 4.6.1 In ‘Manchester’ line encoding, there is a transition at the middle of each bit period. 4.6.2 The mid-bit transition serves as a clocking mechanism (and also as data): a low to high transition represents a ‘1’ and a high to low transition represents a ‘0’. FIG 11 – Manchester Encoding 4.6.3 ‘Manchester’ line encoding has no DC component and there is always a transition available for synchronizing receive and transmit clocks. 4.6.4 It has the added benefit of requiring the least amount of bandwidth compared to the other line encoding. 5.0 DIGITAL TRANSMISSION RATE 5.1 Bit Rate 5.1.1 ‘Bit Rate’ is the number of bits transmitted during one second. 5.1.2 It refers to the speed with which information is transferred and is measured in bits/sec (bps). 5.2 Baud Rate 5.2.1 ‘Baud Rate’ refers to the number of signal units per second that are required to represent those bits. 5.2.2 If the voltage used to represent signal has only two values, e.g. +5V and -5V, then Baud Rate is the same as Bit Rate. (i.e. only two possible state: 0, 1) 5.2.3 If the voltage used to represent signal has more values, e.g. 0V, 1V, 2V, …. ,7V, then each value of the voltage can represent 3 bits, then ‘Bit Rate’ value will be 3 times of ‘Baud Rate’. 5.2.4 The total number of outputs signaling states (L) depends on the number of bits represented by each signal element. It can be determined by the formula: L =2n 5.2.5 The ‘Baud Rate’ determines the ‘Bandwidth’ required to send the signal. Chapter (2) Baseband Signals - Page 7 Wireless Communication (EC43107FP) Bits (n) Levels (L) Codes 1 2 0,1 2 4 00,01,10,11 (Represent: 0V, 1V, 2V, 3V ) 3 8 000,001,010,011,100,101,110,111 4 16 0000,0001,0010,0011,0100,0101,0110,0111,1000,...,1111 5 32 00000,... ,11111 FIG 12 – Output Signalling States and No. of Bits 5.3 Bit Rate & Baud Rate Calculations 5.3.1 Bit Rate = Baud Rate * Number of Bits per Signal Element 5.3.2 Baud Rate = Bit Rate / Number of Bits per Signal Element 5.3.3 Example #1 An Analog signal carries 4 bits in each signal element. If 1000 signal element are sent per second, find the ‘Baud Rate’ and the ‘Bit Rate’. Solution Baud Rate = Number of Signal Elements = 1000 bauds per second Bit Rate = Baud Rate * Number of Bits per Signal Element = 1000 * 4 = 4000 bps 5.3.4 Example #2 The ‘Bit Rate’ of a signal is 3000. If each signal element carries 6 bits, what is the ‘Baud Rate? Solution Baud Rate = Bit Rate / Number of Bits per Signal Element = 3000 / 6 = 500 baud per second Chapter (2) Baseband Signals - Page 8 Wireless Communication (EC43107FP) 6.0 CHARACTER ENCODING SCHEMES 6.1 The ‘American Standard Code for Information Interchange’ (ASCII) became the first widespread encoding scheme. 6.2 ASCII is limited to only 128 characters definitions. Which is only sufficient for the most common English characters, numbers and punctuation. Hence many other different encoding schemes emerged. 6.3 ‘Unicode’ standard was created to unify all the different encoding schemes so that the confusion between computers can be limited as much as possible. 6.4 Unicode standard defines values for over 100,000 characters. FIG 13– ASCII Table Chapter (2) Baseband Signals - Page 9  Wireless Communication (EC43107FP) 7.0 PULSE CODE MODULATION (PCM) 7.1 ‘Pulse Code Modulation’ (PCM) technology is a means by which analogue audio signals (which are represented by waveforms) are converted to digital audio signals (which are represented by 1's and 0's - much like computer data) with no compression. FIG 14 – Pulse Code Modulation 7.2 This allows the recording of a musical performance, or movie soundtrack in digital form, which can be fit in a small space, while still approaching the quality of the original performance. 7.3 Analogue to PCM conversion is done through the following 3 steps. Sampling Quantization Encoding 7.4 Sampling 7.4.1 In order to ‘capture’ analogue sound using PCM, specific points on the sound wave must be ‘Sampled’. 7.4.2 In Telephony, voice signal is encoded at 8,000 analogue samples per second, of 8 bits each, giving a 64kbps digital signal. 7.4.3 In CD Audio, music is encoded at 44,100 analogue samples per second (or 44.1 kHz), with points that are 16 bits in size (depth). In other words, the digital audio standard for CD audio is 44.1 kHz/16-bits. FIG 15 - Sampling 7.4.4 The ‘Sampling Rate’ must be adequate to capture a sufficient number of samples to represent the analogue signal. 7.4.5 Otherwise, the high frequency information in the analogue signal cannot be retained (lost). Chapter (2) Baseband Signals - Page 10 Wireless Communication (EC43107FP) FIG 16 – Insufficient Sampling - Lost of High Frequency Information 7.4.6 Otherwise, the high frequency information in the analogue signal cannot be retained (lost). 7.4.7 The minimum sampling frequency required for reliable reproduction of the modulating signal can be obtained using ‘Sampling Theorem’. 7.4.8 ‘Sampling Theorem’ states that: ‘Sampling Frequency’ (fs) in any pulse modulation system must be more than twice the highest signal frequency (fm) for all the information contained in the original signal to be transferred.’ fs > 2 fm 7.4.9 The ‘Sampling Rate’ at a frequency equal to twice the highest signal frequency is known as the ‘Nyquist Rate’ fs = 2 fm 7.4.10 According to the ‘Nyquist Criterion’, the sampling frequency (fs), must be at least twice the maximum frequency component in the signal or else a phenomenon known as ‘Aliasing’ occurs. 7.4.11 In an under-sampled case, the result is an aliased signal that appears to be at a lower frequency than the actual signal. FIG 17 – Under Sampling – Aliasing Chapter (2) Baseband Signals - Page 11 Wireless Communication (EC43107FP) Example 1: Calculate the minimum sampling rate for signals in the telephone channel with a bandwidth of 300 Hz to 3.4 kHz. Solution 1: Sampling rate must be more than 3.4 kHz × 2 = 6.8 kHz Minimum sampling rate is > 6.8 kHz Actual sampling rate is 8 kHz. Example 2: A modulating signal has frequency components 30 Hz, 50 Hz, 100 Hz, 200 Hz, 1 kHz and 1.4 kHz. Calculate the bandwidth and minimum sampling rate. Solution 2: Bandwidth = Highest Frequency – Lowest Frequency Bandwidth = 1.4 kHz – 30 Hz = 1370 Hz Minimum sampling rate > 2 x 1.4 kHz > 2.8 kHz Example 3: A signal varies from 15 Hz to 8 kHz is to be processed via a pulse modulation system. Determine the minimum sampling rate that will allow adequate reproduction at the receiver. Solution 3: Minimum sampling rate > 2 x 8 kHz > 16 kHz Chapter (2) Baseband Signals - Page 12  Wireless Communication (EC43107FP) 7.5 Quantization 7.5.1 Next, the voltage amplitude of each sample is converted to the nearest standard amplitude, called the ‘Quantum Level’. 7.5.2 This process is known as ‘Quantization’ and is equivalent to ‘rounding off’ in mathematics. FIG 18 - Quantization 7.6 Encoding 7.6.1 The final step is to code each discrete amplitude value into binary digital form using a ‘PCM Encoder’ circuit. 7.6.2 In general, the no. of quantum levels = 2n (where n = no. of bits). Hence, 8 quantum levels must be represented by 3-bit binary code. Level Code 0V 000 1V 001 2V 010 3V 011 4V 100 5V 101 6V 110 7V 111 FIG 19 – Encoding Chapter (2) Baseband Signals - Page 13 Wireless Communication (EC43107FP) 7.7 Quantization Noise 7.7.1 Some of the sampling points are not at a quantum level. In those instances, the sample amplitudes are represented by the nearest quantum level. Example: Refer to FIG 2 Amplitude of Sampling Point # 6 is about 7.3V is quantized to level 7. Amplitude of Sampling Point # 10 is about 4.6V is quantized to level 5. 7.7.2 The difference between sampling point amplitudes and quantum levels is a distortion called ‘Quantization Noise’. 7.7.3 ‘Quantization Noise’ is random as the difference between any quantum level and the amplitude of the signal at any instant is unpredictable. 7.7.4 The ‘Maximum Quantization Noise’ is equal to half the separation (step) size. 7.7.5 The step size can be calculated by. Vmax − Vmin = No of levels − 1 V −V = max n min 2 −1 7.7.6 ‘Quantization Noise’ can be reduced by reducing the step size. This in turn implies increasing the number of quantization levels. 7.7.7 However, increasing the number of quantization levels requires the use of more bits for the encoding. This has the disadvantage of increasing the transmission bandwidth requirement. 7.7.8 Therefore, a compromise must be made between an acceptable transmission bandwidth and an acceptable quantization noise. 7.8 PCM Calculation Example 1: The quantum levels in a PCM system are 0.1V, 0.2V, 0.3V and 0.4V. Calculate the quantization noise when the sampling voltage is 0.16V. Solution 1: Nearest quantum level is 0.2 V Quantization noise = 0.2 – 0.16 = 0.04 V Chapter (2) Baseband Signals - Page 14 Wireless Communication (EC43107FP) Example 2: If the number of quantum levels is doubled, calculate the quantization noise when the sampling voltage is 0.16 V. Solution 2: Nearest quantum level is 0.15 V Quantization noise = 0.16 – 0.15 V = 0.01 V Chapter (2) Baseband Signals - Page 15 Wireless Communication (EC43107FP) Tutorial #2 1 Define the following terms: (a) Frequency (b) Wavelength (c) Period 2 The wavelength of a radio frequency signal is 3m. Determine its: (a) Frequency (b) Period 3 A radio signal has a frequency of 88MHz. Determine its (a) Wavelength (b) Period 4 Complete the table shown below using the waveforms shown. Wave Characteristic Waveform Waveform A Waveform B (a) Louder (b) Higher Pitch (c) Softer (d) Lower Pitch Waveform C Waveform D 5 State four common types of ‘Line Encoding’. 6 Draw the ‘Manchester’ Line Encoder Output for the data ‘1011’ 1 0 1 1 INPUT DATA ENCODER OUTPUT 7 Define ‘Baud Rate’. Chapter (2) Baseband Signals - Page 16 Wireless Communication (EC43107FP) 8 An Analogue Signals caries 8 bits in each signal element. If 1000 signal elements are sent per second, determine its ‘Baud Rate’ and ‘Bit Rate’. 9 The ‘Bit Rate’ of a signal is 2000bps. If 500 signal elements are sent per second, calculate the number of bits in each signal element. (4 bits) 10 Determine the ‘Baud Rate’ of a data communication network that has a data transmission rate of 64kbps with each signal element carrying 8 bits (8k baud per sec) 11 State the three steps involved in ‘Pulse Code Modulation’ (PCM). 12 Explain ‘Quantization Noise’ in a PCM system. 13 How can ‘Quantization Noise’ be reduced in a PCM system? 14 A PCM system has 4 quantum levels at 1V, 1.5V, 2V and 2.5V. a) How many bits does the PCM system use? b) A sample has amplitude of 1.8V. Calculate the quantization noise. What is the corresponding code for this sample? c) What is the largest quantization noise possible in the system? d) If 5-bit codes are used, how many quantum levels are there? Chapter (2) Baseband Signals - Page 17