Modulation Third Meeting
Bandwidth • Analogue bandwidth • Sharp cut-off frequencies f1 and f2, has bandwidth f1 – f2 • Idealized spectrum is impossible to achieve in practice • The cut-off frequency has dropped to 1/√2 ≈ 0.707 of its maximum value • Digital Bandwidth • Known as the signalling rate, • Measured in baud. • One baud is one (bit) symbol per second • B Hz < S baud < 2 × B Hz Idealized frequency spectrum Typical spectrum of an analogue signal
Signal • Analogue signal • A signal that can take any value in a continuous range. • An example of an analogue signal is the temperature. • Digital signal • A signal that can only take values which are in a set of discrete values, (no intermediate values) • An example of the use of digital signals is the tone dialling. • Digital signal is not necessarily restricted to just two, ( binary values)
Regeneration of digital signals • Signals are attenuated (reduced) as they are transmitted, • but with both analogue and digital signals this can be compensated for by amplification. • Signals are also corrupted by noise when they are transmitted. • If the received signal is amplified, so is the noise. • the greater the distance between transmission and regeneration, the greater the probability of error )bit error)
Sound • Sound digitization • It is a process of digital representation of sound
Sound Digitizing • Sampling • Measuring at successive instants in time • In practice a voltage range of 256 volts for an analogue signal • A realistic range might be, say, 10 volts, from +5 volts to –5 volts. • Resolution • Using a resolution of 8 bits, • +5 volts at largest 8-bit number, • –5 volts at the smallest. • All intermediate values would be scaled appropriately, • 8 bits give 256 numbers to cover the range from +5 volts to –5 volts.
Other Definitions Quantization Interval • Quantization interval • the size of the interval between adjacent levels. • Quantization error • The difference between the actual (analogue) value of a signal and the quantization level used to represent it. • The higher the resolution, the smaller the quantization error. • The peak quantization noise • Equal to half the quantization interval. • Digital telephone system = 8-bit words • Audio compact discs = 16-bit wods. • Sampling rate • The frequency at which an analogue signal is sampled to create a digital representation. (Hz). • Alias • Alower-frequency waveform that fits the samples Sampling Rate Alias
Modulation • The modification of some property of the waveform of a signal (the carrier) • In a sinusoidal wave, the properties modified are: • amplitude, • Frequency, • phase or • a combination of these • Modulation is to make the message signal more suitable for: • transmission, • processing or • storage. • Demodulation • the process of recovering the original signal from the modulated one is called.
Amplitude modulation (a) the original sawtooth waveform; (b) the sinusoidal carrier; (c) after amplitude modulation
Frequency modulation (a) the original sawtooth waveform; (b) the sinusoidal carrier; (c) after frequency modulation
Digital signals and modulation A frequency-modulated binary signal; A phase-modulated binary signal An amplitude-modulated binary signal
Multiplexing • Combining a number of signals so that they can share a single transmission channel • Why (hint: channel capacity) • Demultiplexing • The process of extracting the individual signals from the multiplexed combination • Frequency-division multiplexing (FDM) • Different signals are transmitted using different parts of the frequency band
Time-division multiplexing (TDM) • Samples of the individual signals are transmitted in turn at regular, repeating, time slot. • What has to happen at the other end? • Synchronization
FrequencyBan medium wave band for use by European radio stations Frequency spectrum • How many frequencies can you have in one frequency band? • A frequency spectrum is the complete set of frequencies allocated to a frequency band.
Error Detection • The techniques that are used to reveal to a receiver that an error has occurred in data transmission • Parity check • Add one further bit. (example 4 bits becomes 5) • Even-paritysystem • Ensure even number of 1s in any correct code. • Thus, any received pattern with an odd number of 1s in it must be in error • Odd-parity (opposite) • Redundancy • 1100 11001100 • What combination of two errors would the receiver be unable to detect? 1 0 0 1 0 1 0 0 1 1 Is there an error?
Error correction: Hamming Code • Add three redundant bits, X, Y and Z, to each 4-bit pattern ABCD • X = even parity for BCD • Y = even parity for ACD • Z = even parity for ABD Z Y A X 2 = 0010 1 1 0 A = 0, B = 0, C = 1 D = 0 B C D
Unicode • ASCII is unable to cope with languages that use non-Latin characters, • A longer term solution is Unicode. • Unicode assigns a unique, standard character string for every character in use in the world’s major written languages. • Unicode uses 16 bits, enabling over 65,000 characters to be coded. • Has room for expansion