Modulation Third Meeting Bandwidth l Analogue bandwidth l
Modulation Third Meeting
Bandwidth l Analogue bandwidth l l Sharp cut-off frequencies f 1 and f 2, has bandwidth f 1 – f 2 Idealized spectrum is impossible to achieve in practice The cut-off frequency has dropped to 1/√ 2 ≈ 0. 707 of its maximum value Idealized frequency spectrum Digital Bandwidth l l Known as the signalling rate, Measured in baud. One baud is one (bit) symbol per second B Hz < S baud < 2 × B Hz Typical spectrum of an analogue signal
Signal l Analogue signal l A signal that can take any value in a continuous range. An example of an analogue signal is the temperature. Digital signal l 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)
Analogue and digital signals
Regeneration of digital signals l l l 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 l Sound digitization l It is a process of digital representation of sound
Sound Digitizing l Sampling l l 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 l Using a resolution of 8 bits, l l +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 l Quantization interval l l Equal to half the quantization interval. Digital telephone system = 8 -bit words Audio compact discs = 16 -bit wods. Sampling rate l l 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 l l the size of the interval between adjacent levels. Quantization error l l Quantization Interval Sampling Rate The frequency at which an analogue signal is sampled to create a digital representation. (Hz). Alias l Alower-frequency waveform that fits the samples Alias
Modulation l l The modification of some property of the waveform of a signal (the carrier) In a sinusoidal wave, the properties modified are: l amplitude, l Frequency, l phase or l a combination of these Modulation is to make the message signal more suitable for: l transmission, l processing or l storage. Demodulation l 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; An amplitude-modulated binary signal A phase-modulated binary signal
Multiplexing l l Combining a number of signals so that they can share a single transmission channel Why (hint: channel capacity) Demultiplexing l The process of extracting the individual signals from the multiplexed combination Frequency-division multiplexing (FDM) l Different signals are transmitted using different parts of the frequency band
Time-division multiplexing (TDM) l l Samples of the individual signals are transmitted in turn at regular, repeating, time slot. What has to happen at the other end? l Synchronization
Frequency spectrum l l How many frequencies can you have in one frequency band? A frequency spectrum is the complete set of frequencies allocated to a frequency band. Frequency Ban medium wave band for use by European radio stations
Error Detection l l The techniques that are used to reveal to a receiver that an error has occurred in data transmission Parity check l l Add one further bit. (example 4 bits becomes 5) Even-parity system l l Ensure even number of 1 s in any correct code. Thus, any received pattern with an odd number of 1 s in it must be in error Odd-parity (opposite) Redundancy l l 1100 What combination of two errors would the receiver be unable to detect? 10010 10011 Is there an error?
Error correction: Hamming Code l l 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 Parity check results on Error at Number A B C D 0 0 0 1 2 0 0 1 0 3 0 0 1 1 4 0 1 0 0 5 0 1 6 0 1 1 0 7 0 1 1 1 BCDX ACDY ABDZ 0 0 0 1 Z 8 1 0 0 1 0 9 1 0 0 1 1 Y A 1 0 0 X 1 0 1 B 1 1 0 C 1 1 1 D No error 2 = 0010 1 1 0 A = 0, B = 0, C = 1 D = 0
8 -bit ASCII code
Unicode l l l ASCII is unable to cope with languages that use non-Latin characters, A longer term solution is 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
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