Formatting and Baseband Modulation

Dr. Syed Anwar Lecture 3&4 Digital Communication Formatting

• A transformation on the message or source signal to make it compatible with digital processing.

• Source Coding – Data compression in addition to formatting

• Digital messages (0/1) transformed using pulse modulation into pulses (baseband waveforms) that can be transmitted over cables. Baseband Systems Textual Information

• Alphanumeric data encoded using one of the widely used character encoding formats (ASCII, EBCDIC)

• Character Coding – Transform text into bits.

• ASCII – 7-bit code to encode 128 characters (8-bit with parity check) Textual Information

• Textual Message --- Alphanumeric characters

• Characters --- encoded into a bit stream (baseband signal)

• Symbols --- formed by grouping k bits, resulting in a symbol alphabet M with 2k symbols.

• M-ary system --- system using a symbol set of size M, for k = 1, system is termed as binary with symbol size M = 2. Textual Encoding (Example)

• You want to transmit the word ‘UET’ using an 8- ary system,

– Encode using 7-bit ASCII, followed by an eight bit for error detection. How many bits are there in the message? – For k = 3, how many octal symbols are there in the message? – If the system were designed with 16-ary modulation, how many symbols would be needed to represent ‘UET’? Analog Information

• Sampling --- produce a discrete pulse amplitude modulated (PAM) waveform.

• Sampling Theorem – A band-limited signal having no spectral components above fm HZ, can be determined uniquely by values sampled at uniform intervals of,

– uniform sampling theorem. Nyquist Criterion

• The sampling theorem can be stated in terms of Nyquist criterion as

• The sampling rate fs =2 fm is called the Nyquist rate, – theoretically a sufficient condition for a complete analog signal reconstruction.

• Different sampling approaches, – Impulse sampling – Natural sampling – Sample-and-Hold operation Impulse sampling

• Ideal sampling with a sequence of unit impulse functions.

• The periodic train of impulse functions can be defined as,

• The analog signal is multiplied by the impulse train, using the sifting property of impulse function.

• The multiplication in time domain is converted to frequency domain using frequency convolution property. Natural Sampling

• Multiply the analog signal with a pulse train having pulses with width T and amplitude 1/T. • Equivalent to opening and closing of a switch. • The sampled signal can be expressed as,

• Natural sampling

– Top of each pulse in xs(t) retains the shape of its corresponding analog segment during the pulse interval. – Uses the frequency shifting property of Fourier transform Sample and Hold

• Convolution of sampled impulse train with a unity amplitude rectangular pulse of width Ts

• The hold operation results in attenuation of higher-frequency spectral components. • Non uniform spectral gain Aliasing

• Results from undersampling

• Aliased spectral components represent ambiguous data in the frequency band.

• Can be eliminated by employing higher sampling rate (minimum criteria = nyquist rate) Aliasing

• Aliasing eliminated using anti-aliasing filters

• Pre-filtering – the new maximum frequency of the analog signal is ’ reduced to f m, such that it is less than or equal to fs/2. • Post-filtering – Use a low pass filter on the sampled data

• Both filtering techniques results in signal information loss Transition Bandwidth

• Finite bandwidth of realisable filters for transition between passband and out-of-band attenuation.

• Narrower transition bandwidth – Filter complexity and cost • Higher sampling rate – Storage and transmission rates

• For 20% transition bandwidth for anti-aliasing filters, we have Aliasing Oversampling

• The process of analog to digital conversion with and without oversampling can be broken down into following steps

• Without oversampling

– Limit the signal bandwidth by using a high performance analog lowpass filter,

– Sample at nyquist rate for (approximately) bandlimited signal,

– Process the samples using analog-to-digital converter. Oversampling

• With Oversampling

– Use a low performance analog low pass filter to limit the bandwidth,

– The pre-filtered (approximated) bandlimited signal is sampled at (a higher) Nyquist rate,

– Samples are processed using analog-to-digital converter

– Digital samples processed using high performance digital filter to reduce the bandwidth

– Sample rate at the output of digital filter reduced in proportion to the bandwidth reduction. Analog-to-Digital

a) Analog b) PAM c) Quaitisation d)Sample and Hold Sources of Corruption

• Sampling and Quantisation

– Quantisation noise – Quantisation Saturation – Timing jitter

• Channel Effects

– Channel noise – ISI Quantisation Noise

• Approximate the analog signal with quantised samples

• Round off or truncation error

• Inversely proportional to the number of levels employed in the quantisation process. Sampling and Quantisation

• Quantiser Saturation

– The range of inputs for which the difference between input and output is small is called the operating range of the converter

– If the input exceeds this range the converter is said to be operating in saturation.

• Timing Jitter – According to sampling theory, exact reconstruction possible when the signal sampled uniformly.

– Timing jitter results in non uniform sampling, a random process Channel Effects

• Channel Noise – Thermal, interference from other users, interference from circuit switching transients – Threshold effect: Rapid degradation of output signal with channel induced errors.

• Intersymbol Interference – Band limited channels – Spreads the waveforms passing through such channels – Causes signals to overlap and hence system degradation SNR for Quantised Pulses Assignment 1

• Hand In – Before Wednesday 03-10-2012, 8:40 AM

• No late Hand In, Plagiarism

• Assignment should be handwritten