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Syllabus: Digital Communications: PCM, DPCM, digital modulation schemes (ASK, PSK, FSK, QAM), bandwidth, inter-symbol interference, MAP, ML detection, matched filter receiver, SNR and BER.
8 hand-picked visual resources on this topic, 4 of them little-known gems — under each card, look for See it. Every link is checked against the live site before it ships.
Sampling, quantisation and PCM
Quantisation noise is the price of digitising, and it falls 6 dB for every extra bit. The rest of PCM is bookkeeping: bits per sample at samples per second.
Nyquist; below this, aliasing folds to
Where marks are lost
-law/A-law companding does not reduce the noise power — it makes the SQNR roughly constant across signal levels, which is a different and better thing for speech.
Matched filter and optimum detection
The matched filter maximises SNR at the sampling instant, and that maximum depends only on the pulse energy, not its shape. ML detection picks the nearest signal point when priors are equal; MAP weights by the priors.
ISI and Nyquist pulse shaping
A channel of finite bandwidth smears each symbol into its neighbours. The Nyquist criterion says zero ISI needs a pulse that is zero at every other sampling instant; the raised cosine achieves it with a roll-off that costs excess bandwidth.
Digital modulation and bit error rate
Memorise the BER table — it is worth a mark nearly every year. Coherent BPSK and QPSK have the same BER per bit; QPSK simply carries twice the bits in the same bandwidth.
DPCM and delta modulation
Successive speech or video samples are strongly correlated, so encoding the prediction error instead of the sample needs fewer bits for the same quality. DPCM does that with a multi-bit quantiser; delta modulation is the one-bit limit of the same idea, which is why it needs a much higher sampling rate.
uniform quantiser noise power
for a full-scale sinusoid
delta modulation
lets a band-limited signal be sampled well below
impulse response is the time-reversed pulse
independent of pulse shape
reduces to ML for equiprobable symbols
binary, equiprobable — the master formula
= symbol rate; is the ideal brick wall
M-ary: more bits per symbol, narrower bandwidth
unrealisable, and very sensitive to timing error
an eye diagram's vertical opening is noise margin, its width timing margin
See it
— the best of the binary schemes
3 dB worse than BPSK
Non-coherent FSK is
conversions the paper expects you to know
Where marks are lost
Bit error rate and symbol error rate differ for M-ary schemes. With Gray coding, — read which one the question asks for.
See it
the predictor runs on the quantised history at both ends
prediction gain; each 6 dB of it saves one bit per sample
a staircase that follows the signal
the step cannot keep up — distortion on fast transitions
the staircase hunting about a slowly varying signal
the only way to fix both at once, since trades one against the other
Where marks are lost
Increasing cures slope overload and worsens granular noise; decreasing it does the reverse. Any DM question asking for an "optimum" step size is asking where those two curves cross.