Analog Data, Digital Signal

Pulse code modulation relies on the following result.

Sampling Theorem. A signal can be reconstructed from a sample taken at

The conversion has three stages

The quantization of the PAM pulse introduces quantization error, not allowing the recovery of the original pulse.
A reduction in the signal distortion can be obtained by adding bits. The quantizing noise satisfies S/N = 6n + 1.8 dB.
A reduction in the signal distortion can be obtained by nonuniform quantization which is finer at low amplitudes.
For voice signals, nonlinear encoding improved the PCM S/N ratio by 24-30 dB.

signal	bandwidth	no of samples per second	bits per code	rate in bits	rate in Hz
voice	4 kHz	8000	7	8000 × 7 = 56 kbps	28 kHz
color TV	4.6 MHz		10	92 Mbps

Digital techniques are getting popular due to

Use of repeaters, instead of amplifiers, implying no additive noise.
Use of time-division multiplexing, instead of frequency-division multiplexing, implying no intermodulation noise.
Availability of efficient digital switching techniques.
Development of more efficient coding techniques. For instance, taking into account that large portions remain unchanged between consecutive video frames.

The time and amplitude axes are quantized
A staircase function approximation is derived, going up when the approximation is below the signal and going down otherwise.
The output modulation signal represents upward stair by 1 and downward stair by 0.
The receiver may use smoothing algorithm when reconstructing the input signal.
Finer division on time slot provides better approximation with the cost of extra data.
Finer amplitude division reduces the quantizing noise for small slops. Coarser amplitude division reduces the slope-overload noise for high slops.
DM is easier than PCM to implement, but it exhibits worse signal to noise ratio for the same data rate.