Pulse Amplitude Modulation (PAM)

PAM sampling in an analog-to-digital chain

Pulse Amplitude Modulation (PAM) samples a continuous analog signal at regular instants so that its samples can enter a later digital conversion stage. The resulting sequence records the signal value at each sampling instant while retaining analog amplitude information.

In PAM, the amplitude of regularly spaced pulses is varied in direct proportion to the instantaneous values of the original analog signal. The sample sequence is discrete in time (one value is assigned to each sampling instant) but remains analog in amplitude (a pulse can have any value within the permitted range). In a physical flat-top waveform, each held sample occupies the finite pulse interval.

The PAM process: sampling

The core operation in PAM is sampling. An analog signal is measured at a constant rate, and each measurement's value is used to determine the amplitude of a corresponding pulse.

PAM sampling methods

Two standard sampling methods are used:

• Natural sampling: The top of each pulse follows the input waveform during the pulse interval. The operation is modeled by multiplying the analog signal by a periodic train of rectangular pulses. It is useful for analysis and is less common in practical sample-and-hold circuits.
• Flat-top sampling (sample-and-hold): The analog signal is sampled at one instant, and that value is held for the entire pulse duration, creating a flat top. A sample-and-hold (S and H) circuit performs this operation and supplies a stable input for quantization in the next digital-conversion stage.

PAM in a communication system

PAM is one stage in a signal-conversion and transmission chain. A typical system looks like this:

Key stages of the system

1. Low-pass (anti-aliasing) filter: Before sampling, the input signal is band-limited so that components above the usable baseband do not fold into it. This prevents a distortion called aliasing, preserving the intended baseband.
2. Sample and hold (S and H): This circuit performs flat-top sampling by capturing the analog voltage and holding it steady for one PAM pulse. The sampling rate ($f_p$) is selected using the Nyquist-Shannon theorem.
3. Receiver and reconstruction filter: The receiver recovers the PAM samples, then a low-pass reconstruction filter suppresses sampling images and restores the baseband waveform. An equalizer may compensate for the frequency response of the held rectangular pulses.

PAM in digital conversion

In an analog-to-digital chain, sampled PAM is an intermediate representation because its pulse amplitudes remain analog and are affected by noise and distortion. In high-speed links, multilevel PAM can be used directly, but the receiver must resolve the smaller distance between amplitude levels. For example, PAM-4 uses four amplitude levels and carries two bits per symbol.

In many conversion chains, PAM is the first stage of a digital representation called Pulse Code Modulation (PCM). In PCM, after the analog signal has been sampled into PAM pulses, the samples undergo quantization and coding, forming a digital bitstream. Digital regeneration can then restore logic levels along the link, while quantization introduces a controlled representation error.