When Is Envelope Detection Possible? AM, PAM, and DSB-SC Explained

Carrier Sign Problem in Modulation

The carrier sign problem means that an envelope detector cannot determine whether the message signal is positive or negative because it only detects signal magnitude.

Envelope detectors measure amplitude but cannot detect phase inversion.

1. DSB-SC (Double Sideband Suppressed Carrier)

The transmitted signal is:

s(t) = m(t) cos(ω_ct)

Where:

• m(t) = message signal
• cos(ω_ct) = carrier signal

Case 1: m(t) > 0

s(t) = +m(t) cos(ω_ct)

Case 2: m(t) < 0

s(t) = -m(t) cos(ω_ct)

When the message becomes negative, the carrier is flipped by 180° phase.

However, the envelope detector only follows the amplitude and produces:

|m(t)|

Therefore the original message cannot be recovered correctly. This is called the carrier sign problem.

Conclusion: Envelope detection is not practical for DSB-SC. Coherent detection must be used instead.

2. AM (Amplitude Modulation)

The AM signal is:

s(t) = [A + m(t)] cos(ω_ct)

Here a large carrier component A is transmitted along with the message.

Since A + m(t) always stays positive (when modulation index < 1), the envelope exactly follows the message signal.

Thus the envelope detector can correctly recover the original signal.

Conclusion: Envelope detection is practical and widely used in AM receivers.

3. PAM (Pulse Amplitude Modulation)

In Pulse Amplitude Modulation, the signal consists of pulses whose amplitudes follow the message signal.

Each pulse height is proportional to the instantaneous value of the message signal m(t).

By detecting the pulse peaks or envelope and passing the signal through a low-pass filter, the original message can be reconstructed.

Conclusion: Envelope or peak detection is practical for PAM.

Comparison

Modulation Type	Envelope Detection	Reason
DSB-SC	Not Practical	Envelope gives |m(t)| and loses sign information
AM	Practical	Carrier ensures envelope follows A + m(t)
PAM	Practical	Pulse amplitude directly represents the message signal