Analytic Signals and Envelope Detection : MALMIJAL-M Blog

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Analytic Signals and Envelope Detection

Analytic signals provide a way to represent real signals using complex-valued functions that contain only positive frequency components.

Definition

Given a real signal x(t), its analytic signal is

analytic function

where x̂(t) is the Hilbert transform

Envelope(Amplitude) Extraction

The amplitude is given by

amplitude of analytic function

This represents the instantaneous amplitude.

Phase angle Extraction

The phase angle is given by

angle of analytic function

This represents the instantaneous angle.

MALMIJAL implementation

The analytic signal separates

Amplitude (envelope)
Phase (instantaneous angle)

Practical Uses

Speech analysis
AM modulation
FM modulation
Biomedical signals

AM signal and its Envelope

FM signal and its Envelope

angle of analytic function Angle

Instantaneouse Frequency

Instantaneous Frequency