Hilbert Transform Explained: From Theory to Application : MALMIJAL-M Blog

Signal Processing Concepts and Engineering Insights.

Explore signal processing concepts, algorithm comparisons, and practical engineering insights.
Topics include FFT vs STFT, FRF analysis, filtering techniques, and other signal processing methods used in real engineering workflows.

Blog

Hilbert Transform Explained: From Theory to Application

The Hilbert transform is a powerful tool used to construct the analytic signal and extract envelope and phase information.

Mathematical Definition

The Hilbert transform of x(t) is

In the frequency domain

Key Property

Keeps magnitude unchanged
Positive frequencies are shifted by −90°
Negative frequencies are shifted by +90°
Hilbert transform acts as a 90-degree phase shifter for each frequency component

Analytic Signal

analytic function This allows extraction of

Amplitude
Instantaneous phase

Applications

AM demodulation
Envelope(amplitude) detection
Instantaneous frequency estimation

AM signal and its Envelope curve AM signal and its Envelope

instantaneous frequency estimation of up-chirp signal

Key Insight

Hilbert Transform converts a real signal into a complex analytic signal. This enables Amplitude, Phase, Frequency to be defined instantaneously.

Signal Processing Concepts and Engineering Insights.

Category

Signal FundamentalsHilbert Transform Explained: From Theory to Application

Hilbert Transform Explained: From Theory to Application

Mathematical Definition

Analytic Signal

Applications

Key Insight

Suggested Further Reading