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.
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
where x̂(t) is the Hilbert transform
Envelope(Amplitude) Extraction
The amplitude is given by
This represents the instantaneous amplitude.
Phase angle Extraction
The phase angle is given by
This represents the instantaneous angle.
MALMIJAL implementation
The analytic signal separates
Practical Uses
Instantaneous Frequency
Suggested Further Reading