MATLAB Envelope Detection: Methods and Implementation

Envelope detection is a crucial concept in signal processing, commonly used to extract signal contours or amplitude variation trends. MATLAB provides multiple methods for calculating signal envelopes, with the most frequently used approaches including the Hilbert Transform and Peak Detection techniques. Hilbert Transform Method The Hilbert transform can be used to compute the analytical signal of an input, thereby extracting its envelope. The core algorithm utilizes Fast Fourier Transform (FFT) for frequency domain processing, followed by inverse transformation to reconstruct the envelope. This method offers high computational efficiency and is particularly suitable for smooth signals. In MATLAB implementation, the hilbert() function returns the analytical signal, where the envelope can be obtained by taking the absolute value: envelope = abs(hilbert(signal)). Peak Detection Method This approach detects local maxima and minima of the signal, then uses interpolation methods (such as spline interpolation) to fit the envelope. Compared to the Hilbert transform, peak detection performs better with noisy signals but has slightly higher computational complexity. MATLAB implementation typically involves findpeaks() function for extreme value detection, followed by interp1() with 'spline' option for envelope reconstruction. Simulation Applications In practical simulations, envelope detection is widely used in modulation signal analysis, mechanical vibration monitoring, and biomedical signal processing. For example, in AM (Amplitude Modulation) signal demodulation, the original baseband signal can be recovered by extracting the envelope. MATLAB's Communications Toolbox provides built-in functions like envelope() for such applications. For simulation programs involving complex signals, it's recommended to combine filtering preprocessing to improve envelope detection accuracy. Implementation typically involves designing appropriate filters using filter design functions (butter, cheby1) before applying envelope detection algorithms to enhance robustness against noise.