envelope

The magnitude of a complex signal, that is, its vector length. Intuitively, the envelope is the overall shape of the amplitude maximae of the signal. For example, for a constant amplitude sine wave, the envelope is a straight line, and for a damped exponential sine wave, the envelope is the exponential function. The envelope of time domain signals can be computed by low pass filtering and curve fitting techniques, or by using the Hilbert Transform to compute the analytic signal. This means that the time domain signal now gets both a real and imaginary part (or, a sine and cosine component). Hence, it can be considered a vector. The envelope of the signal is then the length (magnitude) of that vector.

LabVIEW includes Hilbert transform capabilities to make this computation easy. Click demo for an interactive demonstration of how the Hilbert Transform can help detect hidden echoes by computing the envelope of a signal.