# Methods of Calculation for Signal Envelope

The envelope of a signal is an important concept. When a signal is modulated, meaning that information is combined with or embedded in a carrier signal, the envelope follows the shape of the signal on it’s upper and lower most edges.

There are a number of methods for calculating an envelope. When given an in-phase and quadrature signal, the envelope is defined as:

E = sqrt(I^2  + Q^2).

This envelope, if plotted will contain the exact upper or lower edge of the signal. An exact envelope may be sought, depending on the level of detail required for the application.

Here, this data was collected as a return from a fiber laser source. We seek to identify this section of the data to determine if the return signal fits the description out of a number of choices. The exact envelope using the above formula is less useful for the application.

The MATLAB formula is used to calculate the envelope:

[upI, lowI] = envelope(I,x,’peak’);

And this is plotted below with the I and Q signals: Here are two envelopes depicted without the signal shown. By selecting the range of interpolation, this envelope can be smoother. Typically it is less desirable for an envelope to contain so many carrier signals, as is the following where x=1000, the range of interpolation. Further methods involving the use of filters may also be of consideration. Below, the I and Q signals are taken through a bandpass filter (to ensure that the data is from the desired frequency range) and finally a lowpass filter is applied to the envelope to remove higher frequency oscillation. 