Hello all:
I have a random signal whose time domain is from 0s to 0.01s. I hope to simplify this signal so that it has the following two characteristics:
1. a infinite time domain
2. a certain funtion which could express this signal
Therefore, I wonder if I could approximate the random signal to the superposition of harmonic signals.
Any information will be appreciated!
From your description, I suppose you know the random signal value (denoted by r(t)) within the time interval from 0 to T=0.01 seconds, but don't know (or, do not care) the signal value outside this interval. In order to approximate this signal as a superposition of harmonic signals, you may try the following.
1) Define a signal s(t) which is equal to r(t) within the interval from 0 to T, but is zero outside this interval.
2) Define a signal x(t) which is a sum of s(t-kT), where k is integers from minus infinity to infinity.
In this way, x(t) is an infinitely long periodic signal with its value same as the random signal r(t) within the interval from 0 to T, and, it can be expressed as a superposition of harmonic signals since x(t) is periodic.
Hope it helps. Good luck.
Through practical experiments, it showed that the duration or time period of random waves must be known, therefore, a frequency spectrum analyzer and its type RSA61016A can be used to detect and isolate the received signals, especially when using sensors of type Lo Ra , and the amount of frequency used in the frequency spectrum analyzer must be Include the frequency the sensor is operating on.