2.  In communication systems, the received waveform is usually categorized into the desired part containing the information and the extraneous or undesired part.  The desired part is called the signal, and  the undesired part is called noise.

3.  The waveform has significant nonzero values over a composite time interval that is finite.  There is no known waveform that has existed forever.  The spectrum of the waveform has significant values over a composite frequency interval that is finite.  All practical systems have limited bandwidth which would no allow for infinite bandwidth.

4.  The waveform is a continuous function of time.  A discontinuity in the function would require infinite bandwidth.  The waveform has finite peak values.  Any physical device would be destroyed before producing an infinite peak value.  The waveform is a Real function.  Only real waveforms have been observed in the real world.