There's one thing I've been wondering for quite a while - is there such thing for smells as white noise is for sounds?
Probably not a linear equivalent in the sense that for a given time period, white noise contains all frequencies across the audible spectrum.
However, there are many situations where a complex mixture of odours exists. If you want to use such an analogy, think of the olfactory sense as a kind of tuned circuit, where sensitivity and selectivity determine whether a "signal" is received and processed or not.
In a radio receiver with poor sensitivity and selectivity ( S & S), this may equate to a distant radio station not being heard, or being lost amidst stronger signals from higher level stations, either because they are located closer, or simply because their transmission power is greater. However, a receiving circuit with good S & S may discern between the louder and fainter signals - perhaps employing some form of automatic gain control (agc) which attenuates the louder signals before processing. Thus the weaker, more distant transmission is easily heard among the louder and dominating signals, as these are more effectively filtered out.
Likewise, a human nose can be compared to a dog's nose by saying the former has poor Sensitivity ( less specific receptors in the nose), and the human brain is often unable to detect weaker signals (less selectivity). This can be thought of as being analogous to a "white noise" mixture of odours; the normal human olfactory sense lacks the ability to filter out the more dominating odours (agc of the radio circuit = neuro processing) .
Hope that doesn't sound too much of an abstract analogy?