AVERAGER THEORY:
WAVEFORM AVERAGER THEORY:Real-world signals are often contaminated with noise, which is any unwanted component of a more-or-less random nature. Often the noise component may be much larger than the desired signal, completely obscuring it when the waveform is viewed. Waveform averaging is a way to extract the desired signal from a noisy background. Of course, if there is a way to reduce the noise directly, that is usually (but not always!) a better approach.
INTERFERENCE:In addition to random noise, there may be other unwanted signals of a more periodic nature, known as interference. The most common interference source is the 60 Hz power line in the US (or 50 Hz in many other countries). There may also be interference due to harmonic multiples of this generated by fluorescent lights, motors, and so forth. Spurious signals may arise from nearby radio transmitters as well. These are all best dealt with by arranging to reduce them directly wherever this is feasible, either by avoidance (like using incandescent lighting near the experiment and removing appliances from the area) or by shielding out radio frequencies with a metal cage around the experiment. In addition, careful attention must be paid to equipment grounding and isolation.Beyond direct reduction, interference may also be reduced by many of the same techniques used for random noise. We will thus lump them together for discussion, noting any differences where appropriate.
NOISE:Noise is typically due to many simultaneous uncorrelated processes acting at once, each adding a small component to the whole. In mechanical systems, small thermal motions due to absolute temperature may mask the ability to resolve a desired motion. In acoustics, random motion of air molecules driven by temperature or turbulent air flow may impinge on a microphone diaphragm and generate noise. In electronic circuits, random thermal motion of charged particles in semiconductors and resistors causes noise currents to flow. In biological systems, there is always a level of background activity due to the many neurons or muscle cells that are always firing even when not specifically stimulated.Often, if you look at a fine enough scale, you can find that the noise is made up of components that would look periodic if seen in isolation, and it is only the summation of many of these in an unsynchronized fashion that gives the overall random nature. This is like the difference between hitting one note on a piano, versus having a whole roomful of pianos with squirrels scurrying along the keyboards. Electronic filters are one common approach to noise rejection, often used in combination with other methods. If you know that the signal of interest has a limited range of frequency components, you may be able to use filters to reduce all other frequencies that are only contributing to the noise, but not to the signal. For example, in biological recordings of neural signals, you might use a filter that reduces all components below 300 Hz and above 3000 Hz if you know that the neural signal that you want is strongest around 1000 Hz. This same filter might be inappropriate for recording heart rate, since at 60 beats per minute the fundamental rate would be only 1 Hz, which would be blocked by the filter. CAUTION: Do not connect any electrical equipment to a living subject without proper signal isolation techniques. A lethal shock could result. However, as well as removing unwanted components, filters may modify the shape of the desired signal through the process of phase shift. This phenomenon is where different frequency components of the signal are delayed by different amounts as they pass through the filter. All else being equal, filters with sharper transitions (cut-offs) between accepted and rejected frequency regions have more severe phase shift. Also, you can't use filters to reduce noise in the same frequency region as the signal.
WAVEFORM AVERAGING:This takes advantage of the fact that random noise is just that: Random. So if we can arrange to repeat our desired signal over and over, we expect that the noise components will be different on each repetition, while the signal remains the same. If we can synchronize the waveform display to the signal we will see (if the noise is not TOO large) our desired signal waveform... but it will be boiling and churning due to the noise, as though drawn with fat, fuzzy lines. What we would really like to see is a thin line that goes through the middle of the fuzzy line... the average value.The averager does just this. It averages the waveform on a point-by-point basis, and displays the average value at each point. The more repetitions (or "sweeps") that are averaged together, the closer the final waveform will get to the true noise-free waveform. This "synchronous" or "coherent" averaging should not be confused with "smoothing", which provides cosmetic improvement in a display but does not reveal the true underlying waveform. In fact, smoothing destroys detail and transient signal peaks because it does not distinguish between true signal and random noise.
EXPERIMENT:
Now, in the Virtual Source menu, raise the Noise level up to half of full scale and observe the waveform grow fuzzier. Use CTRL-A to go to the Averager menu and set:
One thing you will notice is that most of the improvement due to averaging comes at the start. In fact, the reduction is proportional to the square root of the number of sweeps, so in order to reduce the noise by half, you need to quadruple the sweeps. That is one reason why Daqarta offers only power-of-two sweep selections: You would be hard-pressed to see any difference between, say, 100 and 128 sweeps, whereas this way it is easy to double or halve the reqested sweeps by simple scrolling. The diminishing benefits put a practical limit on averaging, since you eventually get to a point where you can't wait around for twice as long just to get the noise reduced by another 30%. (0.707 is the square root of 2.) Even if you are willing to go eat lunch while the averager runs, you may be limited by the experiment itself: Conditions may deteriorate, a subject may get fidgety, or the phenomenon being studied may not persist. Averaging is very often the only technique available for extracting a signal that is buried in noise. Averaging makes it possible to record from simple scalp electrodes and see the tiny neural potentials evoked by an acoustic click or tone burst stimulus, where without averaging you would see nothing but noise. The source of the potentials, deep in the brain, must compete with all the other brain activity. But the other activity that is unrelated to the auditory response slowly averages out to zero, and only the auditory evoked potential remains. This allows hearing tests to be given to infants or animals who could not otherwise "raise one finger/paw if you can hear this tone". CAUTION: Do not connect any electrical equipment to a living subject without proper signal isolation techniques. A lethal shock could result.
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