Microphone Oscilloscope

Ferdinand Braun invented the cathode-ray oscilloscope in 1897, as a physics curiosity: an oscillating signal applied to the deflector plates of a phosphor-coated tube. The idea has outlived the glass tube.

Its job is easily stated. An oscilloscope is a test instrument that draws the varying voltage of a signal as a function of time, with voltage up the screen and time across it. A microphone turns sound into exactly that kind of signal, so the machine on your desk that records your voice is, in principle, one input stage away from Braun’s invention. In practice it is an odd member of the family. It tells the truth about time and shrugs when asked about volts.

What a trace keeps that a spectrum drops

Most people who look at sound on a screen look at a spectrum. A spectrum sorts a stretch of sound by frequency and reports how much of each it found. It is the right picture for questions about content: is there a whistle near 3 kHz, how fast does the treble fall away.

It is the wrong picture for questions about order. A power spectrum is the Fourier transform of a signal’s autocorrelation, which is a measure of how well the signal matches a delayed copy of itself. Both describe how strongly the sound repeats at each rate. Neither has a time axis.

A trace has nothing else. It shows the moment a note begins and how long it takes to bloom, whether the peaks are sliced flat by clipping, whether the wave leans forward or back, and whether two channels rise together or one after the other. Those are facts about when, and when is the oscilloscope’s whole subject. The two pictures answer different questions, and the trace answers the ones that a tally of frequencies cannot even pose.

Time base and trigger

Two controls turn a moving voltage into a readable picture. The first is the time base, usually written as seconds per division. A screen is expected to show ten major divisions across, so at 1 ms per division each one is worth 1 ms and the whole screen is worth 10 ms. Halve the setting and you look twice as closely at half as much.

The second control is the trigger, and it solves a problem that is easy to miss. A live signal never stops, so the screen must be redrawn many times a second. If each redraw began at a random point on the wave, the result would be a jumble. The trigger starts every sweep at the same selected point on the signal, and that is what holds a repeating waveform still. An edge trigger needs two choices. The level sets the threshold the signal must cross, and the slope says whether it must be rising or falling as it does.

Three modes decide what happens when no edge qualifies. A purely triggered sweep can leave the screen blank, so automatic mode adds a timer that fires by itself whenever no trigger arrives, and a trace is always visible. In normal mode, as this tool defines it, a sweep is drawn only on a real trigger and the last waveform stays on the screen until the next one. A single sweep is armed, takes one trigger and stops. Digital instruments add a quiet advantage. They store the signal as samples, so many of them can show the waveform from before the trigger as well as after. Put the trigger point in the middle and you see the approach and the aftermath.

Noise spoils a naive trigger. A wave that wobbles as it passes the level crosses it several times, and each crossing looks like an edge. Counter designers met this long ago. A classic application note on electronic counters explains that the input behaves like a Schmitt trigger with two thresholds, and that to register one count the signal must cross both the upper and the lower hysteresis level. Ringing between the two is ignored. Make the input too sensitive, the note adds, and noise can cause false triggering. A small band below the trigger level, which the wave must leave before it can fire again, is the same cure.

An instrument that cannot read volts

Now look at what sits behind the microphone socket. In audio recording a steady offset is a fault. It shifts the center of the waveform, so the loudest parts clip early, and audio equipment removes it with a capacitor in series with the signal or with a high-pass filter. The Linux driver for one microphone converter chip shows how low such a filter can sit. It offers four corner frequencies, quoted for a 48 kHz sample rate: 1.86, 120, 235 and 466 Hz. Even at the lowest of them, anything steady is thrown away.

An oscilloscope has the same thing as a choice, called AC coupling: set the input coupling switch to AC and a series capacitor blocks DC and low frequencies, so that only the changes are seen. On a bench instrument it is a switch. On a sound card there is no switch, and it is safest to assume the steady part is gone. The tool reports the mean of the trace as its DC reading, which shows what your own input lets through.

The vertical axis has no unit for a plainer reason. Between the sound and the number sit a microphone, a preamplifier whose gain nobody wrote down, and a converter whose full-scale voltage a web page is never told. So the honest unit is full scale itself. In dBFS, 0 is the largest value the digital system can hold and a signal at half of that reads -6. Conventions differ for averages. Some engineers use the mathematical RMS, which puts a sine 3 dB below its own peak, while the AES17 standard assigns 0 dBFS to the RMS of a full-scale sine.

The horizontal axis is far better behaved. Claude Shannon stated the rule in 1949: a function that contains no frequencies higher than W is completely determined by its values at points spaced 1/2W seconds apart. Read backwards, a stream sampled at 48 kHz can carry nothing above 24 kHz. Within that band the spacing of the samples is fixed by the converter’s clock, not by a gain knob.

Anything higher that reached the converter would reappear as a false frequency inside the band, a fault called aliasing, which is why a converter is given an anti-aliasing filter ahead of its sampler. The filter costs a little of the band. Real sound cards tend to have a smaller bandwidth than half the sample rate implies, because of their internal filtering, so the very top of the range is the part to trust least.

Drawing is a separate matter. The theorem promises that the samples determine the wave, not that straight lines between them resemble it. A rule of thumb for digital oscilloscopes asks for a sampling rate ten times the highest frequency to be resolved, which at 48 kHz puts trustworthy shapes below about 4.8 kHz. A 12 kHz tone has only four samples in each cycle, and joined by straight lines they draw a diamond where the sound was a smooth sine. Above the rule’s limit the dots are right and the lines between them are not.

One more layer sits between the hardware and a web page, and it was built for conversation. The WebRTC project’s audio processing module describes its job as applying speech enhancement effects to the microphone signal, effects it calls required for calls: echo cancellation, noise suppression and automatic gain control. Noise suppression filters out background noise and equipment hum. Automatic gain control manages volume to keep the overall level steady. For a call that is kindness. For a measurement it is vandalism, since a steady test tone looks a great deal like hum and a level that corrects itself cannot be measured.

The standard that defines microphone capture admits as much. Of noise suppression, and again of automatic gain control, it says there are cases where it is not needed and it is desirable to turn it off so that the audio is not altered. A page may ask for that, but a request is not a guarantee. The settings a track reports afterwards are the current values of every property, platform defaults included. A measuring tool should read them back and show them.

Reading frequency off a waveform

Period and frequency are reciprocals, so every frequency reading is a time reading in disguise. The oldest method uses the grid: count the divisions that one cycle spans and multiply by the time base. Cursors do the same job without counting. Two vertical lines bracket a cycle and a readout gives the time between them.

Here is a case with clean numbers. The tool on this page starts with a built-in test signal, a 1 kHz sine at half of full scale, and the microphone off. At 0.2 ms per division the screen is 2 ms wide and holds two full cycles. Switch on the cursors. They begin five divisions apart, which is 1 ms, and one divided by that time is 1 kHz. Both frequency readouts say 1,000.0 Hz and the spread between them is zero. The peak reads -6.0 dBFS and the RMS -9.0, 3 dB lower, as a sine requires.

Machines count instead. A counter measures frequency by counting cycles and dividing by the time the gate was open, and it carries a known flaw: a plus or minus one count ambiguity, because the gate and the signal are not synchronized. Counting whole cycles over a fraction of a second therefore gives a coarse answer. The remedy used here is to time each zero crossing between samples and fit a line through all of them.

The second method never looks for an edge. Slide a copy of the signal along itself and note the delay at which the two match best. Paul Boersma’s 1993 paper puts it as a definition: the best candidate for the pitch period of a sound is the position of the maximum of its autocorrelation, and the height of that maximum measures how periodic the sound is. He also showed how to undo the bias that windowing adds, after which a sine with more than three periods in the window is located to better than five parts in ten thousand.

Two methods are worth more than one because they fail differently. An extra wiggle near zero adds crossings and inflates a count. A sound with no steady pitch leaves the autocorrelation without a clear peak. When the two readings agree to a hundredth of a percent, believe them. When they part, the waveform is telling you it has no single period to report.

Two signals at right angles

Give the horizontal axis to a second signal instead of to time and the screen draws a Lissajous figure. The figure is a standard way to track the phase difference between two signals, and its shape depends on the ratio of their frequencies. Two equal tones in step draw a diagonal line.

The figures are older than the oscilloscope. Jules Lissajous published his major study in 1857, having produced the curves by bouncing light off mirrors fixed to two tuning forks that vibrated at right angles. They were visible only through persistence of vision. When the forks were slightly out of tune he saw a rotating ellipse. Nathaniel Bowditch had drawn the same curves in 1815 with a compound pendulum. The curve closes only when the ratio of the two frequencies is rational.

The test signal shows it. Its right channel is 1,500 Hz against 1,000 Hz on the left, and in X-Y mode the trace closes into a figure that touches the top edge three times and each side twice.

None of this makes a sound card a bench instrument. It cannot read volts, it cannot be trusted with DC, it knows nothing above half its sample rate, and its input is built for the small signal of a microphone or a line output, not for a circuit under test. Anyone who does record an electrical waveform through one is advised to add a protection circuit that keeps the input voltage within acceptable bounds. Treat the vertical axis as a ratio and trust the horizontal one, and it will still show you the thing a spectrum never can: what the sound did, in the order it did it.