Suppose we have a sensor that gives us a measure of some quantity such as distance. Clearly distance is unbounded, but a device that measures it might work by measuring the angle of a wheel moving along the surface. The interface of these devices are often a register giving the angle of the wheel.
The problem is that we want to use the device to measure more than the distance of one rotation ( ). To do this we want to keep a tally of how many times the wheel has turned. This is easy if the wheel only turns in one direction:
// Here we have 'value', a byte from the sensor describing its current angle static char oldvalue = 0; char dx = value - oldvalue; static int x = 0; x += dx;
We obviously need to make sure that we read the value of the sensor more often than it can turn one whole revolution, otherwise we might see 10, when actually it was 1010.
How do we deal with wheels that can go backwards as well as forwards? Handily, the same code will work if the wheel can go backwards, although lets be specific about the type of the integers:
// Here we have 'value', a byte from the sensor describing its current angle static signed char oldvalue = 0; signed char dx = value - oldvalue; static signed int x = 0; x += dx;
Again we have to worry about the sampling rate - how do we know that the wheel has turned forwards 3/4 rather than backwards 1/4? Easy, never let it be a problem. We have to make sure that the maximum distance(|value - oldvalue|) between two samples is always less than 1/2. If this is true then we know that we will never get 3/4, it always means -1/4.
Why am I calling this generalised quadrature? quadrature is the method whereby a wheel rotating can be encoded using two out of phase edge detectors. They generate a signal consisting of squarewaves which 'rotate':
This idea can be extended to an arbitrary number of squarewaves, as long as we can track the direction of rotation. sampling at more than twice maximum resolution gives us this. Hardware quadrature decoders use the edges to ensure they are always moving at or faster than 1/2 a rotation, but with a microprocessor we are better off using a repeated task. Note that there is no requirement for the samples to be done at a fixed rate, although that may be useful for the purpose the signal was generated.