I have a small (1/2"sq.) thin film piezoelectric transducer that I would like to use to test the frequency response of musical instruments. I want to be able to stick it on to any instrument , send a white or pink noise signal into the film thereby exciting the instrument with all frequencies and then record the response of the instrument with a spectrum analyzer. Being a purely capacitive load (high pass filter) obviously the transducer will not supply equal drive power at all frequencies, what would be a good reliable approach to assure that I have equal drive power at all audio frequencies?
I don't think trying to get white noise out of a piezo is a good idea. Piezo transducers usually have far from flat frequency response, often with a major and a few minor resonance peaks. They can also be non-linear, meaning they can produce frequencies that they weren't driven with. Then what about the pickup? How do you know how flat that is?
I see two possibilities:
In any case, you have to calibrate the system. Assume you don't know much about the piezo and can't rely on the pickup either. Calibrate it in open air with nothing around it, with the two transducers separated about as far as the input and output of the insturment you want to measure. For example, mount them about 2 feet apart if you want to test a clarinet.
Any one impulse will have a lot of noise on it. The advantage of this system is that you can repeat impulses at a decent rate and accrue signal to noise ratio by getting lots of samples. Ambient noise will also eventually cancel the same way, since presumably it is not synchronous to your impulses.
During calibration, you essentially measure the impulse response of free air and declare that to be a flat spectrum. It will actually be quite a mess, but as long as there is enough signal to noise ratio accross the full spectrum, you use that as a baseline to compare real measurements with later. When making real measurements, you divide the spectrum you get from the received impulses by the spectrum saved from calibration. That should yield the actual transfer function of the instrument.
There are several flaws in approach. The transducer is possibly not exactly a capacitive load. The impedance will be strongly dependent on mechanics of load. So it can be a capacitor, inductor, resistor and everything in between over whole variety of frequencies. At the end it will not even be a linear object, so no complex network or R,C and L components can represent it correctly.
Another problem might be that even perfectly flat power spectrum does not define phases relations between frequencies of interest. From my limited understanding of music, the relative phases across frequencies, the changes between phases relationships (mode switches) is possibly more fast and informative than changes in amplitude. Even more, the single string oscillation is at least 3 independent oscillations in X, Y, making a Lissajous orbits and Z-mode travelling with supersonic speed end-to-end along the string. May be rotational T torsion motion is involved as well.
So simple pickup will capture only minimal information and conversion to power spectrum will represent a crude picture.
So if for instance, the design will do slow radar-like chirp, instead of white noise, ignore the innacuracy of power, but will allow to detect accurate frequency values of maximums and phase relations between peaks, then this might give more insight of how well the instrument performs.