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Measurement of Polarity in Band-Limited Systems
Polarity is usually measured by energizing the system under test with a wide-band asymmetrical test stimulus, such as a raised cosine pulse, and then observing the system's output on an oscillioscope. For a well-behaved flat-response minimum-phase system, such as an electronic device, the polarity determination is straightforward. However, for a general band-limited non-minimum-phase system with non-flat frequency response, such as a loudspeaker, the policy assessment can be quite difficult due to waveform distortion. A measurement method is presented that uses a narrow-band asymmetrical Hann-windowed tone burst, along with synchronous detection, to evaluate polarity at many points across a desired bandwidth. For a general system evaluated with tone bursts over a narrow frequency range, polarity is not just a simple two-valued function, but a continuum of values over the range of +/- 180 degrees, that varies with frequency. A preliminary theory is presented that allows prediction of the tone-burst phase, and hence time-constrained narrow-band polarity (herein called polarity phase), from the systems's conventional steady-state sinusoidal phase and group-delay responses.
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