In various technical applications, like in quality control, the transfer function of a technical component or of a technical device, like an electro-acoustic device, such as an electro-acoustic transducer, must be determined as a function of frequency.
Generally, a transfer function is a mathematical representation of a relation between the input and output of a system. The transfer function is commonly used in the analysis of single-input single-output electro-acoustic device or analog electronic circuits, for instance. In its simplest form for continuous-time input signal x(t) and output y(t), the transfer function is the linear mapping of the Laplace transform of the input, X(s), to the output Y(s)):Y(s)=H(s)X(s)orH(s)=Y(s)/X(s)
where H(s) is the transfer function of a linear, time-invariant system.
In order to determine the transfer function, an appropriate input signal has to be provided to the component or device causing the component or device to respond with a response signal. If the input signal is assumed to be a pure sine, the response signal can roughly be divided into three fundamentally different portions:                a) a sine function of the same frequency as the input signal,        b) an harmonic portion (sine functions having an integral multiple of the frequency of the input signal),        c) an anharmonic portion (the remainder of the signal after subtracting components a and b).        
It is known to determine the portions a) and b) of the response signal, i.e. the sine function and the harmonic portion, by using a Fourier transform or similar mathematical algorithms. These algorithms require an input signal with a constant frequency. Thus, “stepped” sine signals are used as input signals for determining the frequency dependency of said portions of the response signal. These stepped sine signals have a constant frequency during a certain time period. Then the frequency is switched to the next frequency value to be analyzed within a short switch time (leap).
In principle, portion c) of the response signal, i.e. the anharmonic portion, can be determined by subtracting the determined signal portions a) and b) thereafter. This approach, however, involves a very high calculation effort, since also the phase positions have to be determined precisely and major errors occur when the sampling rates of the response signal are not much higher than the frequencies to be analyzed. In case of technical components which have characteristic frequencies in the transmission route, the said leaps in the input signal arising when the sine signal is switched to another frequency can, in addition, result in an excitation of these characteristic frequencies, which will then be wrongly interpreted as an anharmonic portion of the input signal.
In many cases (e.g. during acoustic measurements of loudspeakers), it is sufficient to determine the anharmonic portions within a frequency band which does not include the frequency of the input signal. An average amplitude or the energy content of the signals in said frequency band constitutes a good index of the quality of the transfer function and can easily be determined by means of known algorithms such as, for example, simple filters or a Hilbert transform etc. In this way, the calculation time can be substantially reduced.
In order to avoid the excitation of resonances in the transmission route by leaps in the input signal (at least the first and second derivations of the input signal should be continuous), it is known to use an input signal whose frequency continuously increases or decreases with time (a so called “Chirp” signal—in acoustics, a logarithmic function is often used for this purpose).
The described known approaches result in two simple methods for determining the portions, however, two different measuring operations have to be carried out. Because of applying two different measuring operations and due to the stepped signal which causes long transient times, the measuring time is extremely long.
From document WO 02/25997 A1 a method of testing an electro-acoustic device is known, wherein a test signal is supplied to the device causing the device to respond with a respond signal. The test signal is preferably a swept or a stepped sine wave signal. The respond signal is captured and analyzed for transients and information is derived from the transients that is indicative of the transients. Analyzing the respond signal involves band pass filtering in one or more distinct frequency bands, rectification of the band pass filtered signals and low pass filtering of the rectified signals. The signals thus analyzed for transients are differentiated. After differentiation the signals represent, in each frequency band, the slope or steepness of the response signal from the device under test, and are a quantitative measure of the presence of possible rub and buzz in the device under test. In quality control of e.g. speaker transducers each of these steepness signals is compared to a predefined threshold value. Only transducers with steepness values entirely below the threshold values are regarded as having passed the quality control test.
The known method, however, suffers from the drawback that the measuring time and calculation effort are extremely high and/or that only a subset of the various portions of the transfer function is determined.