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Angelo Farina |
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Industrial Engineering Dept., University of
Parma, Via delle Scienze 181/A |
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Parma, 43100 ITALY – HTTP://pcfarina.eng.unipr.it |
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The basis of classic MLS and new Log Sine Sweep
methods are presented |
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Theoretical analysis of both MLS and “time
reversal mirror” approaches to the determination of the transfer function
of a system |
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The choice of a special log sine sweep allows
for the symultaneous measurement of distortion and linear response of
not-linear systems |
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Avoiding any kind of averages, the log sweep
method becomes substantially immune to clock mismatch and time variance |
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We are interested in the linear impulse response
h(t). This can be estimated by the knowledge of the input signal x(t) and
of the output signal y(t). The influence of the not-linear part K and of
the noise n(t) has to be minimized. |
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X(t) is a periodic binary signal obtained with a
suitable shift-register, configured for maximum lenght of the period. |
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The re-recorded signal y(i) is cross-correlated
with the excitation signal thanks to a fast Hadamard transform. The result
is the required impulse response h(i), if the system was linear and
time-invariant |
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X(t) is a sinusoidal signal signal, the
frequencing being variable with an exponential function of time. |
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The “time reversal mirror” approach is based on
the convolution with the time-reversal of the excitation signal. If its
spectral content is not white, proper amplitude equalization is required. |
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Many harmonic orders do appear as colour stripes |
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The deconvolution is obtained by convolving the
raw response with a suitable inverse filter |
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The last peak is the linear impulse response, the
preceding ones are the harmonic distortion orders |
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The Log Sine Sweep method outperforms all other
known (TDS, MLS, etc.) |
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The implementation is simple (no specialized
software required, CoolEdit already does it) |
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Specific plugins for CoolEdit were developed for
making even simpler to generate and deconvolve the linear impulse response,
and to extract also information about harmonic distortion |
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Notes