User:Chendy/Log-Swept Sine Chirps Measurements

=Characterising using Log-Swept Sine Chirps Measurements=

Motavation
We wish to find the transfer function of the device under test (DUT). The Transfer Function of the DUT is the Laplace transform (or Z transform) of the Impulse response of the DUT.
 * Any system in a large class known as linear, time-invariant (LTI) is completely characterized by its impulse response!


 * frequency response

= Issues =
 * Log-sine chirp
 * naturally useful pink spectrum,
 * unusual ability to separate non-linear (distortion) responses from the linear response [1,2].


 * Variable speed chirp
 * can reproduce an arbitrary target spectrum, whilst maintaining a low crest factor.1

Because Log-sine chirp and variable speed chirps signals mimic sines that are swept in time, they are known generically as swept sine chirps.


 * When generating pink spectra, these signals posses crest factors more than 6dB better than maximum-length sequence.1
 * log-sine chirp separates distortion products from the linear response, enabling distortion-free impulse response measurements,
 * variable speed chirp offers flexibility because its frequency content can be customized while still maintaining a low crest factor.

Low Crest Factor
 * A signal with a low crest factor contains greater energy than a high crest factor signal with the same peak amplitude, so a low crest factor is desirable.

MLS
 * Maximum-length sequence (MLS) theoretically fits the bill because it has a mathematical crest factor of 0dB, the lowest crest factor possible. However, in practice, the sharp transitions and bandwidth-limited reproduction of the signal result in a crest factor of about 8dB (Fig. 1a). Filtering MLS to obtain a more useful pink spectrum further increases the crest factor to 11-12dB.

Noise Noise is even worse. Gaussian noise has a crest factor of about 12dB (white spectrum), which increases to 14dB when pink-filtered.1

On the other hand, log-sine chirp has a measured crest factor of just 4dB (Fig. 1b), and has a naturally pink spectrum. The crest factor of variable speed chirp is similarly low, measuring 5dB for a pink target spectrum. These crest factors are 6-8dB better than that of pink-filtered MLS. That is, MLS needs to be played more than twice as loud as these chirps, or averaged more than four times as long at the same volume, for the same signal-to-noise ratio.


 * stimulus signal
 * provides energy throughout the frequency range of interest
 * choice of stimulus signal has important implications
 * signal-to-noise ratio  (SNR),
 * distortion
 * speed of the audio measurements

Matlab

 * Creating Input Signals for Estimation
 * A Practical Application of New Features of the System Identification Toolbox