Techniques for the extraction of the impulse response of a linear and time-invariant system.

Abstract

After a brief overview of the simulation of a linear and time-invariant system through the digital convolution, the paper will start with the description of the various kinds of techniques for the calculation of the impulse response (IR) of the system that has to be simulated. For each technique, and for each signal used for the extraction, we will analyze the positive and negative aspects, then the problems and the advantages that can help the choice of one signal, instead of another, for the simulation of certain kinds of systems. Starting with the IR extraction through the reproduction and recording of the Dirac δ (the impulse function), we will analyze the advantages of this simple technique, and the disadvantages connected with the impossibility of a correct reproduction of the impulse function. The second technique discussed in the paper will be the white and pink noise one: we will reflect on the computational advantages of the FFT algorithm and on the phase problems of pseudo-random noise signals. Then, we will move on to describing the Minimum Length Sequence signal (MLS), the shift register and the XOR for its generation, the extraction of the Dirac δ through the auto-correlation between the original MLS and the one passed through the system, and the problems of this technique, which are strictly linked to the linearity of the system used to measure the IR. At the end, we will talk about the sweep signal: a simple sinusoid, modulated in frequency by an exponential function, seems to be the best method for the extraction of IR from various kinds of systems. The simplicity of the inversion of the sweep signal and its independence from the non-linearities of the measuring system, make this technique the most suitable for the IR calculation of various kinds of systems. A brief example of an IR extraction from a dummy head system (Head Related Impulse Response), should then give the idea of how this technique can be used for the simulation of all kinds of systems, from the old style compressors and equalizers, to the best sounding rooms.