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[link] depicts a linear system characterized by an impulse response $h\left(n\right)$ , driven by an input signal $s\left(n\right)$ , and producing the output signal $r\left(n\right)$ . The system identification problem is to estimate $h\left(n\right)$ given known input/output signals $s\left(n\right)$ and $r\left(n\right)$ . This module illustrates the swept-sine and the Golay complementary sequence techniques for identifying finite impulse responses. The firstexample measures the impulse response of a highpass filter using the Golay method, and the second example measures the impulse response ofa weakly nonlinear loudspeaker driver using the swept-sine method.
Consider the causal, single-input single-output (SISO) system shown in [link] . For simplicity, we will take the system to be linear and discrete-time, so that it is characterized by its impulseresponse $h\left(n\right)$ or equivalently its transfer function $H\left(z\right)$ , which is the $z$ transform of $h\left(n\right)$ .
We will assume that both $h\left(n\right)$ and $H\left(z\right)$ exist so that we can discuss measuring them interchangeably. We will further assume that $h\left(n\right)$ has finite length so that we can measure the response to an input signal in a finite amount of time. The goal of this document isto explain how to excite the system with a signal $s\left(n\right)$ , measure the response $r\left(n\right)$ , and use $s\left(n\right)$ and $r\left(n\right)$ to determine $h\left(n\right)$ (and equivalently $H\left(z\right)$ ). In particular, it is useful to pick a signal $s\left(n\right)$ that contains a large amount of energy so that measurement noise will not significantly corrupt the measurement results.
Sound cards and sound interfaces are not designed for making transfer function measurements. They merely provide a cost-effective solutionsince almost all computers have sound cards. We demonstrate these weaknesses given measurements made on a PreSonus Firepod soundinterface. The output from channel 1 was directly connected to the line input on channel 1, and the sampling rate was ${f}_{S}=44.1$ kHz.
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