In practice, it is not possible to perturb a system with a perfect impulse. One can use a brief pulse as a first approximation. Limitations of this approach include the duration of the pulse and its magnitude. The response can be close, compared to the ideal case, provided the pulse is short enough. Additionally, in many systems, a pulse of large intensity may drive the system into the nonlinear regime. Other methods exist to construct an impulse response. The impulse response can be calculated from the input and output of a system driven with a pseudo-random sequence, such as
maximum length sequences. Another approach is to take a sine sweep measurement and process the result to get the impulse response.
Loudspeakers Impulse response
loudspeaker testing was first developed in the 1970s. Loudspeakers suffer from phase inaccuracy (delayed frequencies) which can be caused by passive
crossovers, resonance, cone momentum, the internal volume, and vibrating enclosure panels. The impulse response can be used to indicate when such inaccuracies can be improved by different materials, enclosures or crossovers. Loudspeakers have a physical limit to their power output, thus the input amplitude must be limited to maintain linearity. This limitation led to the use of inputs like
maximum length sequences in obtaining the impulse response.
Electronic processing Impulse response analysis is a major facet of
radar,
ultrasound imaging, and many areas of
digital signal processing. An interesting example is found in
broadband internet connections.
Digital subscriber line service providers use
adaptive equalization to compensate for signal distortion and interference from using copper phone lines for transmission.
Control systems In
control theory the impulse response is the response of a system to a
Dirac delta input. This proves useful in the analysis of
dynamic systems; the
Laplace transform of the delta function is 1, so the impulse response is equivalent to the
inverse Laplace transform of the system's
transfer function.
Acoustic and audio applications In acoustic and audio settings, impulse responses can be used to capture the acoustic characteristics of many things. The reverb at a location, the
body of an instrument, certain analog audio equipment, and
amplifiers are all emulated by impulse responses. The impulse is convolved with a dry signal in
software, often to create the effect of a physical recording. Various packages containing impulse responses from specific locations are available online.
Economics In
economics, and especially in contemporary
macroeconomic modeling, impulse response functions are used to describe how the economy reacts over time to
exogenous impulses, which economists usually call
shocks, and are often modeled in the context of a
vector autoregression. Impulses that are often treated as exogenous from a macroeconomic point of view include changes in
government spending,
tax rates, and other
fiscal policy parameters; changes in the
monetary base or other
monetary policy parameters; changes in
productivity or other
technological parameters; and changes in
preferences, such as the degree of
impatience. Impulse response functions describe the reaction of
endogenous macroeconomic variables such as
output,
consumption,
investment, and
employment at the time of the shock and over subsequent points in time. Recently, asymmetric impulse response functions have been suggested in the literature that separate the impact of a positive shock from a negative one. ==See also==