1. An acoustic field control system comprising: a sound source; speakers; and a signal processing apparatus that processes audio signals input from the sound source, the signal processing apparatus coupled between the sound source and the speakers and comprising a signal processor configured to: a compute, from the input audio signals for a plurality of channels, a first correlation coefficient representing a level of correlation among the input audio signals for the plurality of channels; derive, from the first correlation coefficient, a second correlation coefficient, a value of the second correlation coefficient varying over time more gradually than a value of the first correlation coefficient over time, such that a slope of the second correlation coefficient over time is smoother than a slope of the first correlation coefficient over time; and extract, from the input audio signals for the plurality of channels, a correlation component that is common in the input audio signals for the plurality of channels by using the second correlation coefficient, to produce output audio signals for the plurality of channels in which the correlation components has been reduced compared to the input audio signals for the plurality of channels, the output audio signals being supplied to the speakers, wherein the signal processor converts each of the input audio signals into a signal consisting of a real part and an imaginary part, computes the first correlation coefficient based on the signal consisting of the real part and the imaginary part, computes a square value of a vector corresponding to each of the input audio signals, the computes a specific correlation coefficient by which a value of the imaginary part in a first power is weighted, based on a value of the first power obtained by summing the square values computed and a value of an inner product of the vector, further computes a value of a second power by weighting the value of the imaginary part in the first power by using the specific correlation coefficient, and then computes the first correlation coefficient based on the value of the second power and the value of the inner product, and extracts the correlation component from the input audio signals by multiplying the second correlation coefficient, but not the first correlation coefficient, by a sum of the vectors corresponding to each of the input audio signals.