Before revision: The relationship between coherence time and bandwidth The larger the bandwidth – range of frequencies Δf a wave contains – the faster the wave decorrelates (and hence the smaller τc is): Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum (the intensity of each frequency) to its autocorrelation.
After revision: The relationship between coherence time and bandwidth The larger the bandwidth – range of frequencies Δf a wave contains – the faster the wave decorrelates (and hence the smaller is): Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum (the intensity of each frequency) to its autocorrelation.