Acoustic noise reduction through pulse sequence design: timings, eddy-currents, fMRI

Background and Methods: Guided by both spring and string ideas [1-3], we have previously investigated the manner in which sets of vibrational frequencies can be canceled by the appropriately designed gradient pulse. A picture of the cancellation of vibrations produced with a Lorentz impulsive force by an “anti-impulsive” follow-up force has emerged. This also provided a physical understanding of the oscillatory behavior observed in [4, 5] and showed the utility of studying the dominant frequencies in a string model [6] of the gradient system. The method suggests that properly designed sets of timings for the gradient pulse sequence can be used to attenuate important contributions to the acoustic spectrum. Successive convolutions of boxcars lead to a pattern of additional zeros in the frequency spectrum [3, 7]. With the appropriate timings, a boxcar can kill one frequency (and its harmonics), a trapezoid can kill two different frequencies, and the convolution of each additional boxcar with the original pulse can be used to cancel out one more frequency. The output acoustic power spectrum is P(ω) = | X(ω)H(ω)| , which shows a direct relation between the output acoustic noise power spectrum and the gradient pulse spectrum.