In this study, we present two practical applications of the deconvolution of time series in Fourier space. First, we reconstruct a filtered input signal of sound cards that has been heavily distorted by a built-in high-pass filter using a software approach. Using deconvolution, we can partially bypass the filter and extend the dynamic frequency range by two orders of magnitude. Second, we construct required input signals for a mechanical shaker in order to obtain arbitrary acceleration waveforms, referred to as feedforward control. For both situations, experimental and theoretical approaches are discussed to determine the system-dependent frequency response. Moreover, for the shaker, we propose a simple feedback loop as an extension to the feedforward control in order to handle nonlinearities of the system.
References
Same problems remain in the deconvolution by matrix inversion.
We used the common definition in systems engineering where the associated Fourier transform is defined by . The physics literature mostly uses the opposite sign convention for Fourier transforms.
The associated amplifier PA100E from the company was replaced to achieve a better signal to noise ratio of 100 dB and an extended bandwidth of 5 Hz up to 50 kHz.