Deconvolution of Impulse Response from Time-Limited Input and Output: Theory and Experiment

Since it is impossible to generate and propagate an impulse, often a system is excited by a narrow time-domain pulse. The output is recorded and then a numerical deconvolution is often done to extract the impulse response of the object. Classically, the fast Fourier transform (FFT) technique has been applied with much success to the above deconvolution problem. However, when the signal-to-noise ratio becomes small, sometimes one encounters instability with the FFT approach. In this paper, the method of conjugate gradient is applied to the deconvolution problem. The problem is solved entirely in the time domain. The method converges for any initial guess in a finite number of steps. Also, for the application of the conjugate gradient method, the time samples need not be uniform, like FFT. Since, in this case, one is solving the operator equation directly, by passing the autocorrelation matrix computation, storage required is 5N as opposed to N2. Computed impulse response utilizing this technique has been presented for measured incident and scattered fields.