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The causal lossy impulse response of a circular piston evaluated in the time and frequency domains for power law media

Analytical expressions for the time-domain Green's function that exactly solve the wave equation for power-law media with an attenuation term that is proportional to frequency to the power were recently derived. These analytical expressions are causal for power-law exponents less than one and noncausal for power-law exponents greater than or equal to one. A causal expression for the lossy impulse response for a circular piston is obtained for power-law exponent when the impulse response of the time-domain Rayleigh-Sommerfeld integral is evaluated by superposing the causal Green's function in space and in time. The lossy impulse response is also computed in the frequency-domain for the same piston. Numerical results are computed in the time and frequency-domains for a circular piston with a radius of 15mm. Problems with aliasing are identified in the frequency-domain impulse response calculation, whereas these problems are avoided in the time-domain calculation.