Find the FWHM of the cascade system

In practice the spatial resolution in a clinical nuclear medicine image is determined by three factors: the intrinsic resolution of the camera (I), the collimator resolution (C), and patient effects (P). Suppose the impulse response could be modeled as arising from the cascade of three linear shift-invariant systems, one for each factor.

(a) Suppose each system has an impulse response given by a rect function, and suppose their widths are rI, rc, and rp, respectively. Find the FWHM of the cascade system.

(b) Suppose each system has an impulse response given by a Gaussian, and suppose their standard deviations are σI, σc, and σp, respectively. Find the FWHM of the cascade system

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