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We are given a linear, position-invariant image degradation system with the impulse response: \[ h(x-\alpha, y-\beta) = e^{-[(x-\alpha)^2+(y-\beta)^2]} \] and the input image is modeled as a line of infinitesimal width at \( x = a \), given by: \[ f(x, y) = \delta(x-a) \] ### Step 1: Understanding the Problem Since the system is linear and position-invariant, the output image is the convolution of the input image with the system's impulse response: \[ g(x, y) = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(\alpha, \beta) h(x-\alpha, y-\beta) \, d\alpha \, d\beta \] Since the input image is a ______ ______ _____ _________ _______ ________ _______ _____ ________ _______.
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