Time transient scattering field dur to a line source located at the center of the dielectric cylinder has been calculated. In the analysis, the corresponding time harmonic result has been formulated first rigorously, then the high frequency asymptotic expansion result has been derived. Thus obtained result is found to coincide wiht the one constructed directly by ray approximation. Fourier invesion for an impulsive response has been done by two methods, namely the Singularity Expansion Method and wavefront expansion method. While the former method collects the contributions around the singularities in the complex frequency domain, the latter gives us a result which is a summation of each successive wavefront arrivals. A finite Hilbert transform technique has been introduced to recover the causal responses of odd-time caustic passing wavefronts. Also derived are results of numerical inversion by Fast Fourier Transform Technique for the frequency band limited incident pulses. A Gaussian pulse has been introduced to simulate an impulse response result, and a raised cosine pulse which de-emphasizes the low frequency defects of asymptotically constructed frequency spectrum confirms the usefulness of ray solution.