  We derive a stronger uniqueness result if a function with compact support and
its truncated Hilbert transform are known on the same interval by using the
Sokhotski-Plemelj formulas. To find a function from its truncated Hilbert
transform, we express them in the Chebyshev polynomial series and then suggest
two methods to numerically estimate the coefficients. We present computer
simulation results to show that the extrapolative procedure numerically works
well.
