The blue graph shows a sine function that was created by computing the Discrete Hilbert transform of a cosine function. The cosine function was divided into 4 overlapping segments, which were individually convolved with an FIR Hilbert transform filter, and the 4 output segments were seamlessly pieced together. If the DFT of the FIR filter is replaced by the trivial samples of the DTFT of an IIR Hilbert transform filter, the cosine function segments are effectively convolved with a periodic summation of the IIR filter. That results in some frequency-dependent amplitude distortion and discontinuities at the segment boundaries. Examples of these effects are shown in the red graph.