The approximate backscattered impulse response waveforms of perfectly conducting periodic deformed cylinders for both parallel and perpendicular polarizations are analyzed by a Fourier synthesis technique, in which we use the band-limited scattering data calculated by the mode-matching method. The normalized approximate impulse response waveforms from the nonconvex body become more complicated than those from the convex body, and directly reflect the surface character of the scatterer. In fact, we observe three kinds of specular-type reflections and the reflected creeping waves from concave-to-convex transitions on the shadowed part of the surface in addition to the conventional creeping wave for the perpendicular polarization. The high-frequency spectral contributions in the numerical results can be interpreted by the physical optics method. They contain both contributions from the complex stationary points with real parts located near the (nonspecular) concave-to-convex inflection points and from the conventional stationary points on the illuminated part of the surface.