SUMMARYBandwidth efficiency of all digital modulations is associated closely with baseband pulse shaping waveforms (PSW's) before carrier modulation. Traditional PSW designing approaches usually work in a way such that the design of PSW's in the time domain hardly reveals a direct connection with their spectral characteristics. In other words, designing process of the PSW's offers too little degree-of-freedom to control spectral properties of the resultant signals. This paper will present a methodology, based on which several new PSW synthesising approaches, including time-domain convolution (TDC), steepest sidelobe roll-off (SSR) and zero-point insertion (ZPI) methods, will be proposed to design different PSW's with controllable spectral characteristics, such as sidelobe roll-off rate, main lobe width and null positions in their power spectral density functions. In particular, the SSR and ZPI methods are based on a truncated cosine function series, which can be further generalised to use other seed functions. The results show that the approaches can help us to generate a PSW database containing a wide collection of promising PSW's to suit for diverse wireless applications, such as traditional digital modems as well as emerging ultra-wideband systems.