Scaling function of generic wavelet is proposed to be the radar waveform of a radar signal. Its shows significant advantage on conventional linear frequency modulated (LFM) or chirp radar waveform in side-lobe compression. To increase the bandwidth of the radar waveform, we further propose a new radar waveform named chirp-Z, which is composed of wavelet packets. The generation of the chirp-Z signal is introduced, and the signal is compared with the chirp radar pulse with the same duration and same bandwidth chirp. The result demonstrates that chirp-Z signal has much better side-lobe suppression than the conventional chirp signal. Furthermore, due to the composition of wavelet packets in the chirp-Z signal, subband adaptation in both amplitude and phase adjustment becomes flexible in responding to the variation of environments. The latter enables powerful cognitive radar.