Cognitive radar (CR) has recently been considered as a natural next step for traditional radar. The cognitive property assumes both transmitter and receiver to be able to dynamically adapt to environment changes. In this work, we propose to exploit sub-Nyquist sampling methods that have been originally proposed to reduce the sampling rate bottleneck at the receiver. For CR, we extend this approach by only transmitting the spectral bands that are to be sampled and processed on the receiver side. By considering transmitted and received pulses with dynamic support composed of several narrow bands, we pave the way to sub-Nyquist CR. Both software and hardware simulations demonstrate dynamic transmitted signal support, still allowing for delay-Doppler recovery.