DVB-t and DVB-t2 share the same antenna, but antenna for analog tv has different considerations.
One of the main problem for analog tv is the ghost image, and it needs a much better antenna to reduce the problem, therefore the antenna is much bigger due to the need for high directivity.
My "analogue" rabbit ear telescopic antenna works perfectly, hidden inside the TV console, to receive "digital tv" signal when the elements are shortened to minimum to form a half wave dipole. Similarly, a simple folded dipole of about the same dimension sold locally since decades ago to receive Batam and Malaysian analogue tv, also works perfectly for digital tv signal. Some even managed to pull in weak digital signal from Malaysia
More directional antennae, such as Yagi, were also made long before the advent of digital tv, to overcome the problem of multipath reflections and pull in weak signal in fringe areas. The common denominator in the design of these antennae is the wavelength. For maximum efficiency, the dimensions of the antenna elements is tied to the wavelength of the frequency spectrum.
The terrestrial digital tv standards, such as T1 and T2, has been produced to take care of some issues in analogue tv transmission and reception. The end result is so good that the signal (including that for transmission) required is very much reduced compared to that of analogue tv. Furthermore, multipath and other interferences encountered in reception are also effectively eliminated by digital techniques.
Because of these measures, antennae made for digital tv reception can compromise their physical dimensions even though the signal received is not of optimum strength based on wavelength consideration. In any case, digital tv antennae based on Yagi, such as Funke YagiNX, are being sold. As it's product brochure says: "...put the performance of larger antennas in a small package..."