Ableton's Echo device includes a Character tab that lets you introduce the kind of analog imperfections associated with vintage tape delay hardware. The Noise parameter adds background hiss to the output signal, and the Morph control shapes the character of that noise.
Wobble works in a related but distinct way: increasing its value introduces subtle fluctuations in delay speed, which cause slight pitch instability in the repeated signal. Both Noise and Wobble have their own Morph parameter for reshaping how each imperfection behaves.