Doppler shift in time domain?
The term Doppler Shift is actually a bit of a misnomer. The frequencies are not actually shifted but they are scaled (see http://fourier.eng.hmc.edu/e101/lectures/handout3/node2.html for definition of shifting vs. scaling). It's a relative change not an absolute one. 

Both time and frequency domains are scaled: when the source is moving towards you, the time axis compresses and the frequency axis expands. If the source is moving a away from you the time axis expands and the frequency axis compresses. 

Let's look at a simple example. A car is 100m away from you and moves at a speed of 20m/s towards you. We assume speed of sound to 100 m/s (it's actually 344 m/s but I'm too lazy to do the math that way). Let's now assume that the car honks its horn for 1 second at a frequency of 1 kHz. So the honk consists of 1000 wiggles of air molecules. Let's call the start of the honk time t = 0.

At the beginning of the honk, the car is 100m away so the beginning of the honk arrives at your ear at time t = 1s. It takes one second for the sound to travel 100m. By the end of the honk the car has traveled 20m so it's only 80m away. The end of the honk arrives at time t = 1.8s. The sound only takes 0.8s to travel 80m.

The honk at the listening location is only 0.8s long, so the time has been compressed. It's still 1000 wiggles but they happen in less time. So the frequency is now 1000 wiggles/0.8s = 1250 Hz. The frequency is higher so the frequency axis has expanded. 

It's important to note the frequency doesn't go up by a constant shift frequency but by a multiplicative factor. If the honk would have been 2 kHz the resulting Doppler frequency would be 2500 Hz and NOT 2250 Hz.