What happens to a time interval, emitted from a source far from a blackhole, observed by an observer near a blackhole/massive body? It is obvious that for a time interval emitted from a source near a blackhole, observed by a source far from the blackhole, the time will be longer due to dilation of time near the blackhole. But what would happen in the opposite case as mentioned above? 
 A: It’s the opposite effect. The time interval gets smaller, for light emitted from far away towards the BH.  A wave, electromagnetic or gravitational would get blueshifted.  Inversely, the light emitted from near a BH, going to infinity, gets redshifted.
An easy way to think of it is to realize that for light going from the black hole (BH) to infinity, or let's just say going far away, a natural time interval would be the time between peaks of the wave. That is the period, the inverse of the frequency. Since the interval increases for something emitted from the BH going outwards, the frequency decreases: the period increases. Higher period means lower frequency, which is a redshift. That is, for light going from a BH to far away a redshift occurs. 
Going the other way, from far away towards the BH, it's just the reverse of that. A blueshift occurs. The interval of time, the period, decreases, and the frequency increases.
Those are some of the reasons that you cannot see something hitting the horizon of a BH. It appears to be slowing down as it gets closer to the BH, and its light gets more and more redshifted, as seen from far away. As it comes real close to the horizon, it's frequency redshifts so much that it becomes undetectable (lower frequency, lower energy, till you can't detect it). Going the other way, light going towards a BH gets blue shifted. The same is true with gravitational waves going into a BH, its frequency would increase, get blue shifted. 
There is a practical difference for both light or other electromagnetic waves such as gamma ray, and also for gravitational waves, being emitted from a BH vs waves going into the BH: those kinds of waves emitted around the BH cannot not come from the horizon (nothing escapes the horizon), but rather from outside the horizon. For electromagnetic waves it is usually from accretion discs where matter is infalling, but also very strongly being shot out as jest in quasars: that can happen at different distances from the BH horizon, and not always or necessarily real close to the horizon. Something similar is true for gravitational waves, which is generally emitted (say when something falls in or two BHs merge) on the infall, and the last stage when they are close, but which actually involve gravitational effects all around the BH, and wavelengths on the order of or larger than the horizon radius (which is why we needed some kms sized legs on the interferometers). The redshifts lowers those frequencies when we see it at earth.
[note that if the emitting body is usually also receding from us due to the cosmological expansion, a redshift also occurs and you have to add the effects. The redshift for the LIGO 2015 merger, with the BHs about 1.4 billion light years away, was about 0.1, not much and was accounted for. The emitted wave we detected was in the low freq audible range around 100 Hz (careful in calculations, the freq of about 100 Hz is c/wavelength, not (speed of sound)/wavelength. For electromagnetic radiation from quasars we see microwave and higher frequencies, and up to gamma rays].  
See gravitational redshift and blueshift in Wikipedia at https://en.wikipedia.org/wiki/Gravitational_redshift
and blueshifts at https://en.wikipedia.org/wiki/Blueshift
