I would agree with the above. A binding caliper, due to a sticking piston, is a common problem on older cars with high milage but should have been checked when the discs and pads were replace. As the above writes, check the temp of the wheel after a longish run - but mind you don't burn your fingers, as I once did !!
But don't change the whole caliper, just the cylinder seal, and if one is sticking then the other should be done too.
Or if you have a newish car then it may be you have some air in the system, hence the pumping of the brake pedal, and, if you are a light braker with runs of little braking requirement, the unpolished surface of the discs and pads may be noisy. I have just changed my discs and they do make a grinding noise. Have a look and see if they are polished smooth, or look a bit rough.
Let us know how you get on -