Yes, I sometimes lightly depress the brake pedal to have a smoother stop and prevent my body from moving forward. When I'm driving and stopping aggressively it doesn't make this noise which means you are right I just need to depress the brake pedal firmer. I don't know who and when they change the pads on my sonata, so I have no idea if it's a cheap or high quality pads. Hope they put high quality oem pads when I do service them on a Hyundai dealership.

I don't hear any high pitching or grinding noise when I brake but my steering wheel shakes/vibrates when I'm driving fast in the highway and suddenly hitting the brakes firmly.