A brake pedal that pulses, shudders, or vibrates when you slow down is one of the most common brake complaints. It almost always traces back to the rotors. Here is what causes brake pedal vibration.
Uneven rotor thickness
The usual cause is rotor thickness variation - the rotor is not perfectly flat, so as it spins the pad is pushed in and out slightly, pulsing the pedal. This is often called warping, though it is usually uneven wear or pad deposits rather than a truly bent disc; see warped rotor causes.
Where you feel it
Vibration felt mainly through the brake pedal usually points to the rear rotors; shaking felt in the steering wheel points to the fronts. A pulse that only appears under braking is the classic rotor signature, not a tire or suspension issue.
Other causes
Heat can create hard spots or uneven pad transfer that mimic a warp; see brake heat. Loose or worn suspension and hub parts, or unevenly torqued wheels, can add to it. A stuck caliper that overheats one rotor can warp it and cause the pulse.
How to fix
Resurface or replace the affected rotors in axle pairs, fit fresh pads, and bed them in properly; see replace rotors in pairs. Torque the wheels to spec. Start with quality pads and hardware.