I am driving a 2004 Chevy Impala. When coming to a stop, I press the brake pedal, and I can feel the choppy vibration on the pedal. It's same regardless of weather. Should I get this checked out?
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Yes your brake rotors are out of round. You can resurface them as long as they are not too thin.
The rotor varies in thickness and as it turns when the brakes are applied causes the car to vibrate, and or pulse the brake petal.
It's not an emergency unless it's shaking the car or steering wheel a lot when you brake. I would put a priority on getting it repaired because it will get worse.
More information here Excessive lateral run-out (warping)