Your new brake pads will quite possibly cure your issue, depending what the issue is.
If you have a long, hard stop and hold the brakes while you're sitting at the light you could be depositing pad material on the rotors. This could cause a pulsing feeling in the pedal.
If your car sits for periods of time and the rotors get a bit rusty, where the pads are would not rust equally and you could get a pulsing feeling in the peday.
Both of those things could be mitigated by a couple of days of spiritied and aggressive driving (which would require spirited and aggressive stopping.) This works on my truck, which sees periods of disuse.
It could also be that some corrosion has built up between the rotor and the suspension, causing a slight runout issue, which causes a pulsing feeling in the brake pedal. Take off the wheel(s) and clean the wheel and rotor. Take off the rotor and clean the rotor back and the suspension where it touches. This is what works for me in those instances.
Or, it could be your rotors need replacement...