Speed huh? I suggest weights. A few years back, my sensei told me the same. I bought five pound arm and leg weights and I trained in them along with doing everything else in them. Eventually, my muscles became used to the weight and when I took the weights off I was faster.

What type of speed? Kicks? Punches? Reflexes?

As far as kicks or punches, you need to probably practice them very slowly, with tension, to develop more muscle and then when you do punch and kick fast you'll be able to.

As far as reflexes, get someone you can trust to be a partner and have them shadow box spar with you and you work on blocking and countering with a move.
You could do this with focus mitts or airshields.

If you do not have a partner to train with, try finding a mirror and watch your timing.

If it is speed with endurance, I would recommend jogging and or running.

Light weights too, may help too. Just be careful not to lock your elbows and or knees.

punch 1000 times a day and kick… and spar alot and have people try to hit you so you can work on reflexes to…. and do your kata faster… thats all i can say

Ok there are many techniques for learning to speed up.

the one i was taught was unique and worked and was all done naturally and through focus and concentration, not weights or other periphials.

We would light a candle and place it just at the end of our reverse punch. Men and woman would wear tshirts here over gi tops to reduce wind factor.

the point is to put the candle out using a reverse punch and not touch the candle. Once you can do this on both sides regularly then you go the opposite way, place you hand over the flame and draw back as if you are pulling away from a reverse punch and bring it to chamber. The force from both strikes if done fast enough will create enough air to blow the candles out.

Another trick is with a coin. have your friend hold a coin in his palm, you hold one of a differant kind in your forefinger and thumb, the idea is the grab their coin and replace it with yours before they close their hands. You go with the judge or sense i says go. This helps build speed and focus.

another would be using a partner and standing face to face you put your hands out palms inward and you place your hands either to the outside of the other or the inside.

then you start going in a circular motion faster and faster, the person with their hands in the inside gets to strike at you any time they choose or as many time they choose. YOU must stya with them and block all their strikes. This teaches you to listen to your opponents body movements, once you get htis down, try it blind folded. NOT THE FLAMSES though always do that safely with an extinguisher near by and a Sensei around.

other than that jog do your push ups and stay lean and trim and dont put too much mass on.

good luck

i have found that press ups have strengthened my arms and so my punches are faster. i also have some small dumbell weights that i use every 2-3 days. you wouldn't belive the difference.
my kicks i do against the wall. holding leg up and trying to get say 20 kicks in a 30 second time slot, then doing 20 kicks in a 20 sec. time. sounds wierd but has worked for me.
my sensei helps wiht reflexes in class, which i practice with at home, when ever my mom moves i have to make sure i have shaddowed her faster.
get fit- i have done karate since i was 5 and have got stronger and faster since becoming a 1st dan - but then i do have a lot more training now.
just enjoy yourself. practice and it will come.

I've always felt that Grace and form always trumped speed and power.

You might just be over THINKING your movements, relax and let your training become instinct.