any relay do this?

I want a relay (or combination of multiple relays / circuits) to do the following:

Trigger +12vdc (X = Off, O = On):

Basically I want output be switched on after the trigger be on for certain time (e.g. 3s), then the output only be turned off if the trigger is off for certain time (e.g. 3s). Any on/off change with 3s shouldn't affect the output.

Can anyone help?

This relay setup will extend a pulse for a while.  There is another diagram here somewhere that will delay the output for a time.  A combination of the 2 should do what you want.  However 3 seconds may be a stretch.  It may take a transistor circuit on each relay setup to obtain the required 3 seconds.  I know that someone can find the delay relay setup today, and I will lay out the transistors this evening.

Pulsed to Steady Output

If you have cornering lights and want them to come on only when your turn signal is on and you do not have a steady output, use the following for each side. This will give you a steady output while the turn signal is on. Increasing the size of the capacitor will give you a longer output if needed.

I was thinking about this too, but do you know where can I found the on delay and off delay relay? I search the web and can't found any.

Thanks. 3s just an example, I think anything more than 1.5s should work for my needs. My application for this is for power up the HID low beam. I want to trigger the low beam by the OEM low beam connector, which normally a simple relay harness should be ok, but the problem is my car will turn on both high beam and low beam when I try to flash the high beam, and I don't want the low beam HID to be fried in that 0.5s flash. I also don't want the HID keep switching on/off if there is any rapid power on/off change on the OEM low beam harness.

I think I probably need three circuit put together:

DelayOn - PulseToConstant - DelayOff

Oh, just relized that DelayOn/DelayOff probably not what I want. My understanding for DelayOn is turn on some time after one pulse, but what I want is to turn on only if the trigger is continuously on for certain time. Same for the DelayOff, what I want is turn off only when the trigger is continuously off for certain time.

I thought that was exactly what you said in the beginning. That is exactly how it will work. Build the one that I posted earlier and use a larger capacitor to see how long it will stay engaged when the power is removed from the trigger wire. The above is the delayed off relay. The delay on circuit will trigger that one.

I still have had no luck finding the other diagram.  Give me a minute, I will draw the diagram, you will have to play with the cap and resistor values.

I'm novice on circuit design, and I'm not sure the following will work or not....

i am an idiot wrote:

Is it means the relay will only energized after a couple seconds (delay on), then when low beam off, the capacitor will discharge and energize the relay for a couple more seconds (delay off)? Wow, it is much simpler than what I comes up with.... What resistor and cap size should I start with, if I want aorund 3s delay?