Producing high frequency signals

Hello,
I need to produce 3 different signals to control my system. One will be a direct delta (just like steeper version of gauss distribution function) like function which will rise up and then down in a defined time, usually few ms duration in 1 Hz.

One TTL signal at 3.3V , synced with the dirac delta signals frequency but duration can be defined, usually around 50-100ms.

And one TTL signal 3.3-5V , which I should be able to set duration and frequency.
Duration can be in the range (TTL UP) of nano seconds to micro seconds and frequency can be a few kHz.

Could you please let me know which aurdino board can do this?

Thank you.

None of them or all of them. You are using specific numbers but I still have no idea what you want.

Direct delta = Dirac delta? That's a theory, not a real pulse you can produce with a real device.

Does the third signal vary between 3.3 and 5V or is it just configurable between one or the other, with like a switch?

What is the impedance being driven?

If you need analog signals of a certain wave form, a DSP with DAC will be the best choice. For lower quality an Arduino with built-in DAC may be usable.

Probably you can use the Heaviside (unit step) function instead of Dirac, which can be generated by every digital output.