Yes.

The formula is:

λ' = λ*Sqrt[(c - v)/(c + v)]

λ = wavelenght of the source when it doesn't move with respect to the detector/observer.

λ' = wavelenght of the source when it moves with respect to the detector/observer.

v = velocity of the source with respect to detector/observer; positive if the source is approaching to observer (or the observer is approaching the source, of course is the same).

If you want to find the velocity v knowing the rate λ'/λ:

(v/c) = [1 - (λ'/λ)^{2}]/[1 + (λ'/λ)^{2}].

If you want red to become blue, let's say red with λ = 660nm = 6.6*10^{-7}m, to blue with λ' = 440nm = 4.4*10^{-7}m, you have λ'/λ = 4.4/6.6 = 2/3 and so:

(v/c) = [1 - (2/3)^{2}]/[1 + (2/3)^{2}] = 5/13, so v ≈ 0.385c.

If instead you want microwaves to become X rays, let's say microwaves with λ = 1mm = 10^{-3}m, to X rays with λ = 10nm = 10^{-8}m, you have λ'/λ = 10^{-8}/10^{-3} = 10^{-5} and so:

(v/c) = [1 - (10^{-5})^{2}]/[1 + (10^{-5})^{2}] ≈ 0,9999999998 --> v = 0,9999999998c.

Edit. Soul surfer reminded me this: of course the above formulas hold even when v is negative, that is the source recedes from observer. Then λ' increases (doppler red shift of galaxies, for example)