Distillation, ion exchange resins.

How much water? A simple evaporation chamber can naturally distill water in small quantities, a black (or heated) water barrel with a glass cover and drip pan would work. For large quantities, Deionization and carbon filters are probably going to be best.

If a selective removal of inorganic anions (such as bicarbonate and carbonate) from the water and preservation of the content of cations (Ca, Mg, etc,) is aimed, Donnan dialysis using anion-exchange membranes can be a relevant separation method.

You can use ion exchange method

As told from Antonio first question is: How much water? Second question is: Wich is the concentration of Mg, Ca and carbonates, on the base of these answers an economical method could be set up. Freezing could be an interesting option to remove the most of the hardness if the water quantity is low

Oxalate could help remove calcium, but will not work so well with magnesium.

RO treatment u may go if that water is drinking water

and Ion Exchange method also u may try

The hardness caused due to bicarbonates of calcium and magnesium is called temporary hardness.

calcium carbonate is sparingly soluble in water (0.0013 g/100 mL (25°C)). Temporary hardness i.e., Bicarbonates of calcium and magnesium can be removed by mere boiling

Ca(HCO3)2 + Heat------------> CaCO3 (ppt) + H2O

Mg(HCO3)2 + Heat-------------> Mg(OH)2 (ppt) +2CO2

Calcium carbonate and magnesium hydroxide settle at the bottom and can be removed by filtration.

Other methods are little costly,

But you can use

1) RO

2) Electrodialysis

3) Ion exchange techniques

What is the technical object and/or appliction for which calcium and magnesium should be removed from water?

-- softening ?

-- decarbonsation ?

-- desalination ?

-- what is the concentration (calcium and magnesium, carbonates) of the raw water?

-- how much is the residual concentrtion after removal ?

-- are there some limitation to the conductivity and pH value for the treated water?

-- amount of water to be treated, volume flow rate?

You can use NaOH for water softening.

It is very effective although it will be a bit costly.

Water hardnesa can b eaaily removed by these 3 methods easily like Electrodialysis, Ion exchange techniques and RO.