 Here our aim would be to minimize the error in the frequency domain and not the spatial domain.Due to Parseval's theorem we observe that the mean squared error will be identical to that in the spatial domain.Parseval's theorem states that

formula_327

Also the different norms that are used for FIR filter design such as formula_328,formula_329 and formula_186 can also be used for the design of IIR filters

formula_183

is the required equation for the formula_329 norm and when p tends to formula_30 we get the formula_186 norm as explained above

formula_188

The main advantages of design in the frequency domain are
The main disadvantage of this technique is that there is no guarantee for stability.General minimization techniques as seen in the design of IIR filters in the spatial domain can be used in the frequency domain too.One popular method for frequency domain design is the Magnitude and magnitude squared algorithms.