There is no unique way to get a realization H(s) for a given magnitude response, since there can be many filters with the same magnitude response: As a trivial example, take the filter which is multiplied by -1.

However, there is a unique minimum-phase filter for a given magnitude response. You can get the phase response of the minimum-phase filter from its magnitude response by using a special kind of Hilbert-transform.

http://en.wikipedia.org/wiki/Minimum_phase

http://en.wikipedia.org/wiki/Minimum_phase#Relationship_of_magnitude_response_to_phase_response

Dear Amr,

If you are given the magnitude frequency response of a filter irrespective of the the phase frequency response , and you want to implement it in the sense you want to get H(s), there is formal procedure developed in the design and implementation literature of the filters. 

The concept that any piratical amplitude frequency response can be approximated to one of four major standard filer functions: the butterworh, the chebychev, the bessel and the elliptic filter functions.  The group delay variations with frequency varies among the standard functions with bessel is of the most linear phase frequency response and the elliptic is the worst.

So, one chooses a standard filter function according to the required variations in the group delay time.

After that, one turns attention to the filter complexity, which is the filter order that is determined by knowing the stop band attenuation and  certain steepness factor. The steepness factor is the ratio of the stop frequency to the 3-dB cut off frequency. The filter order is determined by matching the amplitude frequency curve to one of the curves of the selected standard functions

Once the complexity is determined, one gets the poles of the filter from the tabulated poles of the selected standard function.

Then H(S)= 1/ (S-P1) (S-P2) ........(S-Pn)

If you want to filter sound you can use elliptic filters because ear is not sensitive to phase nonlinearity and if you filter pulses you have to preserve the integrity of the wave. thus you use bessel filters.

For much more details please go to the link:pdf4.landbooks.org/pdf/analog-and-digital-filter-design-paperback-_1vy.

wish you success

Yes , It is possible by using 'fir2' command in MATLAB

The filter calculation usually start with the filter settings, the most important of them is the magnitude response. As it has been stated in the "low pass filter prototype", first performed these requirements to the requirements specified filter LPF prototy

Sufficiently long time , filter calculation method selection frequency response using standard units (m-link or k-link). This method is called by application. It was quite complicated and does not give the optimum balance of quality and quantity of the developed filter units. Therefore, methods have been developed mathematical approximation of the amplitude-frequency characteristics with preset characteristics

Approximation in mathematics is called a complex representation of the dependence of some known function. Typically, this feature is quite simple. If you develop a filter, it is important to approximating function could easily be implemented Circuitry. For this function are implemented using pole-zero transfer ratio quadrupole filter in this case. They are easily implemented by means of LC-circuits or active RC-feedback circuits

The most common form of the approximation of the frequency response of the filter is an approximation of Butterworth. Such filters are called Butterworth filters . Second one is Chebyshev approximation !

Many filter designs take only the magnitude spectrum into account.