from the transfer function, of the analog model (R and C), you acn use the Z transform

I have only this set of data

At first, you need to know what kind of filter (type, order) you have to realize. For this purpose, I suggest to make a diagram (magnitude and phase) as a function of frequency. As a next step, it would be necessary to derive the order and the best fit for a approximation method (Butterworth, Chebyshev,..) from the diagram

Covert analog filter transfer function H(s) to H(z) using Z-Transform and get its impulse response to realize the corresponding digital filter.

Thank you for your answers. But I have to at first find the H(S) as I found out. By the way the analog filter is 2nd order low pass filter.  I do not know how to find H(s)? I really need your help. I hope one day I can answer some one else's question.

A second-order lowpass has a phase shift of 0 deg (or -180deg, if inverting) for very low frequencies (including DC). However, the phase deviations in your table are above +20deg (for very low frequencies).  I propose to follow my recommendation and to create a diagram (magnitude and phase). More than that, also the given amplitudes do not behave according to a 2nd order lowpass.

First I like to ask what does the second column stands for? Is it milli volts over newtons? And where did the data set come from? (As long as you can answer) All I can assume is that this column is some sort of amplitude measure, if so, you could convert it to dB, as it is the standard unit in control systems, from that, notice you have the frequency magnitude and phase, from all which you can construct a bode plot diagram, magnitude vs frequency and phase shift vs frequency.

Finally all to do is to derive the transfer function from the bode plot, this is a little bit tricky, you mentioned that is a second order low pass filter, that means that there is a 40 db/decade slope, and every decade corner section would have either two zeros or two poles added to the transfer function, (you can search for how to get the TF from the bode plot) when the analog TF is found (s domain function) you must transform it to the discrete domain (z domain) this can be done by several methods, I suggest tustin method or bilinear transform, as it's the most accurate in this filter cases. 

A first look into the table reveals that there is neither 20dB/dec nor a 40dB/dec slope of the magnitude.

Dear Student,

USe the book Digital Signal Processing by John.G.Proakias and convert your analog transfer function into digital transfer function. Then you simulate it into the matalab.

It's the output of a sensor measuring acceleration. There should be a mathematical formula  to describe the output of such sensor. It's not the output of a analog filter designed. If you know the analog transfer function of this sensor, which can be found from manufacturer who build this sensor, you can use the method suggested by Kishan Rao Kalitkar to find a digital filter. 

thank you for your answers. But the transfer function is not given. I converted the amplitudes to dB. But I do not know how to obtain the transfer function from the bode plots. 

this data is from an accelerometer (second-order oscillator) plus a low-pass filter (in cascade). ( as the person in charge informed me )

Approximate BODE plot to get transfer function.

Dear Seyed Alireza,

The most well-known analog filters are Butterworth, Chebyshev, and elliptic filters.

The simplest of which is the Butterworth. The transfer function H(s) of Butterworth filters for different orders (including 2nd order, as well) are fixed and can be found in any Digital Signal Processing (DSP) book.

For example: 

First Principles of Discrete Systems and Digital Signal Processing , Strum and Kirk, Addison-Wesley, 1989. (Look at page 627).

Once you have the H(s) of 2nd order Butterworth, all you have to do is to convert it into a discrete-time transfer function H[z]. There are different methods for that such as:

* Matched z-transform method

*Impulse invariant design

*Bilinear transform method

These can also be found in the above book (see Chapter 10) or any other standard DSP book.

I wish you good luck,

O. Akay