Dear Nagapuri ,

Yes filters are capable of attenuating noise provided that this noise lies outside its conduction band. The digital filters perform the same functions of the analog filters except they process the signal in a digital manner. So to filter the signal it must be first converted into digital form using A/D converters after sampling it. The sampling rate must be at least twice the highest frequency of the signal to be filtered. So, after sampling and the conversion the signal will be converted int a sequence of numbers.

So, this sequence say x[n] is processed digitally to filter out the unwanted frequencies and pass the wanted frequencies according to the filter specification.

There are two types of digital filters the finite impulse response and the infinite impulse response, FIR and IIR.

A Digital filter is characterized in z-domain which is the discrete laplace transform H(z)

generally H(z)= N(z)/ D(z) N and D are polynomials in Z^-1. The coefficients of these  polynomials completely define the filter and when converted into DISCRETE TIME DOMAIN results in the difference  equation that is implemented by a computing machine or platform to calculate the output of the filter y[n]

To design and implement such filters there are text boos which you have to consult to achieve your goal.

Here is a link:dsp-book.narod.ru/PADFD.pdf

wish you success

Dear Nagapuri ,

Yes filters are capable of attenuating noise provided that this noise lies outside its conduction band. The digital filters perform the same functions of the analog filters except they process the signal in a digital manner. So to filter the signal it must be first converted into digital form using A/D converters after sampling it. The sampling rate must be at least twice the highest frequency of the signal to be filtered. So, after sampling and the conversion the signal will be converted int a sequence of numbers.

So, this sequence say x[n] is processed digitally to filter out the unwanted frequencies and pass the wanted frequencies according to the filter specification.

There are two types of digital filters the finite impulse response and the infinite impulse response, FIR and IIR.

A Digital filter is characterized in z-domain which is the discrete laplace transform H(z)

generally H(z)= N(z)/ D(z) N and D are polynomials in Z^-1. The coefficients of these  polynomials completely define the filter and when converted into DISCRETE TIME DOMAIN results in the difference  equation that is implemented by a computing machine or platform to calculate the output of the filter y[n]

To design and implement such filters there are text boos which you have to consult to achieve your goal.

Here is a link:dsp-book.narod.ru/PADFD.pdf

wish you success

Excellent answer has been provided by Dr. Abdelhalim Zekry. I fully agree with him.

Digital techniques were already used in 1970. For example, in that time engineers did channel equalization on old Caruso records . The subject came again into foreground when the Compact Disc appeared and sound engineers wanted to archive the old sound-recordings.

First, sound-engineers restore the record physically, then they digitize the sound with a high quality record-player and a digitizer. Then digital noise reduction techniques will be applied.

More different algorithms are used together. Special algorithms used for click reduction and other algorithms for hiss reduction. Several algorithms are developed. Unfortunately we cannot discuss these algorithms in details, because they are too difficult and the main reason is that they are secrets. I can show only the basics of these algorithms.

http://www.sciencedirect.com/science/article/pii/S2212017316304844

https://people.ece.cornell.edu/land/courses/ece5760/DE2/fpgaDSP.html

 Dear colleagues,

At first i would like to thank Kaiser for her comment on my answer. 

There are very known steps design a an IIR FILTER:

- The first step is to define the specification of the required low filter; that is its -3 dB cut off frequency fc, the stop frequency Fstop at a predetermined stop attenuation Astop. In addition to the ripples in dB in the pass band. Farom theses specification one can choose a standard filter function such as the butter worth. From the matching of he required specs with that of the standard filter function one can get the order of the filter function, n together with its zero and poles. That is one knows now H(s). 

-Then one transforms H(s) TO H(z) using the bi linear transformation. 

- One can then implement H(z)  using VHDL on FPGA.

Best wishes