While ago there was a soccer game. How to suppress the Vuvuzela sound (but other sounds should pass) was a popular topic at that time. In this case, you analyze the frequency of Vuvuzela sound and design a filter which doesn't pass that frequency. The design of digital filter is: which frequency of the signal will be passed and which frequency of the signal will not be passed.

See the following article for instance, http://blogs.mathworks.com/loren/2010/06/30/vuvuzela-denoising-with-parametric-equalizers/

In chapter 3.9, a simple non recursive filter design is described as an example.

The filter looks like the following.

This filter uses three samples. The design of filter is to determine the

*a,b*to fit to your desire. First, we will calculate the transfer function of this filter. As I explained in a former blog post, a transfer function is an eigenvalue of the filter function. Thus, it shows the output of the input of filter

*F*. Here the input signal

**x**(this is a function of time

*t*,

**x**(

*t*)) and the filter function is

*F*, then the eigenvalue

*λ*is

*F*

**x**

*= λ*

**x**. If you are familiar with linear algebra, you can consider the

*F*as a matrix A, a scalar

*λ*, then you will see that is the same as

*A*

**x**=

*λ*

**x**. Now we compute the transfer function:

Therefore, transfer function is

If you want to make your filter passing the π/3 frequency (=1) and you want to cut 2π/3 frequency (=0), we set this transfer function under that condition.

By solving the system, we get

The filter is:

We design a digital filter, but, it is still not clear what this is. So, next time, I will input the actual signal into this filter and see how this filter works.

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