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nth degree butterworth low pass filter

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mamoun

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Is there a general procedure to design an nth degree butterworth low pass filter. Where can I find such one. I am trying to get the poles and zeros locations for a certain cut-off frequency.

Thanks
 

Well, there are tables that gives you the coefficients of the transfer function, here u can find up to 10th order:

**broken link removed**

other thing u can do is to use matlab to make the filter, matlab gives you the order of the filter and the coefficients, you only give it the atenatuion you eant and your cutoff frecuencies....

this are the commands:

buttord (To get the order of the filter u should use)
butter (To get the coefficients of the filter)

I think those are the commands, i am pretty sure about it, check how to use them on the matlab help.
 

The poles can be found graphically-mathematcally. On the S plane, draw a circle with the radius of your wanted 3 dB cutoff frequency. Double the number of poles and place them at equal angle displacements all around the circle. They should be left-right symmetric across the imaginary axis. Discard the poles in the right half plane. Once you visualize this you can mathematically calculate the locations. To save half the calculations, notice that the poles are also mirror symmetric across the real axis.
 

It must be very clear that every filter is a system.

And output of the filter is what comes from convolution in time domain of your input and impulse response of the filter.

If Bode is always the tool you will see things a lot easier.
 

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