cutoff freq of butterworth filter

Cutoff frequency is that frequency where the magnitude response of the filter is sqr(1/2). For butter, the normalized cutoff frequency Wn must be a number between 0 and 1, where 1 corresponds to the Nyquist frequency, π radians per sample.

[b,a]=butter(n,Wn)

my fs=40 fc=9

so my wn= 9/40 or wn=9/(40/2) ?

can you explain? than you very juch

Answer 1

[Wayne King]

To convert from frequency in Hz to normalized frequency divide the desired cutoff frequency in Hz by 1/2 the sampling rate.

So if your sampling rate is 40 Hz, then a cutoff frequency of 9 Hz is

    9/(40/2)

For normalized frequency multiplication by pi is implied so 0.5 is really 0.5*pi or pi/2 radians/sample. Note that pi/2 radians/sample is 1/4 cycle/sample multiply that by 40 samples/sec and you get 10 cycles/sec or 10 Hz. Therefore a normalized frequency of 0.5(pi) is equal to 10 cycles/sec with a sampling frequency of 40 Hz.

[joo]

so the correct one is 9/(40/2)?

[Wayne King]

yes, if you want a cutoff of 9 Hz for a sampling frequency of 40 Hz. You can see that by the following

   [B,A] = butter(4,9/(40/2));
   fvtool(B,A,'Fs',40)

If you zoom in on the plot at 9 Hz, you'll see that it is the 3-dB down point as required.

[joo]

oh i did not know this set of matlab. sorry i am new at this and also i have never studied filters. could you please explain me the relation between 3 db and 9 hz. i tried to search in the net but i did not find a relation of values. if you please could explain to me i would be very grateful. thank you so much.

[joo]

but still i am confused because i read i should ''%Choose a range of “test cutoff frequencies”, for example,0.01*fs, 0.02*fs, 0.03*fs,…, 0.5*fs. %(Remember that 0.5*fs= the Nyquist frequency.) ''

i have to show a set of cutoff plots. if i want for example

0,1*fs ---> 0,1*40/ 20=0,2 --> [B,A] = butter(4,0.2);

0,4*fs ---> 0,4*40/ 20=0,8 ---> [B,A] = butter(4,0.8);

is this right?

[joo]

this is my .m file, if you can see what i am doing please. thank you so much

http://www.speedyshare.com/Xdmcs/Nova-pasta.rar

if you can't please just answer me the previous comment please

THANK YOU SO MUCH for all your kindness.

[Kenny]

Hello Wayne. Many years late here. But .... could you please explain "For normalized frequency multiplication by pi is implied" ? Why is multiplication by 'pi' implied? What's the origins of that? Thanks Wayne.

[George James]

yes, I wish somebody could answer this. Ive never found an answer before. I second this question

Answer 2

[BHAVATHA BALIGA]

If I hav a pre generated wave how to get it's cut off and sampling frequency??