Normalized value of the pass-band frequency in butterworth filter.

The code uses the buttord function to determine the order and cutoff frequency of the filter, and then the butter function to design the filter. In summary, the normalized pass-band and stop-band frequencies used in a butterworth filter can be found using the code wp=180/4000 and ws=360/4000.
  • #1
jshubham
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1. How do we find the normalized value of the pass-band and stop-band frequencies to be used in a butterworth filter?I am using the following code in MATLAB to design a butterworth filter. Can someone please tell me what is the pass-band/stop-band frequency of the filter in this code? 4000 is the number of samples in the signal.

wp=180/4000; %wp=pass-band freq
ws=360/4000; %ws-stop-band freq
rp=1; rs=60; %rp, rs=ripple factors
[n,wc]=buttord(wp,ws,rp,rs); %finding order n and cutoff frequency wc
[a,b]=butter(n,wc); %low pass butterworth filter
 
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  • #2
The normalized pass-band and stop-band frequencies are wp = 180/4000 = 0.045 and ws = 360/4000 = 0.09, respectively.
 

1. What is the normalized value of the pass-band frequency in a Butterworth filter?

The normalized value of the pass-band frequency in a Butterworth filter is a dimensionless frequency value that is used to design and analyze the filter. It is typically represented by the symbol "ωn" and is equal to the pass-band frequency divided by the filter's cutoff frequency.

2. Why is the normalized value of the pass-band frequency important?

The normalized value of the pass-band frequency is important because it allows for the comparison of Butterworth filters with different cutoff frequencies. By using a normalized value, the design and analysis of the filter becomes more general and can be applied to a wider range of frequencies.

3. How is the normalized value of the pass-band frequency calculated?

The normalized value of the pass-band frequency is calculated by dividing the desired pass-band frequency by the cutoff frequency of the filter. This value is then used in the design equations and analysis of the Butterworth filter.

4. What is the range of values for the normalized pass-band frequency in a Butterworth filter?

The range of values for the normalized pass-band frequency in a Butterworth filter is typically between 0 and 1. A value of 1 represents the cutoff frequency of the filter, while a smaller value represents a pass-band frequency that is lower than the cutoff frequency.

5. How does the normalized pass-band frequency affect the performance of a Butterworth filter?

The normalized pass-band frequency affects the performance of a Butterworth filter by determining the steepness of the filter's rolloff and the amount of attenuation in the stop-band. A higher value will result in a steeper rolloff and more attenuation, while a lower value will result in a gentler rolloff and less attenuation.

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