Butterworth filter Puns

I am applying a butterworth lowpass filter using scipy to many signals in many iterations. I am satisfied with the smoothing/filtering result, however, the function call takes a while (I have already put all the signals into one array when calling signal.filtfilt I also have the a and b values pre-calculated for efficiency. I am using Cupy elsewhere in my code which uses numpy on my GPU, however, there is no support for signal.filtfilt.

There also appears to be a module called Cusignal which expands the functionality of Scipy.Signal (Cupy provides a little), however it does not appear it is supported as it only accepts filters where a=1 and says that IIR filters are not currently supported.

My idea now is to find a manual function definition for signal.filtfilt that solely uses numpy so I can replace the numpy calls with cupy calls. Either that, or if the result of filtfilt can be achieved with some alternate combination of functions supported in either Cupy or Cusignal.

Here is the filter:

def butter_lowpass_filter(data, cutoff_freq, nyq_freq, order=4):
    
    #Note: cutoff_freq = 1 fixed in precalculations
    
    #Pull butterworth filter (precalculated), 
    b,a  = butter_filters[nyq_freq][order]
    
    #Transpose, filtfilt requires multiple signals to
    #be aligned this way to do multi-signal (column) processing.
    data = np.transpose(data)
    data = signal.filtfilt(b, a, data)
    data = np.transpose(data)
    
    return data

Here is a list of the supported Cupy Scipy Signal functions (relevant ones):

cupyx.scipy.signal.choose_conv_method       
cupyx.scipy.signal.correlate
cupyx.scipy.signal.convolve
cupyx.scipy.signal.fftconvolve
cupyx.scipy.signal.medfilt
cupyx.scipy.signal.medfilt2d
cupyx.scipy.signal.order_filter
cupyx.scipy.signal.sepfir2d
cupyx.scipy.signal.wiener
cupyx.scipy.signal.oaconvolve

Cusignals are not as well documented, but digging through it appears it limits a=1 and says IIR filtering is not supported:

https://github.com/rapidsai/cusignal/blob/branch-22.02/python/cusignal/filtering/filtering.py

Hi everyone,

I'm trying to apply a Butterworth filter to some data so I have this in the main body;

hz=480; %sample rate

dt=1/hz; %sample time interval

L=10; %sample time duration

t=(dt:dt:L)'; %time

N=length(t); %number of points

m=1000; %maximum frequency (will actually be 2*m-1)

y=ones(N,1)/2; %set constant to 0.5

for n=1:m

nn=n*2-1; %increase by 2 [1 3 5 7...m]

y=y+(2/pi)*sin(nn*t*pi*2)/nn;

end

cutoff=10;

forder=2;

fy=FILTERNAME (y,hz,cutoff,forder);

fy2=FILTERNAME(y,hz,100,forder);

Then this as my filter;

function fdata = FILTERNAME(data,dt,forder,cutoff,ftype)

if nargin < 5 %if the filter type is not declared

ftype='low'; %assume this is a low pass filter

end

% adjust cut-off to allow for double pass:

cutoff = cutoff / (sqrt(2)-1).^(0.5/forder);

% compute Butterworth coefficients:

[b,a] = butter(forder, 2*cutoff*dt, ftype);

% filter the data (filtfilt does a double pass):

fdata = filtfilt(b,a,data);

end

I am getting this error:

Error using butter>butterImpl (line 85)

The cutoff frequencies must be within the interval of (0,1).

Error in butter (line 59)

[varargout{1:nargout}] = butterImpl(n,Wn,varargin{:});

Error in FILTERNAME (line 11)

[b,a] = butter(forder, 2*cutoff*dt, ftype);

Error in filename (line 33)

fy=FILTERNAME(y,hz,cutoff,forder);

I'm not sure how to solve this, do I need to incorporate Nyquist frequency somehow to lower the cut off frequency?

Any help appreciated :)

https://preview.redd.it/k2cikn4y2c481.jpg?width=1459&format=pjpg&auto=webp&s=b8f63f1d0aa99554c2234268103f6e16b3a698b8

Hi,

I'm looking at this textbook question and trying to get a better idea of exactly what its asking.

For the processing to be real valued each pole would have to have a complex conjugate right?

So for the two points closest to the real axis, we would call e^jω0 & e^−jω0e, then the next two at 45degree angles e^jω1 & e^−jω1 and the two most vertical points e^jω2 & e^−jω2

And these would be our 6 poles.

But then how does this relate to higher order filters being created with minimal algebra?

They're common in EQ and effects, have very nice qualities, and don't lose bass compared to ladder filters. Why aren't Butterworth filters used often in synths? ELI5 please.

** Edit ** Just wanted to thank everyone for your excellent responses. Learned a great deal.

Hello everyone, I am trying to apply a low pass Butterworth filter on my time data but I don't know what value to choose for the cut-off (second parameter).

Here is an example of my data, it is time data taken every 300 seconds.

[111, 115, 113, 109, 101, 103, 107, 110, 114, 113, ...]

My code:

datas = [111, 115, ...]

myFft = fft(np.array(datas))
freq = 1/300.0
nyquist = freq/2

normalizedDatas = [i/datas.max() for i in datas]
#cutoff = ?
#normal_cutoff = cutoff / nyquist

b, a = butter(datas, 0.7, 'lowpass')
y = filtfilt(b, a, normalizedDatas)

plt.xlabel("Time")
plt.ylabel("CGM")
plt.plot(x1, y2, label="Normalized")
plt.plot(x, y, label="Low pass")
plt.show()

This is the graph I get:

Normalized Vs Butterworth Low pass filter

There are almost no differences.

In the official documentation of the butter function, for the second parameter, it is marked:

>For a Butterworth filter, this is the point at which the gain drops to 1/sqrt(2) that of the passband (the “-3 dB point”).

Source

1/sqrt(2) = 0.70. This is why I have normalised my data. So that it lies between 0 and 1.

On this forum, for the choice of the cut-off, one person answered the following:

>The best way to decide what your passband and stopband frequencies are is to first take the fft of your signal. That should tell you the frequency content, and allow you to choose the correct frequency.
>
>The normalised frequency is the frequency you choose divided by the Nyquist frequency, which is one-half of your sampling frequency. The passband and stopband frequencies must be less than the Nyquist frequency.

Source

I have also calculated the FFT but I do not know how to use it.

What should I do to get a satisfactory result ?

Thanks and have a nice day :)

Hello fellow Engineers,

I want to learn more in depth how the synthesis of filters like Chebychev, Butterworth and Elliptic filter works in practice. I don't want to just have to resort to tools in ADS but actually understand the analysis of the transfer functions in terms of poles, the complex plane etc. Is there a good book that treats these concepts from the ground up in a very mathematical way?

Thanks!

I have a set of signals from three different pressure sensors. I am interested in finding the pressure impulse imparted on these sensors so I can have an idea of the impulse imparted on a nearby structure (assuming a spherical pressure wave). The impulse can be found by plotting the transducer data vs time , then finding the area under the curve between certain times. I use MATLAB for this . I do this using “cumtrapz(X,Y)”.

So I have a choice. I have my raw data from the transducer that is noisy or I can use a wavelet digital filter and also a high/low pass custom digital filter to make the data less noisy. When I compare the two different sets of data I notice that the maximum pressures are different. The filtered data generally has higher extreme values . So my question is ...should I find the impulse using the raw unfiltered data or should I find it using the filtered data?

Note that there are no time delays from my high/low pass custom filter (I used butterworth in MATLAB).

Hello, For the past few days I have been trying to simulate FM modulation/demodulation in Mathematica. One of the functions I implemented was LowpassFilter function on my signal, which was a list of data. However, I would like to apply a ButterworthFilterModel instead, but not sure how. How can I just plug in the data into the filter, just like I did with LowpassFilter function? Thanks

Hi,

As the title states, I am working on a project. One part of the project is to create a low pass filter. I want the filter to attenuate frequencies above 2 kHz (cut-off-frequency at 2 kHz(?)). Ideally, I would like to cut those frequencies off, entirely.

I have decided to make a 3rd order filter, but I don't know how to choose components and how much I want the open loop gain to be (gain in the passband).

For the first order butterworth filter I know that fc = 1/(2*pi*RC) and Gain = 1 + R1/R2.

I have tried to look for this on the internet, but to no avail. Can someone just point me toward the right direction?

Hi all, I'm a hobby guitar amp/fx designer. I'm trying to make an audio EQ right now, and I'm using butterworth band-pass filters for the standard 10 bands. My question is, for a second-order Butterworth bandpass, is the bandwidth fixed relative to the center frequency and Q? What about a higher order Butterworth, is the overall bandwidth independent of center frequency and Q/flatness?

Here are some of my numbers for second order. Using Q=1/sqrt(2), BW=ω_0/Q=ω_H-ω_L, and ω_0 is at the logarithmic center of ω_H and ω_L,

log(ω_H)-log(ω_0)=log(ω_0)-log(ω_L) or

ω_0=sqrt(ω_H ω_L),

the -3dB corner frequencies are at sqrt(2±sqrt(3))*ω_0, or about half and double. This is too broad if I want the standard 10 audio bands of doubling frequency. Is this correct? What can I do to decrease bandwidth without sacrificing flatness?

I appreciate your help!! Ideally I'd like to find a way of doing things where overall bandwidth can be independently modified without sacrificing any flatness. In the end if I do this right, the output sum of all the bands at max gain should be about the same as the dry signal, and zeroing out a filter (pot, one side to filter out one side to ground, wiper to mix output) should cut that band from the mix almost entirely. If my math is right, then the corner frequencies' attenuation from the surrounding bands won't be enough, and the cut band will still be there at half volume.

Thank you so much!!

I've got an electronics exam on Monday, and there's a chance we'll be asked to design an nth order low/high pass Butterworth filter. Am I correct in saying that, if I want the cutoff frequency to be 6kHz, I can select all resistors to be 1kOhm and all capacitors to be 0.027uF (1 / (2π(6kHz)(1kOhm)) = 0.027uF), basically making it an equal value filter, or do I have to select different resistor/capacitor values for each stage? Also, would this be the right way to make a Butterworth high-pass filter with a cutoff frequency of 6kHz?

Hello Reddit!

Probably a super easy question for you folks...but here it goes.

I am running in data to a butterworth filter, reversing the signal, feeding data into another butterworth filter (with the same characteristics), and then reversing the signal again. If I select both filters to be a 2nd order, will the final output signal be a 2nd order, or 4th order?

Thanks!

Jake_JAM

EMA/SMA has a huge lag compared to other filters, but is trivial to compute. However, there are many other filters with lower lag that are just as easy to compute, such as Gaussian and Butterworth. Why do charts not usually include these as options?

Hey

I have a homework assignment where I use a Butterworth filter. After I have used it, I need to find the magnitude in dB at a specific frequency. I know i can use fvtool it find it but i really want to know how i can calculate it.

I'm looking for a lowpass filter IC for an project. Yes i know i could assemble one myself but this way i can get something a bit more precise. I found the old MF4CN for really cheap, the cut off frequency is adjustable, the voltages needed are within range (I am using an Arduino powered by a 9V Brick so i have acess to ground, 5V and 9V easily).

Here i am going through the datasheet aaaand ooops, it looks like this IC can only output a signal with voltages between [(V-)+1] and [(V+)-1]. It's a problem since ill be working with analog signals ranging from 0 to 5V and i would like to keep them like that. I kept searching and found some others IC's but or they where outside my price range or i just couldn't find where to buy them. Do you guys know anything to replace the MF4CN?

TL:DR: Need alternative to MF4CN low pass filter that doesn't "clip" the output signal by (V-)+1 and (V+) -1 and it works with 5V or 9V

Data logged at 10 minute intervals with an fz of 600kHz. I need to apply a fourth order Butterworth filter and a cut off frequency of 1/3hrs^-1.

i have done as follows:

[b,a] = butter (4 , wn, 'low');

then i will use filtfilt

I don't know what to input into wn. If anyone can please explain how and what i need to input, i will be very grateful.

Not sure if this subreddit is active, but this is a long post with problem and suggested solution, please bear with me.

I want to design a digital butterworth lowpass filter of nth order, with only freedom of choice to user being order of the filter and the cut off frequency, i already have a 1st order low pass. Code:​

'T = 1/(2*pi*this.fc);'
'this.A = -1/T;'
'this.B = 1/T;'
'this.C = 1;'
'this.D = 0;'

This is a very basic lowpass PT1 filter, i take the state space matrix, descrtize it and apply it to my signal. now i want to extend my library to butterworth. I am trying to use as many minimal matlab commands as possible. So i thought it's better to derive in hand before implementing it. i wanted to know how to deal with damping ratio as the order is progressed.

When i was searching for answer, i came across wiki of butter worth filter which shows the polynominal for each order of the filter.

https://en.wikipedia.org/wiki/Butterworth_filter if you scroll down to Normalized Butterworth polynomials, there's a table.

I can just hard code this, but have they considered damping ratio and how do i covert this to state space. OR

I found another way, where i find zeros and poles based on the order of the filter.

% Poles are on the unit circle in the left-half plane.
n = varargin{1} % order of the filter
fc = varargin{2} % cut off frequency
Wn = (fc*2)/Fs % Fs is sampling frequency, normalizing the cut off frequency
z = [];
p = exp(1i*(pi*(1:2:n-1)/(2*n) + pi/2)); %n is the order of the filter
p = [p; conj(p)];
k = real(prod(-p)); %product of an array element´

%When we get zpk, we just convert them to state space.

[a,b,c,d] = zp2ss(z,p,k);

%Now transforming the abcd matrix to the given cut off frequency
[a,b,c,d] = lp2lp(a,b,c,d,Wn);

The only problem is while applying the cut off frequency, '[a,b,c,d] = lp2lp(a,b,c,d,Wn);' should apply normalized one or in rads/sec or just in Hz. Even though i tried all of them still would like i to ask where i am going wrong ​

I have an assignment in which I have to add noise to a given signal and then implement a Butterworth filter on the combined signal.

The code for the given signal is in the link below:

https://pastebin.com/YDsfiPqJ

Definitions:

1. s(t)sim is a deterministic input signal,

2. n(t) is simulated AWGN generated via MATLAB’s randn function,

3. (S/N)sim is the average signal-to-average noise power at the input of h(t)sys.

4. (S/N)sys is the average signal-to-average noise power at the output of h(t)sys.

The block diagram of the system is:

https://imgur.com/bWqEqy5

The two parts of the assignment that I am struggling with are:

Using MATLAB’s randn function, generate realizations of AWGN for n(t) such that a specific (S/N)sim is achieved. What is the required scale factor for randn which produces (S/N)sim=0.0 dB? In what bandwidth is ALL of the simulated noise power contained?

Using MATLAB’s built-in Butterworth and filtfilt functions implement h(t)sys, filter both the LFM signal and generated noise realizations for (S/N)sim=[−10.0, 10.0] in 0.5 dB steps (minimum). Provide a plot of (S/N)sim vs. (S/N)sys. Use a 6th Order filter having a −3.0 dB bandwidth matching the −3.0 dB bandwidth of the LFM signal.

The code I have written so far is below:

https://pastebin.com/FcyP1igX

The main issues I am having is that I'm not sure if I am implementing the scale factor on my noise signal correctly for the first part.

On the second question, once again I'm not sure if I am implementing the range of signal to noise ratio correctly, and I'm not sure how to match the bandwith of the Butterworth filter and LFM signal.

Any help or pointer would be greatly appreciated.

So I'm trying to design a 6th order Butterworth filter for one of my school clubs. The thing is, I'm going to need 3-4 circuits for my design, all implementing the same thing, with the output of each going to a MCU. I don't want inductors in my design because this is all going to be put on a PCB, and I feel like the inductors would take up too much space. I'm also concerned about their magnetic interference.

Can anyone point me to a Butterworth bandpass filter design that only uses resistors and capacitors?

Thanks Everyone. =D

Problem set, for those interested: Ok so here is the problem:

This is to be integrated into our Autonomous Robotic Boat.

There are going to be 2 under water pingers, set a different frequencies. The frequencies will be between 25kHz-40kHz. They will pulse at .5 sec intervals. The goal is to find the location of the pinger that is assigned to us.

So my plan is to have a line array of hydrophones, then EACH of the hydrophones will have their own circuit, which includes: AMP, 6th order Bandpass filter, and peak detection circuit. Then each of those output will be passed to the MCU to determine, which hydrophone got the signal first, second, third, and the time differences of each, from that plug it into an equation that determines the (x,y) coordinates relative to the current position of the hydrophones.

As for determining which pinger is the one we want to find. The MCU we are using has a freq() function, that I can use for a hydrophone without the peak detection circuit. I could also, use the (x,y) coordinates to determine that the pinger is in the general location of our "exit" gate, which we will know before the start of the run.

Hey guys, I'm working on a class project where I need to design 2 2nd order active butterworth filters, one Low Pass and one High Pass. The first opamp is the filter, the second is just an inverting amplifier to give a 20dB gain.

http://i.imgur.com/Zd0la.png is what I have so far for the Low pass, with the AC sweep simulation on the right. The corner frequency is at 1KHz, and everything looks fine.

but http://i.imgur.com/s7XIM.png is my high pass, (also with fc=1KHz) but getting a drop off after 1 decade.

Can anyone give any insight as to whats going on here? I'm stuck :/

I recently designed this fourth order Butterworth Filter. It is to have unity gain and a pass band between 0-2200Hz. Could you guys provide any insight on how I did? Is this completely wrong? How could I improve it? etc. I'm really interested in this topic of electrical engineering but am just a beginner. Here is my schematic and analysis in LTSpice. Thanks in advance!

I am trying to develop a 5ooMhz 3rd order band pass filter of the Butterworth type. I calculated everything and simulated the filter using pspice. However I am not getting the results I expected.

In order to make a bandpass filter you first have to convert it to the equivalent low pass filter. And this is what I did. But this is the point where I am not seeing what I expected at all.

The value of both resistors you see on the schematic is 5o ohms each.

Could anybody explain me what I am doing wrong for this very first step.

goal: http://imgur.com/XXTjrfY

My calculations: (I calculated the values of the components for the schematic in the middle, the one with the cross beneath it)

http://imgur.com/2A34HQe

The result of the simulation:

http://imgur.com/AndrHCm

I'm trying to use the butterworth command in matlab but getting confused with the normalised frequency bit. It says that normalised frequency is cuttoff frequency / (sampling frequency/2). I don't get why do we have to divide the sampling frequency with 2. Also, how is it that MATLAB treats this in radians, seeing that this frequency is unitless?