Dr. Murthy has the most direct answer

from her very expert experience.

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I did not use the MATLAB approach,

but did work many equations by hand,

than transferred to using PartSIM.com very much for 6 years

to investigate the Analog approach to Active Filters

in large circuit configurations ( 22 OpAmp Filters in one circuit ) .

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Not knowing if you are a grad-academic or a grad-student ,

I am not sure if you are seeking a purely equation based answer

or if you are looking for a more experimental project based answer.

.

Perhaps you would benefit from examining my website

which is a large experimental project in Analog Electronics

based on the application of Butterworth active-filters

of the Multiple-FeedBack topology design.

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My research goal was concerned with active filters to help in receiving

Morse Code in the Amateur Radio Bands.

Our modular project is suitable for student perusal / study.

.

I explore both conventional and radical phase-filtering

based on application of Op-Amp Active Filters,

basically of the Butterworth design ( attached file )

and I use extensive Simulations and plots.

.

If you want a purely academic paper ( theoretical )

then I refer you you to " Deliyanis Continuous Time Filters "

which is 457 pages long. More info on request.

Or direct your questions to Dr. Murthy.

.

I hope this helps.

Yes you can, any signal can be filtered using digital filter design in matlab simulink

Artur,

I assume you are asking about a low-pass Butterworth. Here are three MATLAB functions for you to consider:

1. “LOWPASS_2nd_order.m” is a generic 2nd order lowpass. To make it Butterworth, simply set the pole quality factor Q=1/sqrt(2).

2. “BUTTERWORTH_4th_order_lowpass.m” is a 4th order Butterworth constructed as two cascaded 2nd order lowpass filters.

3. “BUTTERWORTH_8th_order_lowpass.m” is an 8th order Butterworth constructed as four cascaded 2nd order lowpass filters.

To test these and see their impulse responses, simply copy the text after “%TEST” at the bottom of the files and copy it into the MATLAB command window.

Hope it will be helpful.

Artur,

Any filter has a frequency response that describes how it works. Basically, this response is usually defined by the pass band, stop band, and the transition band. The pass band is the range of frequencies you want the filter to pass while the stop band is the range of frequencies you want to reject. Ideally, there is a cutoff value for which every frequency less than this value will pass with a magnitude of 1 and phase of zero (this frequency component passes as is). Any frequency above the cutoff value will not pass at all.

Practically, this is impossible and there must be a transition band. The value that defines the cutoff frequency usually has a magnitude response of 1/sqrt(2) or 1/2 the power of the input signal. Some filter realizations are made to control the filter response such as Butterworth, Chebyshev, and elliptical filters. Each filter has its own desired characteristics. For example, Butterworth has a flat pass band response but relatively slow transition band while Chebyshev has sharper transition but ripples in the pass band.

Back to your main question, is it possible to filter a sine wave, of course yes! Actually, the simple understanding of filtering is with sinusoidal signals. Any random signal or composite signal is a sum of sinusoidal signals which means different input frequencies. So when a composite signal passes through the filter, each frequency component is multiplied by the magnitude at this frequency and shifted by the phase of the frequency response at this frequency. The sum of these attenuated/amplified and shifted components will give you the output signal.

Now what about a sine wave? it is just a single frequency. So, the input signal magnitude will be multiplied by the magnitude of the filter response at the input frequency and the phase will be shifted WHATEVER the filter you chose. Any filter can filter a sine-wave if designed properly. It is important to note that a sine wave (single frequency) passes through the filter will always be a sine wave at the output with the same frequency but the magnitude is different and may be shifted but never distorted (unless clipped by the maximum output voltage of the system).

Example:

Butterworth filter with second degree, and cutoff frequency 100 Hz and let's focus on the magnitude not the shift.

abs(H(f)) = 1 /sqrt(1 + (f/100)^2)

input: sine wave amp = 1, freq = 100 Hz (at cutoff) ---> output: sine wave 100 Hz - amp 0.707

input: sine wave amp =1, freq = 0.01 Hz (in pass band) --> output: sine wave 0.01 Hz - amp 0.9999

input: sine wave amp = 1, freq=10000 Hz(in stop band)--> output: sine wave 10000 Hz - amp 0.0099995

Which means if you want to reject the signal, design your filter so that your signal frequency is away from the cutoff frequency in the stop band. Increasing the filter order make the attenuation stronger but with more complexity.

If you want to reject a 50 Hz signal, make your cutoff frequency much less than 50 Hz. The sampling frequency makes a limit to the input signal frequency to Fs/2. So, if you have Fs = 1000, you can input signals up to 500 Hz to your filter without aliasing. There are other features you can control as I mentioned such as the ripples, pass band attenuation, stop band attenuation, .. etc. You can search online or check the MATALB help for these information such as in this link

https://www.mathworks.com/help/signal/ref/fdesign.lowpass.html

ok