Low pass filter design

Hi,

Is it good Idea to design low pass filters (moving average , FIR filter, Kalman filter, Butterworth and Chebyshev filter) with same filter parameters (cut off frquancy, filter order etc.) for comparision purpose inorder to filter the higer frequancy noise?

For the selction of best filter to filter higher frequancy noise.

Answer 1

[Star Strider]

My preference would be an elliptic IIR filter for efficiency. See the documentation for ellip for details. For best results, begin with ellipord, and get the [z,p,k] output from ellip, then use second-order-section representation for stability with zp2sos. Use that result with filtfilt to do the actual filtering.

[Bob]

Thank you for the answer, it is helpfull. But is it fine to use same filter parameters too?

[Star Strider]

As always, my pleasure!

To get equivalent results, it would be necessary to use the same essential filter parameters (sampling frequency, Nyquist frequency, passbands and stopbands) although those differ in how you present them as function arguments in FIR and IIR filter functions. The elliptic filter is the most efficient filter design I have found, so I generally use it unless I need a multi-band filter, then I use a FIR design.

[Bob]

Thanks :)

[Star Strider]

As always, my pleasure!

I can help with specific designs, if you need it. Also, consider the lowpass function (R2018a and later releases).

[Bob]

Is the second order low pass filtering is good with filter like moving average , FIR filter, Kalman filter, Butterworth and Chebyshev filte ? if yes why ?

If not which order filter can be optimal or best ? to filter high frequancy noise? what are the thinking around selcting the filter order?

[Star Strider]

The order essentially is the number of delay elements (usually corresponding to the number of poles) in the filter. I prefer higher-order filters, since they have narrower transition zones (and steeper cutoff regions). The order depends on what the filter is supposed to do, in the context of the signal it is supposed to work with.

There is no universal order that works best in all situations. An IIR elliptic filter with an order of about 6 can do as well or better than a FIR filter of a much higher order (perhaps at least 10 times that) to do the same essential operation. However to create a filter with multiple passbands and stopbands, IIR filters would have to be connected in parallel, while one FIR filter would work.

There is no one best answer to this, since applications differ and filter designs to accomplish those applications differ. A second-order IIR filter can work quite well if the requirements match what the filter can do (for example filter out high-frequency noise that is not close to the desired signal in the frequency domain). A second-order FIR filter would likely not perform well, regardless of the application.

[Bob]

Really understandable explanation here,

what if I want to use similar filter order for IIR and FIR filter for comparsion purpose for same data, as you mention above that filter parameter must be same to obtain the equivalent results, would 6th order filter do the similar or equvalent job (remove higher frequancy noise) in both FIR and IIR case?

if not which order could fit the best to both the filters

[Star Strider]

Thank you!

I encourage you to experiment with this. For example, for the IIR design, design a 6th-order elliptic filter and a 6th-order Butterworth design to compare it with. For the FIR design, I would use the fir1 function, although others are applicable. Choose the one that works best for you.

Use the freqz function on all of them to demonstrate the filter Bode plots. The freqz documentation explains how to use it with both types of filters.

[Bob]

Thank you so much

[Star Strider]

As always, my pleasure!