How do you design a filter cascade with 4 filters total?

I am looking to pass raw time-series data through a sequence of 4 filters. I've attempted to construct a filter cascade using the DSP Systems Toolbox, but the resulting Bode diagram doesn't make sense. Additionally, the filtered signal has a considerable reduction in amplitude (~10000x smaller than the original). I am assuming there is a way to correct this in the gain settings?

I would ideally like to combine filters H2 & H3 to act as one bandpass filter and H1 and H4 as another. I chose to employ four distinct HP/LP filters, rather than 2 bandpass filters, because they have different orders. Let me know if I need to clarify anything. Thanks.

H1 = dsp.LowpassFilter('FilterType', 'IIR','FilterOrder',3, 'NormalizedFrequency', false, 'PassbandFrequency', 85, 'StopbandFrequency', 95, 'SampleRate', 500, 'DesignForMinimumOrder', false);

H2 = dsp.LowpassFilter('FilterType', 'IIR','FilterOrder',1, 'NormalizedFrequency', false, 'PassbandFrequency', 120, 'StopbandFrequency', 130, 'SampleRate', 500, 'DesignForMinimumOrder', false);

H3 = dsp.HighpassFilter('FilterType', 'IIR','FilterOrder',2, 'NormalizedFrequency', false, 'StopbandFrequency', 0.1, 'PassbandFrequency', 1, 'SampleRate', 500, 'DesignForMinimumOrder', false);

H4 = dsp.HighpassFilter('FilterType', 'IIR','FilterOrder',1, 'NormalizedFrequency', false, 'StopbandFrequency', 0.1, 'PassbandFrequency', 4, 'SampleRate', 500, 'DesignForMinimumOrder', false);

Final_Filter = dsp.FilterCascade(H2,H3, H1, H4);

[Star Strider]

I don’t have the DSP System Toolbox, and since the online Run feature still isn’t working, I can’t run your code here.

It seems to me that the filter orders are too low to provide reasonable filtering. I would probably use at least 6th-order filters. Also, the documentation on cascade (that may be the correct function here) suggests:

• ‘To see the list of System objects you can pass to the cascade method, type dsp.FilterCascade.helpSupportedSystemObjects’

since it seems to support only FIR filters.

One option is to check it with Signal Processing Toolbox filters. The scaleFilterSections function (introduced in R2023b) and sos2ctf function (2024a) now have the ability to cascade second-order-section representations of IIR filters (there are similar functions for other representations), so that might be something to consider.

If the Run feature was up, I could test this and post it as an answer (if it supoprted my hypothesis here). Since I can’t test it, I’ll keep it as a comment.

[Paul]

@G

Would be helpful to get more information, like why you think the Bode diagram doesn't make sense, and the input for which you think the output is incorrect.

Also, when I ran this in 2022a, all four calls resulted in the warning:

Warning: The StopbandFrequency property is not relevant in this configuration of the System object.

Do you see that as well? If so, it might be a clue that that H1-H4 might not be yielding the expecte responses. Hard to say without knowing more on what the end goal is.

[Sam Chak]

@G, The order of the IIR filter is probably too low to meets the filter design specifications. If it is acceptable to let the DSP to auto-design the minimum order filter that meets the filter design specifications, then try the following:

H1 =  dsp.LowpassFilter('FilterType', 'IIR', ...
                        'DesignForMinimumOrder', true, ...
                        'PassbandFrequency', 85, ...
                        'StopbandFrequency', 95, ...
                        'SampleRate', 500)

H2 =  dsp.LowpassFilter('FilterType', 'IIR', ...
                        'DesignForMinimumOrder', true, ...
                        'PassbandFrequency', 120, ...
                        'StopbandFrequency', 130, ...
                        'SampleRate', 500)

H3 = dsp.HighpassFilter('FilterType', 'IIR', ...
                        'DesignForMinimumOrder', true, ...
                        'PassbandFrequency', 1, ...
                        'StopbandFrequency', 0.1, ...
                        'SampleRate', 500)

H4 = dsp.HighpassFilter('FilterType', 'IIR', ...
                        'DesignForMinimumOrder', true, ...
                        'PassbandFrequency', 4, ...
                        'StopbandFrequency', 0.1, ...
                        'SampleRate', 500)
                    
Final_Filter = dsp.FilterCascade(H2, H3, H1, H4)