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

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G 2024-4-1

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评论： Sam Chak 2024-4-1

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);

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Paul 2024-4-1

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 2024-4-1

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@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)