MATLAB: Does the cascade of a lowpass and a highpass Butterworth filter not produce the same results as a bandpass Butterworth filter in Signal Processing Toolbox 6.10 (R2008b)

bandpassbuttercombinationdifferentequalfilterhighpasslowpasssameSignal Processing Toolbox

I created a cascade of lowpass and highpass Butterworth filters and compared the result to a bandpass Butterworth filter – all created using either the Signal Processing Toolbox or the Filter Design Toolbox.
The following is an example of this process:
%%8th order bandpass filter
[b,a]=butter(4,[0.4 0.6],'bandpass');
Hbp=dfilt.df1(b,a);
%%Cascade of 4th order lowpass and highass filters
[b1,a1]=butter(4,0.6);          % Lowpass
[b2,a2]=butter(4,0.4,'high');   % Highpass
H1=dfilt.df1(b1,a1);
H2=dfilt.df1(b2,a2);
Hcas=dfilt.cascade(H1,H2);
I expected "Hcas" and "Hbp" to be equivalent filters. However, executing the following command shows that this is not true:
fvtool(Hbp,Hcas)

Best Answer

This is actually the expected result and is due to the fact that the Signal Processing Toolbox does not cascade a lowpass and a highpass filter to create a bandpass IIR filter. Instead, it first creates a lowpass prototype and then uses a "Transformation Function" to convert it to a bandpass filter as described by the following help documentation in Signal Processing Toolbox 6.10 (R2008b):
web([docroot '/toolbox/signal/f4-9099.html#f4-9199'])
For the theoretical background information, please refer to the references mentioned in the following help documentation:
web([docroot '/toolbox/signal/f4-19497.html'])
web([docroot '/toolbox/filterdesign/ug/f2-4793.html'])
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