Why does the cascade of a lowpass and a highpass Butterworth filter not produce the same

Z
Zayden · Mar 13, 2021 · 1.9K views
Question
Why 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) ? 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)
Expert Answer
Profile picture of Neeta Dsouza
Neeta Dsouza PhD Expert
Answered Aug 25, 2026
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'])
100% Run Guarantee 3-Hour Fast-Track Delivery

Need a Custom Version or Complete Simulation for This Problem?

Our 500+ PhD engineers build, debug, and optimize working MATLAB scripts and Simulink (.slx) models tailored to your exact assignment rubrics with zero plagiarism.

Tested on MATLAB R2024b / R2026a
Turnitin 0% Plagiarism Report
Free 7-Day Revisions Guarantee
Have a different question? Ask here

Get a Free Consultation or a Sample Assignment Review!