Cascading Two FIR Filters
When you cascade two FIR filters together, the output of the
first becomes the input to the second.
The order does not matter.
Either filter can be placed first, it makes no difference.
The final result is the same even though the intermediate
results are different.
The figures below can help you see this idea with two
Note how \(v[n]\) (in the top) differs from \(w[n]\) (in the bottom) but
see how \(y_1[n]\) and \(y_2[n]\) are identical.
You can also click on the filters to
see their respective frequency responses.
Now we switch the order
to see a large version of both systems.
Adding the Outputs of two FIR Filters
We can also add the outputs of two or more FIR filters
and see the combined effect. An informative experiment is the
following: Filter the signal with low-pass filter. Then filter the
original signal with a special high-pass filter having the same cutoff
frequency (called a complementary filter). Now when you add up the
two results, you get original signal back! The system below exhibits
this idea on an image. Click on the various parts of the system to
see how it works.
to see a large version of the system.