There are several different ways that filters can be combined together. One way is to put individual filters together in series, cascading one after the other.
As an example, consider what would happen if a signal is fed through a low-pass filter followed by a high-pass filter. A block diagram of the total process is shown below.
The question is: “What is the combined effect of using these filters together?”
One of the filters reduces the amplitude of high frequencies and the other filter reduces the amplitude of low frequencies. This sounds a lot like a band-pass filter.
The total effect of the entire system can be measured and analyzed using an impulse response. If we are particular with the LPF and HPF we use, the impulse response of the series filters is the exact same as the BPF shown before.
It is also interesting to consider the result of putting multiple LPFs (or multiple HPFs) together in series. By using two LPFs, the result is also a LPF. However, it has a different slope of attenuation. The combined effect has a steeper slope.
This is one approach to create a LPF with customizable specifications.
An important thing to observe is the impulse response of putting two LPFs in series. The impulse response has a longer length. Another way to describe this is: the new LPF has a higher order.
More precisely, the new LPF uses up to 2 samples of delay. Our original, simple LPF only used 1 sample of delay.
In general, different types of LPFs can be created with 2, 3, 4,…, 10,…, 100, or more samples of delay. This allows for control over the filter specifications. We can use built-in MATLAB functions to design many different types of filters.