One misconception that I had early on with this: since a lowpass filter keeps low frequencies, and a highpass filter keeps high frequencies, and a bandpass filter keeps a range of frequencies, then a bandpass filter is equivalent to simply a highpass and a lowpass filter in series. Further, I thought, since a bandpass filter always has an even number of poles, that must be because there is one pole for the highpass part and one pole for the lowpass part. Although one can create such a filter, a true bandpass filter is different than just a highpass and low pass filter, and the even number of poles has nothing to do with one for each part. Practically, it is important to understand this distinction since a two pole pair bandpass filter has a much sharper cutoff than a one pole lowpass and one pole highpass filter combined in series.
