# Difference between filters in serial and parallel

I am trying to understand the difference between filters in serial and filters in parallel. As I understand it, serial is the more natural approach: A is applied then B, and the result is the product. Parallel filters confuse me though. If I think about it, I'd assume their outputs are added. Is this like a resistor in an electric circuit?

The book I'm reading (DSP by Jonathan Stein) says capicitors in series are high pass, while in parallel are low pass. Inductors the other way around. Not knowing much about electrical engineering, this confuses me.

Is the understanding I have shared at least correct? Any help with the capacitor and inductor example? Thanks!

If you're talking block diagrams, a pair of filters in series would yield $$H(z) = H_1(z) H_2(z)$$ The only sensible way to connect filters in "parallel" in a DSP application would be to sum them: $$H(z) = H_1(z) + H_2(z)$$ The response would be completely different (work it out with a couple of different transfer functions for $$H_1$$ and $$H_2$$ and see what I mean).

Analogies should be an aid to understanding, not a barrier. That book must be assuming folks who are familiar with circuits. So I'm going to give you a short course -- but finding a book that doesn't assume an intimate knowledge of circuits may be a good idea for you.

Here's two lowpass filters and two highpass filters, and two filters usin resistors and caps, and two filters using resistors and inductors.

Basically, a capacitor is an open-circuit at low frequencies, and a short at high frequencies. So when you arrange the capacitor as a shunt to ground, at high frequencies all the signal goes to ground, but at low frequencies it all goes to $$V_{out}$$. Conversely, when you use a cap as a series element and a resistor to ground, at low frequency the cap blocks the signal, and the resistor passes whatever is left to ground.

An inductor is the opposite -- it's a short circuit at low frequencies, and an open circuit at high frequencies. So the circuits are opposite.

But I want to stress here -- if what I just said still confuses you, get a different book. DSP is about math, not electrical circuits. If the author is relying on an intuition about electrical circuits to give you an intuition about DSP, and you don't have an intuition about electrical circuits, then you need a book that's done a better job aiming itself at you, not the electrical engineer standing next to you.

Even if it's for a class, you may want to get a different book as a suppliment.

• Thanks that was very helpful. On the book, this is a rare case of using circuitry. I actually find most of it well targeted at me compared to a couple other dsp books I've picked up, but thanks for raising the suggestion. Mar 6 at 21:49