Dear Group,
I am a non-engineer looking to understand the frequency response to
first, second order systems. My background is not in math or
engineering, but I have read up on some books for signal processing
(eg fft).
Would anyone be able to recommend a good beginner book (like
undergraduate level or less) that I could read to gain a good
understanding of this topic? A book called, "Signals and Systems" by
Oppenheim had been recommended to me before, but I found that book
rather difficult.
Thanks!

What part of frequency response analysis are you trying to understand?
Perhaps if you could give a synopsis of your story.
Oppenheim is the classic signal processing book in the field; anything
that you read about signal processing or system dynamics is going to
touch on that material. Oppenheim _isn't_ a good self-help book, IIRC
(although it's a great book to be taught out of, and it makes a great
reference).
If you're primarily concerned with controlling systems that you've
modeled, then you want to look for titles that have the phrase "Dynamic
Systems" and the word "Control" in them.
The primary thing to remember about frequency domain analysis is that in
many ways it's a really screwy way of looking at the world. Its utility
doesn't come from how easy it is to learn -- its utility comes from how
much you can do with it once you've gotten your head wrapped around it.
It provides a huge bag of tools that can be used to analyze linear
systems. Since many real-world systems can, to some extent, be
described with linear models, this means that frequency domain analysis
can allow you to do huge amounts of work with relative ease. So
everyone who does this seriously gets their heads wrapped around it (to
the point where several people may well respond by saying "what do you
mean, 'screwy'?"), even though it can be difficult at first.

Thank you for responding to my post. I will try to describe what it
is I would like to understand. I came across this analysis by looking
at some papers that looked at frequency response (single input/output)
of real life data, not from a simulation or model in which amplitude
and phase were used to describe the "system". I came to find out this
is what is refered to as bode plots. Since then I have been trying to
"play" with some data to see what it would look like. I have read
some easier to understand signal processing books (i think it was a
book by lyon) that was not very difficulty to read considering I do
not have a math background.
Since then, I have come across some engineers who do this stuff, and
they all recommended Oppenheim's text, but as I mentioned it was a bit
difficut for me to understand (because I don't have a background in
differential equations, and has been a long time since complex
numbers). I do understand the basics of looking at the say a second
order system that has 2 integraters and gains fedback, but I would
like to learn more about that part of it. Something simple that
starts from the beginning...like "What is a first, second order
system?", "How can you look at a bode plot and interpret
it?"...something basic, that may allow me to move to the next level.
From the engineers I heard they "model" these systems, and I would
also like to understand what exactly is meant by "modeling" the system
as well.
I know this is like skipping steps as I don't have the math
background, but was hoping there would be something like the signal
processing book I read which as I mentioned was not so difficulty due
to the authors explaination and simplification. I realize a strong
background in differential equations will probably help, but I was
hoping there would be something that may help explain things in simple
terms, or started from the beginning so that I could handle the
reading.
Thanks again for the response!

Thank you for responding to my post. I will try to describe what it
is I would like to understand. I came across this analysis by looking
at some papers that looked at frequency response (single input/output)
of real life data, not from a simulation or model in which amplitude
and phase were used to describe the "system". I came to find out this
is what is refered to as bode plots. Since then I have been trying to
"play" with some data to see what it would look like. I have read
some easier to understand signal processing books (i think it was a
book by lyon) that was not very difficulty to read considering I do
not have a math background.
Since then, I have come across some engineers who do this stuff, and
they all recommended Oppenheim's text, but as I mentioned it was a bit
difficut for me to understand (because I don't have a background in
differential equations, and has been a long time since complex
numbers). I do understand the basics of looking at the say a second
order system that has 2 integraters and gains fedback, but I would
like to learn more about that part of it. Something simple that
starts from the beginning...like "What is a first, second order
system?", "How can you look at a bode plot and interpret
it?"...something basic, that may allow me to move to the next level.
From the engineers I heard they "model" these systems, and I would
also like to understand what exactly is meant by "modeling" the system
as well.
I know this is like skipping steps as I don't have the math
background, but was hoping there would be something like the signal
processing book I read which as I mentioned was not so difficulty due
to the authors explaination and simplification. I realize a strong
background in differential equations will probably help, but I was
hoping there would be something that may help explain things in simple
terms, or started from the beginning so that I could handle the
reading.
Thanks again for the response!
Remember that all this frequency-based stuff is essentially for *linear*
systems, so the DEs involved are also linear. The laplace notation used is a
shorthand way of representing those equations, if you're focussing on things
like Bode and Nyquist, then you work almost exclusively with the laplace
form, *but* remember that these days, where sampling is almost unversal, the
sampled, or 'z' domain is at least as common.
You really need to make the effort to understand the basic maths behind both
laplace and z transforms if you want to work with dynamic system analysis,
without both you'll encounter stoppers all the time. If your final objective
is process control, eg. refineries, then you'll find that the frequency
domain stuff is almost never applied in practice, the process models are
mostly too fragile to support anything more than its most basic application.
But a thorough study of time, frequency and sampled domains will give you a
basis that you need, whatever area you're working in.

You may also try the ARRL Handbook. It's written from a radio
perspective, but it tries to aim at a person with a non-math background.
Unfortunately, frequency response stuff is highfalutin math disguised
as simple algebra -- try to use it without understanding the underlying
differential equations part, and you'll be constantly bumping into
places you can't go, and you won't know why.
Essentially, an n-th order system is one with n integrators (or delay
stages, if it's sampled time). So a 2nd-order system has two
integrators, 3rd has three, etc.
Try this. It's a bit ragged -- it badly needs an upgrade -- but it may
get the point across.

formatting link

They mean "mathematical model", which is a set of differential equations
that describe the system behavior over time, and in response to
stimulus. This is a combination of mathematics (getting the equations
to represent what you think you need to represent), and art (choosing
what behaviors you think need to be represented, while leaving out the
infinite number of other factors that would take forever to include, and
forever to analyze if they were there).
You could try my book. It's written for someone who's been out of
school a long time, and has forgotten much. Unfortunately it's aimed
primarily at the practitioner who's working on a sampled-time system, so
I really don't go into continuous-time systems much at all. Moreover,
the comments I get back from it indicate that it's best for someone who
got the training long ago but then forgot -- even though I tried to make
it a gentle slope, folks who haven't had training in differential
equations find it a bit of an uphill battle. So make sure you find a
site that'll let you browse through it before you commit to any money.
It may be a good idea to just see if you can take a differential
equations class. If you don't have a community college local, I'll bet
there's some on-line thing you could do.

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