Math of DSP Primer Anywhere?

I found this INCREDIBLE research paper of DSP for what appears to be a graduate study project (iinm) of an effect module that I wanted to work on to give myself an exciting new challenge, and build it as a (late) holiday gift for those of you that are more artistically brilliant than myself, and with which make something really remarkable, however, I have hit a rather large snag… I don’t have any idea what the symbols in the equations represent (I feel like maybe I should have learned Greek in high school or the one year of college I actually finished? Lol).

Kidding aside, I know these are upper level trig and possibly calc concepts, of which I learned many in my AP math classes in high school, but my life took a swerve off the path I was on and I drove the car off the bridge to early success and into the river of a REALLY hard life I had to learn on my own because I was stubborn and thought I had life figured out :rofl: and I figured, “where am I going to apply the ‘solve the equation for the [any concept for advanced university level math]’ knowledge in the real world?” The answer is “Here, in the world of digital audio, where I want to continue diving deeper and easily turn these concepts in my head into an algorithm that I can improve upon to make something revolutionary and new out of the idea”.

I so badly want to regain the knowledge of the math in the DSP logic that is so well understood by the likes of @taylor, @stschoen, @robertsyrett, @biminiroad, etc. and pick their brains constantly, but this is years worth of lessons I have completely forgotten in the last 17 years of my life. The forum unfortunately isn’t a university, and even though some of you seem quite qualified to be professors of these concepts, I know you have real lives that don’t include giving enormous free math classes to people who had a chance to also be where you stand now, but threw away their brain thinking they knew better as a stupid kid :laughing:

So my question in this long winded post is, “can anyone point me to a sort of “Cliff’s Notes” style of math lessons that will explain the meaning of the the Greek alphabet characters, the sub-1, sub-2, and what all the symbols mean (i.e. FOR THINGS LIKE ∆k ∗2π∆k = (φk(m+1)−φk(m)−hana ∗2πΩk)mod2π AND xˆ(n−N−α) = x(n−N)+α·[x(n−N−1)−x(n−N)]
BECAUSE I HAVE GOOGLED AND I NEVER HAVE GOTTEN TO A PAGE THAT MAKES ANY MORE SENSE THAN THE ONE I CAME FROM), so I can begin to go through it and hopefully put the :brain: puzzle back together?”

I know I am capable of picking these things back up, I just need to jog my memory to recall things like what the ‘=‘ with the ‘~’ on top of it means, and none of it can make sense again until I can clearly read the equations’ intents. Also, I have included a PDF copy of the effect thesis below, for anyone else that is Interested. Thanks in advance for any resources anyone can point to! :smiley:

A Pitch Shifting Reverse Echo Audio Effect.pdf (1.1 MB)

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≅translates to approximately equal to or isomorphic to, depending on context. This Wiki is pretty useful for when you just want to find out what the Weird looking Q is supposed to mean.

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Thanks @robertsyrett, wow there is a lot of shared meanings in the symbols I had never realized! I appreciate the guidance toward it so I can begin to sort this out :smiley:

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This is a pretty steep curve to climb if you have not had a full year of undergraduate calculus or studied discrete time mathematics/DSP at the upper division level. There is just so much encoded language in the equations that it is hard for someone that does not share the same coursework.

However, you can break some of it down because variables (in greek) are often either conventions (ω = omega = frequency), m or n or i or k are indices - others are abbreviations like φ = phi = phase derived from the first letter. The calculus comes in because ω is the first derivative of φ. The subscripts are simply to indicate a given sample (DSP is simply discrete time representation of continuous functions).

Some of the usage, like h(ana - lower case) is a rather clunky expression for an adjustment of the true frequency, Omega (capital letter). This text is complicated by the use of the English language by the author, and it appears that is not his/her first language.

The complicated expression with x (hat)(n - N - alpha) =… is describing how you would estimate a delay that is not an integer index of the signal. It uses linear extrapolation to derive that point in time.

A good way to start is to read the text very carefully since in most cases, the variables are defined in the text preceding the first use (unless it is a conventional symbol like t = time, n = sample/index, f= frequency).

But frankly, I can read the paper (maybe not fully understand, however) because I understand DSP, notation, and what they are trying to do as described in the abstract. You can’t really google this because there is too much that is unique to this author’s expression (e.g. equation) so literal searches will not yield what you are looking for.

You can send me a DM and we can talk about it over the phone, if you wish. I am not sure I fully understand the paper, but I can help you piece it together.

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Hey @jcfrgmn! Thanks for the reply :smiley: It’s been a while since I last heard from you, I hope all is going well with you and your loved ones.

I also hope that my assistance helped you to decide on a DAW that you are happy working with. There is certainly no shortage of time for working on music during this pandemic!

Thanks so much again for you willingness to help me out with this. I will reach out shortly to speak about it more in depth and I look forward to catching up soon. Thanks again, and I hope you are having a pleasant evening! :blush:

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Yes, I owe you for your advice. I went with both Logic and Live. :slight_smile:

Let me know when you would like to talk.

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