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I have a DSP exam coming up this summer and I got an abysmal mark on an assignment earlier this year. Obviously, the lecture slides are not enough for me to understand DSP, so I am wondering where can I go to form an understanding of DSP from the ground up. The topics are purely math-based and do not include any programming or Matlab skill

My skills in calculus are also quite bad.

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so I am wondering where can I go to form an understanding of DSP from the ground up.

There is a great list of resources in this answer What Resources Are Recommended for an Introduction to Signal Processing (DSP)? You should spend half an hour with each one and then decide which fits your own learning style the best.

My skills in calculus are also quite bad.

That's a problem. DSP is by nature fairly math heavy and if you lacking some fundamental skills, you will we miserable the entire time. It's like trying to build a house but all you have is a hacksaw and a bent hammer. Get the right tools first. At the very least make sure you are familiar with complex number and the associated math. There are plenty of resources to do that, including Khan Academy.

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My skills in calculus are also quite bad.

This is going to be a barrier. It may be the whole barrier. Basically, DSP is a branch of analysis -- it's a collection of mathematical techniques that you can use to easily solve a certain class of differential and difference equations. It may not look like that, but that's because for the differential equations that it makes easy, the first thing you do is abstract away the "differential equation" part, and you often don't need to go back to it.

So -- you can't wrap your head around differential equations until you've wrapped your head around calculus, and you can't wrap your head around DSP until you've wrapped your head around differential equations.

I suggest going back to some good base material (the textbook for your course, perhaps?) If you've got a textbook with problems, then start working them. If you're having trouble with the calculus involved -- go back and get sorted on that part of calculus, then get back to the DSP at hand.

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