Pitch/Time Shifting of a PCM byte array

Question

I am searching for a universal algorithm that shifts pitch and time while keeping the sample rate. (I am trying to program a sound generator (sine, triangle...) as an exercise)

I just want to squeeze the samples of the sound together so it appears to be shorter and pitched higher.

It's easy if you want to speed it up with a nice number like 2 (leave out every second sample) but what if you want to speed it up by 2.5?

Can someone name an algorithm for this? (preferably in C++, but other languages are also fine)

(I spent the last 30 minutes writing an algorithm that computes averages of decimals of a number (Like the average of every 2.5 numbers). Then I realized it's totally useless so please help)

Does this approach make sense?: (Will be adding pseudocode shortly)

N is the amount of the pitch
Divide the index of every sample of the sound by N (2/2.8=0.71; 3/2.5=1.07)
For every whole number, compute the distances to the next samples (0.29; 0.07)
Value portions of distance (1-(0.29/0.36)=19%; 1-(0.07/0.36)=81%
New number (New Sample = (19%*SampleA + 81%*SampleB)/2)

Code:

byte[] input;
double f = factor;
byte[] output = new byte[ceil(input / f)];
output[0] = input[0]
for(int i = 1; i < output.length) {
    output[i] = (input[floor(i*factor)] + input[ceil(i*factor)]) / 2;
}

Answer 1

As a commenter said, look up 'Audio Resampling'. Also, maybe buy the book called 'The Art of Digital Audio' or similar. Basically, what you are doing is linear interpolation, should work. But resampling at a much higher rate should allow you to pick samples (from the denser set) close to the sample points you need for e.g 2.5 speedup. Analyzing the error from such heuristics is non-trivial, for that you need a good book.

If you like maths, read this practical classic: https://www.amazon.com/Fourier-Transform-Its-Applications/dp/0073039381 This 2nd book helps you understand what happens to the signal if you do linear interpolation between samples (it is an exercise...)