fun stuff! For people wondering what FFTConvolve does, here it is a short bad explanation. The FFTconvolve would convert Time-domain to the frequency domain and do 1 multiplication. That changes the operations to be executed from many to 1. After an FFT all it takes is just a multiplication, while in the time domain you would have to perform many operations to get to the result. Convolution can be thought of as a polynomial multiplication, so there are a lot of multiplications involved to get the result, but if you go in the Frequency domain via FFT, then you only have 1 multiplication. So as long as the Time-domain to Freq domain Transformation can be done cheaply, then you can reduce operations from many to 1. Luckily the Fourier transform can be done cheaply on a computer as it is a mechanical transform, hence the name Fast Fourier Transform. FFT can be thought as a fixed scrambling of the bits in the bytes of the data. Please do correct all my mistakes, as I have not looked into FFT and signal processing in over a decade.
Yeah I think that's basically right. The only thing I would clarify is the frequency domain convolution becomes 1 multiplication per sample between the input signal and the filter after the FFT.
Hey Dan, the second part of the video, when you synthesize your response, is crazy *awesome* !! I still need to understand some stuff in there ( like when moving from frequencies to phase values ), but seeing how to tweak things little by little was really super useful !! thank you for this !!
Spyder is far from perfect but it makes sense in my head coming from Matlab. Lots of people like Jupyter notebook as an interactive numerical IDE, but I've never taken the time to try it.
@@DanPrince I've been using the python tools to learn DSP for a while now but I use the XCode text editor or BBEdit to write the scripts and run from the command line. Seems, even with a few headaches, Spyder would spare some of my time (especially the variable preview). Using XCode for all of it would be nice also but haven't yet assessed the amount of work involved.
Very interesting! One suggestion though, when you present functions that are related to python's library, could explain a bit more what there're doing so we can try to apply them in another environment/language, please? For instance, I have in mind the calculus/phase part. I work with Hise for my plugins and try to understand DSP. I'd like to be able to translate everything to this platform, but I don't know what's behind these functions (although I have a good idea of the overall principle thanks to your explanations, going inside the functions is THE difficult part) Cheers!
Sure! In this video I did gloss over the details faster to try and get to a more complicated demo than I have in the past. Was there a particular function that you wish I described more?
Hello Dan !! In first example, when loading the tubby file, at line 19, when keeping only sample_value != 0, aren't we getting rid also of any zero-crossing sample contained in the actual audio sample ? Great video, thank you so much for all this. I've never heard about convolution and all this explanation opens a whole new world for my hobbies =)
Its true, this line crops out any samples at exactly zero amplitude regardless of their position in the file. In practice though, it's rare for a 16 bit audio signal to have exactly zero amplitude when there are 2^16 possible values for it to take on. It's more likely that the quietest part of a recording or any zero crossings would be a small non-zero value because of the signal's noise floor, and for any samples that are exactly zero to be added digitally where it's much easier to have a perfectly silent signal.
Dan Prince loving where this series is going. I’d personally love to follow the process of getting these working on live signals, as well as getting further into different delay and reverb types. Keep up the great work!
DSP theory says a linear time-invariant system can be perfectly modelled by convolution with its impulse response. An actual spring reverb unit is probably not perfectly LTI, but close enough that convolution gives a reasonably convincing impression of it. Since the spring reverb impulse response is just an audio signal, what I'm doing in this video is to try and reconstruct it from a model of some of its components that I analyze with the plots I show in this video.
