Often it seems that old papers are the most insightful. Back then, the research cycle was shorter and scientists had more institutional support. They had more time to think.
This paper has always amazed me. It's an incredibly creative means to getting the characteristics of a recurring shape from a noisy time series signal. It's sort of like what wavelet analysis does. It's remarkably effective.
The author skips a lot of steps in his work in the paper. Here is a link to a stepwise derivation of the method.
These ramp functions are actual quite powerful and beautiful sounding when implemented in analog electronic synthesizers - by controlling the ratio of the quiescent and moving phase, and by controlling the ratio of the rise and fall times in the moving phase, you can achieve all sorts of very beautiful, rich timbral modulations with interesting harmonic behavior - particularly if your pulse generator and the envelope duration are decoupled in terms of durations. Wind, brass, reedy sounds are all possible, some cool undertones can be created, etc etc.
This is so cool! Thanks for sharing! Would you mind pointing me to where I could listen to some of the sounds produced by analog electronic synthesizers running ramp functions? I'd love to hear it. I looked through the repo and didn't find an easy way to listen.
The novel part of the method is in how it separates noise from the recurring shape in the time series. In the paper, they are separating random noise from recurring ramp shapes. But the same procedure could be implemented for other recurring asymmetric shapes in time series.
The method is really good at getting the characteristics of the recurring shapes. In the case of ramps, it's good at getting the average height of the ramps and the average duration of the ramps.
This paper has always amazed me. It's an incredibly creative means to getting the characteristics of a recurring shape from a noisy time series signal. It's sort of like what wavelet analysis does. It's remarkably effective.
The author skips a lot of steps in his work in the paper. Here is a link to a stepwise derivation of the method.
https://drive.google.com/file/d/1ytbqe-zL9j7hddm4TTU3egXdnm7...