You may take a look at Volumes of Solids of Revolution. A Unified Approach which cites the article by Walter Carlip, Disks and Shells Revisited and Eric Key, Disk Shells and inverse functions, both collected in A calculus collection
There is an area of differential geometry that has the...
In analyzing a microphone signal, I imagine you could be intrested in understanding if it has any structure that can be explored by other algorithms, or you may be intrested in seperating the sound into perceptual components, such as voice and a guitar, or you may be trying to reduce the noise...
Assuming you have are using the same conventions as matlab does for the fast Fourier transform, then when Fourier transforming an array of real numbers, the result should satisfy xk = conjugate(x1024-k) for arrays that start at zero and have 1024 entries. The frequency calculation for the...
I think it is correct. The Fourier transform of sin(a t) is a sum of two Dirac deltas up and down from the base frequency a. Your plot shows the discretization of those deltas at 1/4 and 3/4 of the range.
I imagine this sounds confusing because the sine is a "pure tone" and the power...
I suspect that the passage you quote from Nowlan, reflect some remarks Mandelbrot penned in his A maverick's apprenticeship. In the Self-Discovery section he explains how he used geometrical tricks to solve algebra and analytical geometry problems. He does not give details, but the method of...