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this output: $$ y[n] = A \cos(\omega_0 n + \phi) \qquad \forall n \in \mathbb{Z} \ge 0 $$ and with double-precision floating point is stable to the extent that I have run it overnight and no change in amplitude …

there are a lot of misconceptions in the question. "The received signal is an arbitrary waveform and not [only] a sine wave of frequency $f$." it's a collection of sine waves at different frequencie …

if the two audio signals are totally uncorrelated, the the squares of the two crossfade gains should add to 1. so, to prevent that dip, your crossfade function will look more like $\sqrt{\frac{1}{2}( …

This is a continuation of the (music-dsp) thread started by Element Green titled: "Algorithms for finding seamless loops in audio" As far as I know, it is not published anywhere, although I have rece …

(The amplitude in the power spectrum is zero for all $|f|>\frac{f_\mathrm{s}}{2}$. This is what makes it bandlimited.) So now you have "white" noise that is finite energy. … , then you have to multiply that constant amplitude of $\frac{\sigma^2}{f_\mathrm{s}}$ times the magnitude-squared of the pinking filter to get the frequency-dependent amplitude of the pink noise. …

I read online that the human ear starts to hear near -10-10dB. The thing that bothers me is that this reference: is used instead of this reference: I've always thunked that the 0 dB curve is what …

same applies for $w[n]$ with an amplitude scaling factor of $A$. $$ \begin{align} \text{DFT} \left\{ w[n] \ A e^{j 2 \pi \frac{m}{N}} \right\} & = \sum\limits_{n=0}^{N-1} \left( w[n] \ A e^{j 2 \pi \frac … we're trying to find, we would take the value of the peak, wherever $k=m$, and divide that value by $S_w$ to get the amplitude of the complex sinusoid. …

I am thinking of two numbers. They add to the number 15. Tell me what the two numbers are.

I would recommend multiplying the input to the FFT by a good window and zero-padding to double the length.. Perhaps a good Kaiser with $\beta \approx 6$ or $7$. Perhaps a better window for this would …

This paper by me is a little more general in that it not only are the amplitude and phase and frequency of each sinusoid derived, but also the sweep rate on frequency and the "ramp rate" of the amplitude …