If $f$ is a function on $R^1$ of $\Lambda$-bounded variation and period $2\pi$, then its $n$th Fourier coefficient $\hat{f}(n) =O(1/\sum^n_1 1/\lambda_j)$ and its ...

The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field.

A mathematical theorem stating that a periodic function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which ...

The representation of a periodic sound or waveform as a sum of Fourier components (i.e. pure sinusoidal waves). According to the Fourier theorem, periodic sound may be shown to consist of sine waves ...

The first part of this series described how data flows through processing steps that create a moving average of stock prices over 65 days. Finite-impulse-response (FIR) filters use the same data-flow ...