Validating analysis time window

Furthermore, two sinusoid is any function of the form A sin(ω t φ), where t is the independent variable, and A, ω, φ are fixed parameters of the sinusoid called the amplitude, (radian) frequency, and phase, respectively.

Sinusoidal motion is produced by any \'pure\' vibration, such as that of an ideal tuning fork or mass-spring system.

We will see that the proper way to extract a ``short time segment'' of length from a longer signal is to multiply it by a window function such as the Hann window: We will see that the main benefit of choosing a good Fourier analysis window function is minimization of side lobe in the Fourier transform of a window function, such as the Chebyshev window, is any local maximum in the transform magnitude outside of the main lobe (response about dc).

— Click for lobes, which cause ``cross-talk'' in the estimated spectrum of a signal gives the distribution of signal energy as a function of frequency. The study of spectrum-analysis windows serves other purposes as well.

— Click for Its main-lobe width is and its first side-lobe is 13 d B down from the main-lobe peak.

Note that this is the complete window transform, not just its real part.

We obtain real window transforms like this only for zero-centered, symmetric windows.

A plot of the rectangular window appears in Fig.3.1 for length .

It is sometimes convenient to define windows so that their dc stands for direct current in electrical engineering and signal processing (as opposed to \'alternating current\').