Sentence examples for basis of complex exponentials from inspiring English sources

Now, to apply the RR method, we choose the Fourier basis of complex exponentials on [0, 1], { exp { 2 π j k } } k = - ∞ ∞.

In the same manner as Fourier transform can be defined as being a projection on the basis of complex exponentials, the wavelet transform is introduced as projection of the signal on the basis of scaled and time-shifted versions of the original wavelet (so-called mother wavelet) in order to study its local characteristics [25].

The latter of the following two questions has been raised by Khrushchev, Nikolskii, and Pavlov: Can every frame of complex exponentials {eiλnx} in L2 be made into a Riesz basis by removing from {eiλnx} a suitable collection of the functions eiλnx.; can every Riesz sequence {eiλnx} in L2 be made into a Riesz basis by adjoining to {eiλnx} a suitable collection of exponentials eiλnx ∉ {eiλnx}?

Due to multipath propagation, a large number of complex exponentials must be evaluated and summed up.

with Q = ∑ k = 1 K L k being the total number of complex exponentials in the signal.

The time variation of each tap is then composed of a superposition of complex exponential basis functions with frequencies on the same DFT grid as the BEM of the time-varying channel.

We discuss the stability of complex exponential frames in,.

We describe the theoretical solution of an approximation problem that uses a finite weighted sum of complex exponential functions.

The candidate basis functions include complex exponential (Fourier) functions [14, 16], polynomials [17], wavelet [18], discrete prolate spheroidal sequences [19, 20], etc. BEMs can well describe the time variations of channel, and thus achieve better approximation performance than symbol-wise AR models [21].

Stated more generally, this problem asks for a determination of those bounded Borel sets Ω in Rk such that L2 has an orthogonal basis of Fourier frequencies (spectrum), i.e., a total set of orthogonal complex exponentials restricted to Ω.

This method models the waveform samples by means of a linear combination of M complex exponentials.