Search results
Results from the WOW.Com Content Network
4.1.3 Frequency shifting. 4.1.4 Time scaling. ... the corresponding inversion formula for "sufficiently nice" functions is given by the ... that the Gaussian ...
Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is encoded on a carrier signal by periodically shifting the frequency of the carrier between several discrete frequencies. [1]
As was our expectation, the frequency distribution can be separated into two parts. One is t ≤ 0 and the other is t > 0. The white part is the frequency band occupied by x(t) and the black part is not used. Note that for each point in time there is both a negative (upper white part) and a positive (lower white part) frequency component.
While the ordinary DFT corresponds to a periodic signal in both time and frequency domains, = / produces a signal that is anti-periodic in frequency domain (+ =) and vice versa for = /. Thus, the specific case of a = b = 1 / 2 {\displaystyle a=b=1/2} is known as an odd-time odd-frequency discrete Fourier transform (or O 2 DFT).
Thus, the maximum frequency deviation is δ = 0.5 f m where f m is the maximum modulating frequency. As a result, the modulation index m is 0.5. This is the smallest FSK modulation index that can be chosen such that the waveforms for 0 and 1 are orthogonal. A variant of MSK called Gaussian minimum-shift keying (GMSK) is used in the GSM mobile ...
Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for only a short period of time. The Fourier transform (a one-dimensional function) of the resulting signal is taken, then the window is slid along the time axis until the end resulting in a two-dimensional representation of the signal.
Taking the Fourier transform (unitary, angular-frequency convention) of a Gaussian function with parameters a = 1, b = 0 and c yields another Gaussian function, with parameters , b = 0 and /. [2] So in particular the Gaussian functions with b = 0 and c = 1 {\displaystyle c=1} are kept fixed by the Fourier transform (they are eigenfunctions of ...
In this case, the angular frequency is given by = where = + is the reduced mass and and are the masses of the two atoms. [ 19 ] The Hooke's atom is a simple model of the helium atom using the quantum harmonic oscillator.