2001 IEEE International Conference on Acoustics, Speech, and by Utah) ICASSP (26th : 2001 : Salt Lake City

By Utah) ICASSP (26th : 2001 : Salt Lake City

The themes during this textual content comprise: audio and electro-acoustics; layout and implementation of DSP platforms; picture and multidimensional sign processing; speech processing; DSP chips and architectures; communique applied sciences; biomedical functions; and rising DSP purposes.

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Example text

3. The Real Field The real PB field is given by taking the real part of (80) [see (71)]. To clarify the structure of the real field we shall express it in terms of the real waveform f y (t) defined via (see (23)) Clearly, f,,( t ) decays as the parameter y increases: On the beam axis y = 0 and fy = f is strongest, but as the distance from the axis increases, y increases and the waveform f,,weakens. Substituting (87) in (81) and taking the real part, using also A(z) = AR i A I , the real PB field has the form + where y ( x , z ) is given in (83).

Noting from (45) that the far-field pattern is related to the spectral pattern via 161 + sine, we may express the beamwidth of the radiation pattern in terms of the spectral width of (60) + sin@ = D (64) Under the well-collimated conditions (54)-(53, we have a narrow spectral spread, that is, @zD<<1. (65) D. Special Case: Well-CollimatedCondition Under the well-collimated conditions (54)-(55), we can evaluate the timedependent plane-wave integral (31) with (56) in closed form. Noting from (65) that D << 1 here, we may approximate here [ = 2: 1 The resulting integral obtains the form of the inverse transform (31) for z = 0 applied d w SPACE-TIME REPRESENTATION OF ULTRA WIDEBAND SIGNALS + to Go of (56) with a!

E. , t ) = 2 8 coseiib((, t)l+nl, (45) where iio is calculated from uo(x0, t ) via (33) and 8 is the observation angle relative to the z-axis. Thus, the time-dependent radiation pattern is determined by the time-dependent plane wave iio((, t) that propagates in the spectral direction a = 3. In view of (29), Eqs. (44)-(45) can readily be identified as a Fourier transform into the time domain of the time-harmonic radiation pattern representation in (18)-( 19). Equations (44)-(45) may be derived alternatively from either the time-dependent Green's function integral (25) or the time-dependent plane-wave integral (32), thereby explaining the properties of these integrals for points in the far zone.

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