Roger G. Pridham

A novel approach to digital beamforming

For many sonar applications, the sensor outputs of a hydrophone array are sampled at a rate significantly higher than that required for waveform reconstruction when digital beamforming is used. The reason for this is that the number of synchronous, or ’’natural,’’ beampointing directions is proportional to the beamformer input rate. This paper presents an implementation of a digital beamformer that achieves the desired synchronous beams while minimizing the sensor channel sampling rate requirement. The technique employs zero padding of sensor data followed by digital interpolation filters to achieve vernier beamformer delays. Interpolation filtering can be done either at the beamformer input or output to minimize processing requirements. The resulting structure realizes a hardware savings since both A/D converter and cable bandwith requirements can be traded off against digital processing complexity to achieve an optimal partitioning.

Shifted sideband beamformer

A fundamentally different time domain beamformer structure is described which can be used to process bandpass sensor signals efficiently. The beamformer operates directly on complex, frequency translated, single sideband representations of the input signals to obtain a similar representation of the beam output. Such representations are typically obtained by complex demodulation of the signals to facilitate the use of bandwidth sampling procedures. This new technique, which is referred to as the shifted sideband beamformer, is functionally a time-domain beamformer but it combines attributes of both time-domain and frequency-domain beamforming. Shifted sideband beam-forming has the advantage that beamformer vernier delay and throughput requirements depend on the frequency content of the translated band rather than of the original band. This paper discusses the potential hardware savings associated with shifted sideband beamforming in terms of analog to digital conversion, cable bandwidth, digital processing and, also, signal conditioning hardware. The impact of delay quantization on beam-pattern structure is compared for a shifted sideband and a conventional digital implementation. Beamformer throughput is also analyzed for both implementations. A further reduction in the beamformer throughput requirement is demonstrated by the use of digital interpolation in conjunction with the shifted sideband beam-forming concept.

Sonic direction system

A system for the determination of the direction of a source of sound in water utilizing the finite amplitude effect. A narrow beam of sonic energy at a frequency higher than that of the source is projected in a direction opposite the direction of the source. A hydrophone receiving beam intercepts the projector beam at a distance from the projector thereof, the distance being sufficient to permit a finite amplitude non-linear interaction of the projector beam energy and the energy of the source via a virtual end-fire array. Cross-modulation products resulting from the non-linear interaction are received by the hydrophone, the precision of measurement being dependent on the directivity pattern of the virtual end-fire array.

Imaging of Volume Objects by Shadow Casting

A novel technique for imaging the spatial distribution of radio isotopes is described that has application in diagnostic Nuclear Medicine. The penetrating nature of gamma and X-ray radiation renders conventional imaging techniques useless, and scanning methods or shadow casting techniques employing restrictive apertures comprised of an opaque material are required. The new technique consists of using coded apertures that enclose or partially enclose the object to cast shadow patterns on a recording media. For cylindrical and spherical shadowing configurations, the shadow pattern is shown to specify the three-dimensional Fourier Transform of the source on concentric cylinders or spheres. By appropriate aperture design, this sampling contains sufficient information to permit true volume reconstruction. This is unlike previous shadowing techniques using planar geometries, where the encoding of depth by the scale of the aperture pattern placed a fundamental restriction on the relation between depth and lateral resolution. The new imaging configuration is such that the physical constraints of the aperture construction, that prohibited the planar system from achieving high spatial resolution, are largely removed. In deriving the new imaging concept, this paper addresses the fundamental dimensionality-reduction question of how three-dimensional source information is encoded onto two dimensions, with detailed results presented for the cylindrical and spherical geometries. In addition to identifying the factors that affect the fidelity of the new system, results are presented regarding the trade-off between resolution and noise behavior.

Relationship of second harmonic absorption coefficient to nonlinear attenuation of the fundamental

Woodsum [J. Sound Vib. 69, 27–33 (1980)] proposed a method for suppressing the saturation that arises from the distortion of a finite‐amplitude wave during propagation. The method is based on the introduction of an agent into the medium that selectively absorbs the second harmonic of the fundamental. While the validity of the proposed method is not in question, the method of analysis used in the original paper was based on numerical solutions of coupled nonlinear equations, which offered no simple intuitive explanation for the effect. Derived here is a simple, intuitive, analytical solution for the amplitude of the fundamental, which supports the previous result and which is valid for a medium having arbitrary dissipation and dispersion properties. The original conclusion is generalized to include saturation reduction via introduction of dispersion as described by Zablotskaya and Soluyan [“A Possible Approach to the Amplification of Sound Waves,” Soy. Phys. Acoust. 13, 254–256 (1967)].

Shifted band beamformer: Theory and concept

This paper introduces a fundamentally different beamformer structure which can be used to process bandpass sensor signals.The beamformer operates directly on frequency translated versions of the input signals to compute a frequency translated version of the beam output. This new technique, which is referred to as the shifted band beamformer, is functionally a time domain beamformer but it combines attributes of both time and frequency domain beamforming. It is especially compatible with systems where the sensor data is initially basebanded to facilitate the use of bandwidth sampling procedures. Beamformer vernier delay and throughput requirements are relaxed since the delay quantization and beam output rate depends on the highest frequency component of the basebanded signal rather than that of the bandpass signal. The shifted band beamformer can also use interpolation [R. G. Pridham and R. A. Mucci, “A Novel Approach to Digital Beamforming,” J. Acoust. Soc. Am. 63, 425–434 (1978)] to achieve further hardw...

Nearfield parametric sources of rectangular aperture

This paper describes a useful nearfield parametric source model for rectangular apertures of large aspect ratio. The model is based on a technique which has been successfully applied to circular apertures by J. C. Lockwood in a companion paper presented in this session. Specifically, the interaction region is subdivided into elemental virtual source apertures which radiate difference frequency energy. The existence of diffraction effects depends on the size and curvature of the virtual aperture and its distance from the field point. When diffraction is important, a field point may reside in the nearfield, cylindrical region, or farfield of an aperture. Lossless correction factors are derived which permit nearfield secondary source level and beampattern predictions to be made using a farfield parametric source model such as that developed by Moffett, Mellen, and Konrad (7th Int. Symp. Nonlin. Acoust. (August 1976), p. 19–21. This relatively simple model permits rapid computation of parametric source perfor...

Digital interpolation beamforming; concept and theory

For many applications, digital beamformers require an input rate which is significantly higher than that required for waveform reconstruction to achieve an adequate set of synchronous beams. Typically, this high rate is realized in the A/D conversion of the sensor outputs. A novel alternative, discussed in this paper, is to sample the sensors at a rate consistent with the Nyquist criterion and implement vernier beamformer delays by digital interpolation. This technique, which is referred to as digital interpolation beamforming, permits an efficient partitioning between A/D converter and cable bandwidth requirements and digital processing complexity. The basic structure of an interpolation beamformer is presented. It is shown that interpolation filtering and beamforming can be interchanged to minimize digital processing. Beam‐pattern degradation due to interpolation error is derived and interpreted for the special case of a line array.

Simple model for describing the interaction of infinitesimal and finite‐amplitude waves

A phenomenological model is given that approximately describes the interaction of infinitesimal and finite‐amplitude waves in a viscous medium. The model, which represents the interaction as a modulation process, can treat realistic propagation eases, including spreading and nonlinear attenuation. For the parametric receiver, the model gives the correct expressions for arbitrary pump propagation (including the nearfield of a source) with nearfield and farfield signals. When applied to the problem of sound absorption by sound, the model yields the induced attenuation coefficient given by Westervelt [P.J. Westervelt, J. Acoust. Soc. Am. 53, 384(A) (1973)] for the case of an infinitesimal wave propagating in an intense isotropic noise background.

A Modified Coupled Modal Form of Burgers' Equation

The coupled modal form of Burgers equation is modified as follows: (1) Only the primary frequencies and first‐order field (i.e., sum, difference, and double) frequencies are retained in the spectral vector. (2) The amplitudes of the first‐order field components are approximated by substituting the unknown values of the primary wave attenuation into the results of first‐order perturbation theory. This procedure, which is similar to Westervelts energy conservation approach [P. J. Westervelt, in Proc. Int. Congr. Acoust., 3rd, L. Cremer, Ed. (Elsevier, Amsterdam, 1960), p. 316] results in a set of modified equations which can be decoupled. These modified equations are used to solve for the attenuation of the primary waves for several cases of interest.