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Time and frequency constrained sonar signal design for optimal detection of elastic objects
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10.1121/1.4794370
/content/asa/journal/jasa/133/4/10.1121/1.4794370
http://aip.metastore.ingenta.com/content/asa/journal/jasa/133/4/10.1121/1.4794370

Figures

Image of FIG. 1.
FIG. 1.

Model of received signal , and associated detector . is the transmitted signal; is the impulse response of a random LTI filter that models channel interference induced by the transmit signal; is the LTI impulse response of the object to be detected; and represents ambient noise.

Image of FIG. 2.
FIG. 2.

Diagram of spherical target used in examples.

Image of FIG. 3.
FIG. 3.

(Color online) Example: Elastic target in colored noise and white reverberation. (Top) Spectrum of optimal signal based on the Resonance Scattering Theory (RST) model of the sphere (solid line with large dots), spectrum of optimal signal assuming point target (dashed-dotted line) LFM (dashed line), target spectrum (small dashed line with large dots), and additive noise spectrum (solid line), (bottom) ROC curves for optimal design based on the RST model of the sphere (solid line with large dots), optimal design based on point target assumption (dashed-dotted line), and LFM (dashed line).

Image of FIG. 4.
FIG. 4.

(Color online) Minimum duration solution yielding narrow pulse width and high peak energy. (Main panel) Spectrogram with 20 dB dynamic range, (left panel) magnitude spectrum of optimal signal , (bottom panel) time series of optimal signal .

Image of FIG. 5.
FIG. 5.

(Color online) Block diagram showing the relationship between signal design approaches.

Image of FIG. 6.
FIG. 6.

(Color online) Example 1: Signal design results for . (Upper left) Time-domain signal from modified formulation (dashed-dotted line) and minimum duration solution (solid line). (Upper right) Optimal spectrum (solid line) and spectrum from modified solution (dashed-dotted line). (Bottom) ROC curves for optimal spectrum (solid line), spectrum from modified solution (dashed-dotted line) and LFM spectrum (dashed line). Note that in each of these three subfigures the minimum duration solution overlays closely with the modified Slepian solution since epsilon is small.

Image of FIG. 7.
FIG. 7.

(Color online) Example 2: Signal design results for . (Upper left) Time-domain signal from modified formulation (dashed-dotted line) and minimum duration solution (solid line). (Upper right) Optimal spectrum (solid line) and spectrum from modified solution (dashed-dotted line). (Bottom) ROC curves for optimal spectrum (solid line), spectrum from modified solution (dashed-dotted line) and LFM spectrum (dashed line). Note that in each of these three subfigures the minimum duration solution does not overlay closely with the modified Slepian solution since epsilon is large.

Image of FIG. 8.
FIG. 8.

(Color online) Magnitude spectrum of target (dashed-dotted line) for each shell thickness 1 cm (top), 5 cm (middle), and 10 cm (bottom). Solution to Eq. (39) (solid line) is given in each of the three panes, while the optimal magnitude spectrum based on only the 5 cm shell (dashed line) is given in the center pane.

Image of FIG. 9.
FIG. 9.

(Color online) ROC curves assuming 1 cm shell (top), 5 cm shell (middle), or 10 cm shell (bottom) is insonified by optimal design based on 5 cm shell (dashed line), the solution to Eq. (39) , or a LFM signal with bandwidth . From these ROC curves we see that the performance loss that results from incomplete knowledge of the target is not as severe when using the solution to Eq. (39) .

Tables

Generic image for table
TABLE I.

Material properties of shell and surrounding environment.

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/content/asa/journal/jasa/133/4/10.1121/1.4794370
2013-04-03
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Time and frequency constrained sonar signal design for optimal detection of elastic objects
http://aip.metastore.ingenta.com/content/asa/journal/jasa/133/4/10.1121/1.4794370
10.1121/1.4794370
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