Time-domain amplitudes of a two-band signal with a 24% (upper) and 67% (lower) bandwidth of center frequency fc . The second band is 1/2 the amplitude and approximately 1.8 times wider and twice the center frequency of the fundamental. The dotted line shows the fundamental’s time-domain amplitude for comparison.
Overlapping chirp signals due to scattering from three objects. The second and third objects are 0.5 and 5 mm, respectively, from the first.
(Top) Amplitude of the Fourier transformed signal consisting of odd harmonics acquired by summation of a signal and its inversion (left) and even harmonics produced from the signal differences (right). (Middle) Derivative of phase with respect to frequency for the odd harmonic (left) and even harmonic (right). (Bottom) Derivative of phase with respect to frequency after application of a weighting factor to remove quadratic terms.
(Color online) The experimental setup configured for (upper) normal scattering and (lower) backscattering.
(Color online) Simulation results for (left) minimization of the secondary peaks, shown for the case when the second harmonic bandwidth is twice the first. (right) Minimization of the FWHM for the same case.
(a) Impulse response of the transducer used for backscatter measurements. A linear chirp (b) is compared with a modified shaded chirp (c) created in the frequency domain and (d) a shaded chirp further modified to compensate for the transducer response. Waveforms here are for the 100% bandwidth case.
Compressed signals scattered from three wires, when the second and wires are situated 1 and 5 mm from the first, respectively. Standard first (a) and second (b) harmonic compression are compared with the extended and amplified signals using two harmonics (c) and three harmonics (d).
Compressed signals scattered from three wires, when the second and third wires are situated 1 and 5 mm from the first respectively. Standard first (a) and second (b) harmonic compression are compared with the extended and amplified signals using two harmonics (c) and three harmonics (d).
The extension method’s SNR (squares) closely follows that of the second harmonic signal (circles), and is significantly lower than when the amplification step is omitted (triangles). SNR of the first harmonic compression (diamonds) is appreciable even when the pre-compression SNR approaches 0 dB.
Compressed echoes from three 0.1 mm wires placed 0.5 and 5 mm from the first. Chirp input signals (top) modified in the frequency domain (middle) increased compression, particularly when the transducer’s response was accounted for (bottom).
Summary of FWHM measurements using first harmonic compression, second harmonic compression, extended bandwidth compression with two harmonics, extended bandwidth compression with two harmonics plus uplifting (amplification) of the second harmonic, and extended bandwidth compression with three harmonics plus uplifting of the second and third harmonics.
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