Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Rectangular and Triangular Pulse Function01:19

Rectangular and Triangular Pulse Function

The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Convolution Properties II01:17

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
Impulse Response01:17

Impulse Response

The impulse response is the system's reaction to an input impulse. In an RC circuit, the voltage source is the input, and the capacitor's voltage is the output. The system's state and output response before and after input excitation are distinctly defined.
Kirchhoff's law forms an input signal equation, with the capacitor's current and voltage providing the output. Substituting the current and dividing by RC yields a differential equation. The output for an impulse input is the impulse...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Feasibility of a novel blood noise reduction algorithm to enhance reproducibility of ultra-high-frequency intravascular ultrasound images.

Circulation·2000
Same author

Automated contour detection for high-frequency intravascular ultrasound imaging: a technique with blood noise reduction for edge enhancement.

Ultrasound in medicine & biology·2000
Same author

Multifrequency holography using backpropagation.

Ultrasonic imaging·1986
See all related articles

Related Experiment Video

Updated: Jul 7, 2026

A Stable Phantom Material for Optical and Acoustic Imaging
04:54

A Stable Phantom Material for Optical and Acoustic Imaging

Published on: June 16, 2023

An improved approximation for the spatial impulse response of a rectangular transducer.

T J Teo1

  • 1Boston Scientific Corporation, 2710 Orchard Parkway, San Jose, CA 95134-2012, USA. teot@bsci.com

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
|February 5, 2008
PubMed
Summary
This summary is machine-generated.

A new quadrilateral function improves spatial impulse response approximation in 1.5 D arrays. This method is superior to the trapezoidal approximation for transducers with an aspect ratio near 10.

More Related Videos

A Methodological Protocol and Considerations for Transcranial Ultrasonic Stimulation in Exploratory Clinical Human Studies
09:47

A Methodological Protocol and Considerations for Transcranial Ultrasonic Stimulation in Exploratory Clinical Human Studies

Published on: December 12, 2025

The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements
09:10

The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements

Published on: December 5, 2025

Related Experiment Videos

Last Updated: Jul 7, 2026

A Stable Phantom Material for Optical and Acoustic Imaging
04:54

A Stable Phantom Material for Optical and Acoustic Imaging

Published on: June 16, 2023

A Methodological Protocol and Considerations for Transcranial Ultrasonic Stimulation in Exploratory Clinical Human Studies
09:47

A Methodological Protocol and Considerations for Transcranial Ultrasonic Stimulation in Exploratory Clinical Human Studies

Published on: December 12, 2025

The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements
09:10

The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements

Published on: December 5, 2025

Area of Science:

  • Acoustics
  • Array Signal Processing

Background:

  • The spatial impulse response (SIR) is crucial for accurately modeling acoustic fields.
  • Current approximations, like the trapezoidal function, have limitations in specific scenarios.
  • Transducer element geometry significantly impacts the accuracy of SIR approximations.

Purpose of the Study:

  • To introduce a novel quadrilateral function for approximating the spatial impulse response.
  • To demonstrate the superiority of the quadrilateral approximation over the trapezoidal one.
  • To define the conditions under which the quadrilateral approximation is most effective.

Main Methods:

  • Developing a generalized quadrilateral function to model the spatial impulse response.
  • Comparing the accuracy of the quadrilateral and trapezoidal approximations.
  • Analyzing the performance based on transducer element aspect ratio, specifically around 10.

Main Results:

  • The proposed quadrilateral function encompasses the trapezoidal function as a special case.
  • The quadrilateral approximation demonstrates superior accuracy for the true spatial impulse response.
  • This improvement is particularly notable for transducer elements with an aspect ratio of approximately 10.

Conclusions:

  • The quadrilateral function offers a more accurate approximation of the spatial impulse response in the far field.
  • This enhanced accuracy is significant for 1.5 D array applications with specific transducer geometries.
  • The findings provide a valuable tool for improving acoustic field modeling and transducer design.