The Zoom Wigner transform and its application to the analysis of blood velocity waveforms

R I Kitney1, H Talhami

  • 1Department of Electrical Engineering, Imperial College, London, U.K.

Related Concept Videos

Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...
Doppler Effect - I00:56

Doppler Effect - I

The Doppler effect and Doppler shift were named after the Austrian physicist and mathematician Christian Johann Doppler in 1842, who conducted experiments with both moving sources and moving observers. Consider an observer standing on a street corner, observing an ambulance with a siren sound passing by at a constant speed. The observer experiences two characteristic changes in the sound of the siren. Initially, the sound increases in loudness as the ambulance approaches and decreases in...
Doppler Effect - II01:05

Doppler Effect - II

The Doppler effect has several practical, real-world applications. For instance, meteorologists use Doppler radars to interpret weather events based on the Doppler effect. Typically, a transmitter emits radio waves at a specific frequency toward the sky from a weather station. The radio waves bounce off the clouds and precipitation and travel back to the weather station. The radio frequency of the waves reflected back to the station appears to decrease if the clouds or precipitation are moving...
Properties of the z-Transform I01:17

Properties of the z-Transform I

The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
Relation of DFT to z-Transform01:20

Relation of DFT to z-Transform

The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the terms of...
Applications of Integration to Find Blood Flow01:27

Applications of Integration to Find Blood Flow

Blood flow through a cylindrical blood vessel can be mathematically described using the principles of laminar flow, a regime in which fluid moves smoothly in parallel layers. In this model, the velocity of the blood is not uniform across the cross-section of the vessel; rather, it varies with the radial distance from the center. The maximum velocity occurs along the central axis, decreasing progressively toward the vessel walls, where it reaches zero due to viscous drag.Approximating Blood...