1. What is Coded Excitation? (Coded Excitation이란 무엇인가)

Significance of coded excitation in ultrasound

The image quality of the ultrasound scanning system depends on resolution and penetration depth. Ultrasound is always attenuated when they pass through human tissue, bone, blood, and so on.

There is a trade-off relationship between resolution and penetration depth of ultrasound.

A transmitting wave with a short wave $it means it has high frequency$ shows high contrast resolution while it shows low penetration depth. it is because high-frequency waves are easily scattered and attenuated in the medium. $that's why the sky color is blue$

Fig 1. three different ways of modulation (출처는

여기)

On the other hand, when you transmit a wave of long wavelength, you would get a low contrast resolution $it looks blurred$ but it has better SNR and more energy $Signal to Noise Ratio$ so it goes deeper than short-wavelength wave. $That's the same reason why sunset is red color.$

In order to get a high-quality image, there are several ways to get there. First, we can make the amplitude of a transmitted wave of a short wavelength. It works well but we can't do it when we observe the human body because of safety issues. Second, we can process a received wave after transmitting a long-wavelength wave. We can make the resolution high with low-resolution data. However, We should first modulate our transmit wave. It is called 'Coded Excitation'.

We can classify different kinds of coded excitation by how we modulate a transmitted wave. There are three different kinds of modulating ways: phase modulation, frequency modulation, and amplitude modulation. $figure 1$.

Phase Modulation $PSK in digital$

In every modulation, there are three-component. unmodulated carrier wave$input$, modulating wave$input$, and a modulated carrier wave$output$. In phase modulation, we modulate a phase of carrier wave along the y-component of modulating wave. As the definition of phase modulation from Wikipedia, It encodes a message signal as variations in the instantaneous phase of a carrier wave. (more information is here)

Fig 1. Blue: carrier signal, red : modulating signal , green : modulated signal carrier. $Wikipedia$

Barker Code

As the definition of Barker code in Wikipedia, Barker code is a finite sequence of digital values with the ideal auto-correlation property. The auto-correlation is the convolution between a signal and its flipped one. The auto-correlation of a barker code shows high amplitude at zero and small amplitude at the other side. The Ratio between the main lobe$center$ and side lobe is exact the same as the length of the code. for instance, if we auto-correlate a barker 7 code and we can get the main lobe whose amplitude is 7 times bigger than that of side lobes. By the simple characteristic and easy way to make matched filter of itself, Barker code is one of the representative methods of Phase Modulation in Ultrasound coded excitation. (more information is here)

 

Fig 2. Auto-Correlation of Barker 7 Code $Wikipedia$

Frequency Modulation $FSK in digital$

According to Wikipedia, Frequency Modulation$FM, FSK in digital$ encodes the signal of a carrier wave by changing the instantaneous frequency of the wave. In digital data, the frequency may represent 0 or 1 digit. (more information is here)

 

Fig 4. Compare Amplitude Modulation and Frequency Modulation $Wikipedia$

Chirp

Chirp is a signal whose frequency is increasing or decreasing to the time domain. The former is called up-chirp and the latter one is called down-chirp. In ultrasonic coded excitation, a single linear chirp $sinusoidal function$ and its filtered one with Blackman-Harris window. As same with the Barker code, we can apply auto-correlation to the chirp signal to get a center-focused wave. (more information is here)

Fig 5. A single sinusoidal wave $up-chirp wave$ $Wikipedia$

 

Fig 6. Autocorrelation of a sinusoidal wave

Simple Matlab code for making Fig 6. is below.

clear all 
%% Generating Chirp Wave 
% Set characteristic 
hchirp = dsp.Chirp( ... 
					'InitialFrequency', 0,... 
                    'TargetFrequency', 10, ... 
                    'TargetTime', 10, ... 
                    'SweepTime', 100, ... 
                    'SampleRate', 50, ... 
                    'SamplesPerFrame', 500); 
chirpData = (step(hchirp))'; 
evenFlag = mod(minute(datetime('now')),2); 
if evenFlag 
	chirpData = fliplr(chirpData); 
end 
%% Autocorrelation  
% You need a matlab toolbox to use xcorr() method in matlab 
[c,lag] = xcorr(chirpData); 
%plot 
plot(lag, c) 
title('auto correlation of a sinusoidal wave')

 

Send me an email if you find something wrong with this article. $gotocern@dgist.ac.kr$

 

 

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