Ultra sound problem

Tackle today – ideas for Assignment 2

Describe the ultrasound problem XPI lifecycle Stage 1 – Discuss with research team

(customer)

Proposed solution XPI lifecycle Stage 2 – Work out algorithm in Matlab XPI lifecycle Stage 3 – Move to C++ code XPI lifecycle Stage 4 – Move to optimized C++ code

(and learn how to use all C++ pragmas properly)

NEW XPI lifecycle Stage 5 – Move code to custom DSP accelerator

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Research Team discussion Ultra-sound probe (20 MHz) that sends out

signals into body that reflect off moving blood cells in (Artery? Vein?)

Ultra-sound frequency received is Doppler shifted compared to transmitted frequency Same as sound when ambulance goes by. Higher

if approaching, lower if receding They get the positive frequencies (towards)

on the left audio channel and negative frequencies (away) on the right audio channel.

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Picture looks like this

Note that the display loses all direction information Can I help them to output the maximum frequency?

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My response

No -- it can’t be done

But

I am willing to negotiate that answer – we might get a rough answer

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Doppler Effect – Understand the Math

Sound frequency we hear is governed by frequency * wavelength = velocity of sound

Not velocity in air, but in human body – which means it might be changing as it passes through different body parts. Also get noise from sound reflections from body part boundaries W. A. I. L. – assume constant velocity

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Understand the MathObject moving away from us

Object stationary Sound pressure waves are bouncing off object Maximum in sound pressure waves are a

distance of wavelength apart Object moving away from us at speed Vobj

First sound pressure maximum bounces off object

Second sound pressure maximum has to catch up with moving object which has moved a distance Xobj in the time between maximums

Apparent wavelength = wavelength + Xobj

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Doppler numbersfrequency * wavelength = velocitySound BecomesapparentFrequency * apparentWavelenth = velocitySound

apparentFrequency = velocitySound / apparentWavelength = velocitySound / (wavelength + Xobj)

wavelength = velocitySound / frequency

Xobj = velocityObject * (time for sound wave to catch up)Time to catch up = Xobj / velocitySound

Xobj = velocityObject * Xobj / velocitySound 1 = velocityObject / velocitySound -- OOPS Something

wrong

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Try again If object was not moving – next sound pressure

maximum arrives in time deltaT = 1 / freq (s)

Object has moved a distance Vobj * deltaT in that time Therefore when the pressure maximum bounces off the

object, the distance between pressure maximum has increased to wavelength + Vobj * deltaT

WAIT-A-MO – By the time the pressure maximum has gone that distance object has moved again!

True – this means that the changed wavelength is longer than wavelength + Vobj * deltaT . In fact if the object is moving fast enough – no sound waves will bounce off the object

Assume that Vobj is much slower than Vsound. Expect this to be valid in body – but might not be – not domain

expert

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Doppler numbersfrequency * wavelength = velocitySound BecomesapparentFrequency * apparentWavelenth = velocitySound

apparentFrequency = velocitySound / apparentWavelength = velocitySound / (wavelength + Xobj)

wavelength = velocitySound / frequency

Xobj = Vobj * deltaT = Vobj / frequency

apparentFrequency = velocitySound / apparentWavelength = velocitySound / (velocitySound / frequency + Vobj /

frequency) = frequency * velocitySound / (velocitySound + Vobj)

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Physiological B of E calculation

apparentFrequency = frequency * velocitySound / (velocitySound + Vobj)

FrequencyChange = apparentFrequency – frequency = frequency * (velocitySound / (velocitySound + Vobj) – 1) = frequency * (-Vobj / (velocitySound + Vobj) = frequency * (-Vobj / velocitySound); velocitySound >> VobjVobj = - FrequencyChange * velocitySound / frequency

Are the body measurements consistent with the theory? Assume – ultrasound is 20 Mz and change in frequency maximum = 6 kHzVobj = - 6 * 10^3 * velocitySound / 20 * 10^ 6 = 0.3 * 10 ^-3 *

velocitySound

Assume –velocitySound = 5 * velocitySoundAir = 1500 m / s Vobj = 0.3 * 1.5 m / s = 0.5 m/sCar = 50 km / hour = 50,000 / 3600 m / s = 15 m / s Blood cells moving around 2 km / hour – is that correct?

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Look at customer picture

We said (B of E calculation) Max velocity = 0.5 m / s = 50 cm / s

Actual maximum around 150 cm / s velocitySound = 15 * velocitySoundAir = 4500 m / s

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XPI-Inspired Life cycle Stage 1

Further talks with customer Positive frequencies (towards) on the left

audio channel and negative frequencies (away) on the right audio channel

GUESS WHATS HAPPENING – Model correct, details ??? Signal is 20 MHz + 4 kHz and 20 MHz – 5 kHz from

two blood cells Filter signal 20 MHz 20 MHz + 4 * MaxFrequency.

Down shift to 0 Hz, and output on Left Channel Filter signal 20 MHz 20 MHz - 4 * MaxFrequency.

Down shift to 0 Hz, and output on Right Channel Guess why – audio interpretation of blood flow

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XPI-Inspired Life cycle Stage 2

Move to Matlab Many built-in “trusted” algorithms (have found some wrong) Easy to visualize via plots Have not found a good automated testing framework

Algorithm pseudo code Gather blocks of audio data – size N – left and right

NO hassle – 6 kHz will be easily handled by SHARC A/D Perform DFT on both channels (discrete Fourier transform)

Engineering problem 1 – Complex math (a + jb) on SHARC! Find maximum frequency left and right from DFT

Engineering Problem 2 – Define maximum frequency zillions of blood cells – therefore distribution of frequencies

If (max Forward > max Reverse) return Forward else return –Reverse Send DC representation of frequency to 1 of 16 channels of (OLD?)

analogue digital chart recorder to record along side other physiological signals Engineering Problem 3 – SHARC D/A can’t handle DC signal Engineering Problem 4 – Can SHARC handle all this in real-time?

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Captured audio signal

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More Engineering Problems

Problem 5 – Is different amplitudes common?

Problem 6 – Why are funny dead spots not lining up in left and right channels? Real or artifact? Guess – channels not recorded at same time for this prototype

Problem 7 – How to remove dead-spots?

Max frequency – definition 1 Frequency

below which X% of the frequencies fall

Noisy signal for large thresholds

> 80%

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Max frequency – definition 2 Frequency

containing most cells – with a certain band of frequencies

There was multiple bands of near similar frequency max

Useful info?

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Special tricks employed Fourier interpolation

to improve frequency resolution

Modulate DC signal on top of 2 kHz audio signal

Output from SHARC Amplify using home

audio system Now rectify and

smooth and send to channel recorder

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After XPI Stage 2 Have a working algorithm concept Engineering problem 1 – Complex math (a + jb) on SHARC! Engineering Problem 2 – Define maximum frequency

zillions of blood cells – therefore distribution of frequencies Workable prototype – discuss more with customer

Engineering Problem 3 – SHARC D/A can’t handle DC signal Workable prototype – discuss more with customer

Engineering Problem 4 – Can SHARC handle all this in real-time? Problem 5 – Is different amplitudes common?

Discuss more with customer Problem 6 – Why are funny dead spots not lining up in left and

right channels? Real or artifact? Guess – channels not recorded at same time for this prototype

Discuss more with customer – Get second set of samples Problem 7 – How to remove dead-spots? –

Discuss more with customer

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XPI Stage 3 – Move to C++ Good starting point – working MatLab code

Start with known signals -- TestVectorIn Pass through Matlab to get known results

TestVectorOut Generate tests that the C++ code must satisfy

OFF-LINE Can TEST with TestVectorIn and TestVectorOut hard-coded in C++ memory

ON-LINE – Biggest worry, need block of data and process it

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Assignment 1, Labs 1, 2 and 3

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Slightly faster version

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New C++ optimization approach

#pragma always_inlineinline void ProcessOnePoint(void) {

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This works PROVIDES deltaT = 1 / 41000 s

Time to do one point Operating system Time to do a task Time to input Time to process Time to output

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Need to process “One Block”

This form of the program does not generate blocks – samples the same point

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Version 2 Captures a

block But outputs

all points very quickly into Left_Out

Hear one point then silence

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Version 3CaptureProcessOutput

CaptureProcessOutput

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Version 3 – Curate’s Egg Famous 1820 joke Works well occasionally

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CAPTURE N * deltaT

PROCESS How long does it take?

OUTPUT N * deltaT

CAPTURE N * deltaT

PROCESS How long does it take?

OUTPUT N * deltaT

Version 3 – Look at efficiency

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CAPTURE WASTED CPU TIME

SILENCE

LOST DATA PROCESS SILENCE

LOST DATA WASTED CPU TIME

OUTPUT

CAPTURE WASTED CPU TIME

SILENCE

LOST DATA PROCESS SILENCE

LOST DATA WASTED CPU TIME

OUTPUTCAPTURE1

CAPTURE2 PROCESS1

CAPTURE3 PROCESS2 OUTPUT1

CAPTURE4 PROCESS3 OUTPUT2

CAPTURE5 PROCESS4 OUTPUT3

CAPTURE6 PROCESS5 OUTPUT4

This code only works if

Time for ProcessOneBlock

< deltaT (1 / 41000 s)

Unnecessary Race problem

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ProcessBlockDONEOUTSIDEINTERRUPT

AVOIDS RACE

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Problems to watch for#pragma always_inlineinline void ProcessOneBlock(float *inBuffer, float *outBuffer) { for (int count = 0; count < PROCESS_BUFFER_LENGTH; count+

+) { outBuffer[count] = inBuffer[count]; }}

inline void ProcessFIROneBlock(float *inBuffer, float *outBuffer) { When doing N point FIR on data block

Processing first point in bufferthen need N – 1 points from previous blocks

}

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Speed issues when processing block

Suppose N points and M tap FIR then time taken Order (N * M) where N = 256 and FIR order = 256 -> k * 256 * 256

Can do filtering in frequency domain Do FFT – takes time Order(N log N) Do Multiplication in frequency domain Order

(N) Do Inverse FFT – takes time Order(N log N) Time roughly Order(2N log N + N)

K’ * (2 * 256 * log(256) + 256) = K’ * 256 * (16 + 1))

Time domain calculation is slower

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Ready to solve the ultrasound problem

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