代写EE-6360-501、代写Matlab编程、代做Matched Filter、Matlab调试

日期：2018-12-03 10:49

Issa Panahi EE-6360-501, Class Project page 1 of 4

EE DEPT, UTD FALL 2018 Sept 18, 2018

EESC 6360-501, CLASS PROJECT

“ESTIMATION OF HEARTBEAT RATE FROM THE ECG SIGNALS

USING MATCHED FILTER”

1. INTRODUCTION

A matched filter is a technique to detect the presence/parameters of a known signal in

additive noise. A template of the known signal is correlated with the noisy signal to

determine the presence of the known signal. Since correlation is a convolution operation,

this type of signal detection is basically convolution of the noisy signal with the timereversed

version of the template signal. The time-reversed template signal can be thought

of the impulse response of a LTI filter called “Matched Filter”. In digital

communications, the receiver has to detect the presence or absence of known waveforms

in noise. Matched filters exactly do that and hence are central to many receiver design. In

this project we will explore a biomedical application of matched filters to detect pulse

duration from a noisy ECG waveform.

2. PROBLEM BACKGROUND

ECG (Electrocardiography) signals record the electrical activity of the heart. They

contain lots of information about the working of the heart and are useful in diagnosis of

heart related conditions. Figure.1 shows a typical ECG waveform which we denote as

x(n) . x(n)

is a clean ECG signal. It can be observed that the waveform is a series of

well-defined pulses. The parameter we are interested to find is the time interval between

two pulses. We call it

i

. The subscript

'i'

denotes the fact that the pulse duration is not a

constant and changes with time.(Shown in Figure. 1). The inverse of

i

gives the ‘Beats per

minute’ (BPM) of the heart. Nominal value of BPM of person under rest is around 72. It can be

seen that it is relatively straight forward to determine

i

from

x(n)

. A simple peak-detection

will do the task.

0 200 400 600 800 1000 1200 1400 1600 1800 2000

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

xn)

i1

i

Figure.1 ECG waveform showing pulse duration

i

Issa Panahi EE-6360-501, Class Project page 2 of 4

EE DEPT, UTD FALL 2018 Sept 18, 2018

Sometimes

x(n)

can get corrupted by noise. This is equivalent to

x(n)

passing through a

noisy channel or medium. The (simplified) effect of the channel is the addition of a

‘white noise’

v(n)

which corrupts the signal. The noisy signal is

w(n) x(n) v(n)

and

this is the signal that is observed or is available. The goal of this project is to recover the

pulse duration information by doing some kind of signal processing on

w(n)

(Shown in

Figure. 2). The ‘signal processing’ element is an LTI filter

h(n)

to which

w(n)

is the

input and

y(n)

is the output. The impulse response coefficients

h(n)

for the case of

matched filter is the time-reversed version of a pre-recorded individual pulse

s(n) , i.e.

h(n) ? s(?n) .

The effect of passing

w(n)

through the appropriate matched filter is the

enhancement of the signal in general. It should be noted that

y(n)

is not exactly an

estimate of

x(n)

but can still retain certain information (like pulse-duration) which are

useful . The scenario is shown in Figure 2.

3. PROBLEM STATEMENT

You are given three data files. These are recorded at 1KHz sampling rate.

Check out the given data files, plot them and analyze them.

w1.txt - This data file contains a noisy ECG signal with a SNR (signal to noise

ratio) of 0 dB. This signal will be referred to as

( ) w1 n . The estimated pulse

duration intervals

s i

' are collected in a vector

T1

. Thus

[ . . . ]

1 1 2 N T

0 200 400 600 800 1000 1200 1400 1600 1800 2000

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 100 200 300 400 500 600 700 800 900 1000

-4

-3

-2

-1

0

1

2

3

4

1.6 1.62 1.64 1.66 1.68 1.7 1.72

x 104

-0.5

0

0.5

1

1.5 Matched Filter h(n) ? s(?n)

2.4 2.42 2.44 2.46 2.48 2.5 2.52 2.54 2.56 2.58 2.6

x 104

-4

-2

0

2

4

6

8

10

12

?

x(n)

? (n)

w(n)

y(n)

0 50 100 150 200 250 300

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

s(n)

Figure.2 Noisy Signal Generation and Processing

Issa Panahi EE-6360-501, Class Project page 3 of 4

EE DEPT, UTD FALL 2018 Sept 18, 2018

w2.txt - This data file contains a noisy ECG signal with a SNR of -5 dB. This

signal will be referred to as

( ) w2 n

As above the estimated pulse duration

intervals

s i

' are collected in a vector

T2

pulse.txt – This data file contains the template waveform

s(n) .

Your task is to find/estimate T1

and

T2

by passing

( ) w1 n

and

( ) w2 n

through the filter

h(n)

whose coefficients are determined from

s(n) . You should use MATLAB and its

features to generate your results.

Specifically, in your report you should

1) Write down the complete mathematical formulation of the block diagram in

Figure.2. Write

y(n)

in terms of

x(n) , v(n)

and

s(n)

2) Plot the time-domain, and Amplitude and Phase Spectra of

s(n)

and the

matched filter

h(n) .

3) Tabulate and plot

T1

and

T2

.

4) Give an intuitive explanation of why the matched filter works the way it does.

Some helpful Matlab routines:

MATLAB Functions

load.m

conv.m

xcorr.m

diff.m

find.m

fft.m

filter.m

Issa Panahi EE-6360-501, Class Project page 4 of 4

EE DEPT, UTD FALL 2018 Sept 18, 2018

4. COMPLETION DATE AND PROJECT REPORT DELIVERY

This assignment must be completed and the professionally written project report

must be submitted individually in class by December 4, 2018. No late delivery!

No report will be accepted after Dec. 4, 2018.

5. REPORT STRUCTURE

Your report must be prepared/typed professionally using MS-Word, Equations, or

MS-Power point. A soft copy of your work/report may be requested.

Your report must have your complete full name, your UTD email, course name

and number - all printed in upper case letters and numbers on the first page.

Your report must include this entire write-up as its first pages.

Pages of your report must be stapled together. Every page must be numbered.

The same notations, variable names used in this write-up must be used

throughout your report.

You must use upper case bold letters for the matrices, and lower case bold letters

for vectors. Functions and variables must be in Italic format (see notations used

in your textbook).

Organize and write your report well. BE BRIEF. Write down and explain only

your own work, equations, answers, and results clearly and efficiently. Avoid

redundancy and writing unnecessary or irrelevant materials.

Figures and plots, if any, must all be easily/clearly seen, numbered and labeled

very well.

Negative credit will be given if any of the report’s requirements is not fully met.

The End.