Digital编程设计代写、代做R程序代写、代写R留学生程序

日期：2020-11-06 11:28

Assignment 2, Digital Signal processing: FIR

filters

The task of this assignment is to filter an ECG with FIR filters and to

detect the R peaks. In contrast the FFT assignment here we write filter

code which can be used for realtime processing. This means that the FIR

filter needs to be implemented with the help of delay lines and the impulse

response is truncated.

1 ECG filtering

Download the ECG according to the last digit of your matric number.

1. Create a Python FIR filter class which implements an FIR filter which

has a method of the form value dofilter(value) where both the

value argument and return value are scalars and not vectors (!) so that

it can be used in a realtime system. The constructor of the class takes

the coefficients as its input:

class FIR_filter:

def __init__(self,_coefficients):

# your code here

def dofilter(self,v):

# your code here

return result

Implement the FIR filter in an efficeint way for example by using a

ring buffer or by smart application of the Python slicing operations.

1

Minimise the amount of data being shifted and explain how / why you

have done it. Put the filter class in a separate file for example fir-

filter.py so that it turns into a module which can be imported by the

main program. [20%]

2. Add a unit test to the module fir-filter.py from 1 which tests if the

FIR filter works properly. For example the delay line and the proper

multiplication of the coefficients. The unit test should be called if one

starts the module with python fir-filter.py. Add the unit test by

calling a function called unittest if run as a main program:

if __name__ == "__main__":

unittest()

[20%]

3. Download a short ECG from moodle according to the last digits of

your matric number. Filter this ECG with the above FIR filter class

by removing the 50Hz interference and the DC. Decide which cutoff

frequencies are needed and provide explanations by referring to the

spectra and/or fundamental frequencies. Calculate the FIR filter coefficients

numerically ( = using python’s IFFT command). Simulate

realtime processing by feeding the ECG sample by sample into your

FIR filter class. Make sure that the ECG looks intact and that it is

not distorted (PQRST intact). Provide appropriate plots. [20%].

2 ECG heartrate detection

The task is to detect the momentary heart rate r(t) over a longer period of

time. For example, after exercise you should see a slow decay of the heart rate

to the baseline of perhaps 60 beats per minute. It is not the average heart

rate but the frequency derived from the times between adjacent heartbeats.

1. Create a matched filter by using one QRST complex from an ECG

and detect the R-peaks. Remember that for matched filters DC free

signals are important. Here, the pre-filtering of the ECGs can be done

differently to the filtering above to reduce as much DC as possible and

any interference. [20%]

2. Use an Einthoven II recording where the person is walking using this

ECG database: https://pypi.org/project/ecg-gudb-database/. The

BEng students take subject numbers 0-9 matching their matriculation

number and the postgraduate students subject numbers 10-19 with

matching matric numbers 0-9. The database has a Python API and

there is an example on github (https://github.com/berndporr/ECG-GUDB)

how to use it. Calculate the momentary heart rate r(t) over time (not

the average!) by measuring the intervals between the detected hearbeats

over the whole period of the ECG. Detect the heartbeats by

employing a threshold. Add code which removes wrong detections and

explain what the code does. [20%]

Every report must be based on a different ECG recording. Please keep it

short but it should make clear what you have done and why you have done

it. Include the Python code as well as plots of the ECGs (timedomain) and

their frequency representation (with proper lables). If necessary enhance the

plots with InkScape, Corel or Illustrator by labelling the ECG peaks and

remember to use vector based image formats, for example EPS, SVG, PDF

or EMF and not pixel based formats for the report. These figures need to

be in the report at the correct place and not attached separately. Also, show

zoomed in ECG traces of one heartbeat so that it is possible to identify the

different parts of a single heartbeat (see Fig. 1) and that it’s possible to check

if it’s still intact.

No high level Python functions except of FFT/IFFT and the window

functions are allowed. Any use of “lfilter”, “firwin”, “conv”, “correl” and

any a-causal processing (i.e. data array in and array out) commands will

result in zero or very low marks. As before submit a zip containing all files

and test the zip before submission by unzipping it and then running python

from the command-line in a terminal (not spyder). Also check that all plots

are generated when running the script from the commandline. See moodle

for the exact filename conventions.

Deadline is 9th November.

Figure 1: A normal ECG with P,Q,R,S,T waves (taken from Wikipedia)