ORT21BMI

1
ORT21BMI

• Topic 6--Being digital

2
Clinical context

• Recall the request from your colleague to record
  a patients ERG and to store it in such a way
  that it could be compared with the ERGs of her
  family members
• Getting an ERG recorded and displayed on an
  oscilloscope display or chart recording is one
  thing how do you store it in a computer?

3
Specific issues

• How do you get the signal into the computer?
• How is it represented inside the computer?
• Where is it in the computer?
• How does its representation in there differ from
  the original electrical signal?
• Once its in the computer, what can you do with
  it?

4
Learning goals

• What is the difference between continuous
  (analogue) and discrete signals?
• What changes when a discrete signal is stored on
  a computer?
• What are the implications of different sampling
  rates?
• What happens if we dont sample fast enough?
• What is the basic anatomy of the PC and what
  parts are relevant to our work?

5
Why digital?

• Recall our clinical scenario where you were asked
  to both record and store for later comparison a
  familys ERGs
• Without the use of digital technology, you have a
  problem!
• With it, you have many tools available

6
Why digital instruments?

• Patients were assessed long before computers
  became common
• Consider the Goldman perimeter
• ERGs were recorded in the early 20th century
• Why bring computers into it?
• The flexibility of digital processing has allowed
  computers to take over functions once done with
  conventional electronics

7
Whats the digital advantage?

• Consider filtering
• To build a filter took many precisely matched
  electronic components
• Want to change the cut-off frequency?
• Simultaneously switch in a number of resistors
  and capacitors or rewire the circuit by hand
• Switches wear out
• You can only use a value wired in already
• With digital processing, all you need to do is
  enter a new parameter value. Thats it.

8
What else?

• Many filing cabinets worth of paper records of
  ERGs, VEPs, etc can be stored on a single disk
• You can re-analyse them whenever you want
• You can compare them against others
• You saw in the last lecture how filtering caused
  a time delay
• With digital filtering of stored data, you can
  make time go backwards and eliminate this

9
Whats the difference between analogue and
digital?

• You know what music is--
• Just what are those MP3 files made of?
• You know what a photo is--
• How do they become jpg files attached to e-mails?
• You know (I hope!) what an ERG is--
• What does it become in a computer?
• So the question isnt just confined to the
  clinic...

10
Discrete signals--the first step to digital

• A fundamental transition is from analogue to
  discrete signals
• Analogue signals are continuous in time that is,
  no matter how tiny a period of time you choose,
  the signal exists throughout that period
• Discrete signals--the kind represented digitally
  on a CD or MP3 file--are defined (have a value)
  only at specific points in time (eg, every 1
  msec)
• What else is like this?

11
How about pictures?

• Consider a photograph taken with a film camera
• Look at it under a strong magnifying glass
• Youll notice, if its a good one with
  fine-grained film, that you can see more detail
• The image exists at every point in the photo
• Printed or on-screen pictures are no longer
  continuous

12
Continuous?
Note what the smooth line is actually like--it
seems to consist of discrete values
13
Discrete Signals

• If something is defined only at separate
  intervals, it may still seem continuous, if the
  intervals are close enough together
• Determining close enough is non-trivial
• Consider the weather

14
From the manual

• How often do you check the temperature?
• Every day?
• Every hour?
• Every minute?
• Lets say you check it every hour
• Does the air still have a temperature, even if
  youre not checking it?

15
Heres a plot of air temperature vs. time

• Youre checking it every hour
• A lot less measuring than infinitely often
• Does that seem to represent the true, continuous
  measured record pretty well?
• What if someone held a match under the
  thermometer between 1320 and 1321 hours?
• Could you tell from those hourly readings?

16
Discrete vs. continuous

• For many purposes, you only need information at
  specific times
• If so, then you can save a lot of work as opposed
  to recording something continuously at every
  fleeting instant of time
• However, doing this does mean that you dont
  really know what happens between measurements
• So, to do this, you must understand both your
  needs and the characteristics of your data

17
Discrete vs. continuous, contd

• For discrete data, each measurement may be made
  with arbitrarily precise accuracy
• That is, we could measure the temperature as
  18.3763933345681103555937 deg Celsius

18
Getting data into the computer

• Discrete data is the first step towards
  computer-friendly data.
• We need to limit how precisely we measure our
  data.
• WHY THESE LIMITS?
• To understand them, we need to confront how
  computers store things

19
Binary numberscomputers native language

• Everything a computer contains is represented as
  a collections of 1s and 0s
• Everything.
• Your e-mails, your music, your snapshots
• This means your ERGs, too.
• Doesnt seem obvious, does it?
• The 1s and 0s make up binary numbers, in the same
  way that the digits 0..9 make up decimal numbers

20
Storing binary data

• Binary numbers can get long
• This limits how precisely we can represent things
  digitally
• Having to store and manipulate long strings of
  binary numbers also limits the precision with
  which we represent things
• These limitations have gotten less stringent as
  computers get faster and storage cheaper, but
  they havent disappeared
• Lets go back to the idea of sampling a signal at
  regular intervals as the first step towards
  digital data

21
Analogue to digital conversion

• This is the electronic version of measuring the
  temperature periodically
• At fixed intervals, the voltage of interest is
  sampled
• Its then assumed not to change till the next
  sample
• The value is stored, and after the appropriate
  wait, the next sample taken
• But how does 0.124799653100824 volts get saved as
  1s and 0s? Well soon see

22
How close are the original copy?

• Depends on 2 things
• How often you sample
• How precisely you measure
• Increase the above and your digital version gets
  closer and closer to the analogue original
• It also takes up more and more storage space
• Well consider how you balance these
• Some of it is techie stuff, but some decisions
  may be yours
• If made badly, they may yield hopelessly invalid
  data!

23
Why is it ever your problem?

• As well soon see, taking samples too slowly can
  create spurious data that cannot be removed
• What determines how slowly is too slowly?
• What the frequency content of the signal is!
• Knowing a bit about your signal lets you set up
  your instrument properlyor at least know that
  you should ask someone if it is set up right
• Does this really matter to non-engineers?

24
Yes.

• Even apparently computerless things like chart
  recorders may actually be digitising the signal
  before they display it to you
• Heres a physiological example

25
Where are we now?

• Were taking measurements at some rate thats
  enough, whatever that means.
• We then have to convert them from our familiar
  decimal numbers to ones the computer is
  comfortable with1s and 0s
• These are known as binary numbers because you
  only have two values to work with
• Well deal with the question of converting from
  our decimal to the computers binary numbers next
  week meanwhile, at what rate do we tell the
  computer to sample our crucial clinical signals?
• Not a trivial question!

26
How fast do we go?

• Recall that all waveforms can be represented as
  sums of sine waves
• From this, it should follow that to accurately
  sample and store a waveform, we need to store all
  of the individual frequency components that make
  it upotherwise, the stored waveform will be
  missing some parts
• So, how fast do we need to sample a sine wave?

27
Heres one thats thoroughly sampled!
28
Do we need to go that fast?

• Remember that the more frequently we sample, the
  more data have to be stored and the more powerful
  the processor thats needed to manipulate them
• Whats the lowest sampling rate we can get away
  with?

29
Hows this?
The result looks funny but its identifiable
(with some effort) as having the frequency of the
original
30
What if we go even slower?
Uh-ohwe seem to have stored a waveform thats
not at all representative of the real
thing! Notice that, once its stored, theres no
way to know that its wrong!
31
What happened?

• The re-creation of a spurious low frequency
  digitised sine wave by means of sampling too
  slowly is called aliasing
• The minimum allowable sampling frequency for a
  sine wave is twice its frequency this is called
  the Nyquist frequency after its discoverer
• If a waveform contains multiple frequencies, as
  clinical data would, then you must sample at
  twice the highest frequency present in the data
• Thus, if an ERG contains 100 Hz oscillatory
  potentials, then it must be sampled at 200 Hz or
  greater

32
Dont forget noise!

• Eye movements recorded with skin electrodes
  results in low frequency eye movements combined
  with much higher frequency muscle noise
• If we digitise these eye movements, we would do
  one of two things
• 1) Filter out the noise before sampling
• 2) sample fast enough to adequately represent the
  noise as well as the desired signal
• Clearly, 1) would be the preferable option, where
  possible

33
And if we forget the noise?

• Then it may be aliased into an unwanted low
  frequency component and stored with the eye
  movements
• From this point on, it could not be corrected,
  because it couldnt be separated from the desired
  data

34
Lets look at an example, using the frequency
domain representation
Heres a motor unit action potential (in red) and
the 10 sine waves that can make a pretty good
representation of it (in blue)
35
Heres its spectrum
What frequency would we have to sample at to
capture this signal accurately?
36
Now lets add some 13 Hz noise
37
What if we still sample at 20 Hz?
Were in trouble!
38
What we need is an anti-aliasing filter!
If we know the noise is there and use an analogue
filter to get rid of it before digitising, then
we can use the lower sampling rate Note that we
cant do this digitally after digitising because
the erroneous component is at the same frequency
as a valid one So we need advance knowledge of
the composition of both the clinical signal and
any noise added to it
39
Next time

• In particular, the tutorials at
  http//www.delsys.com/library/tutorials.htm under
  the heading Fundamental Concepts in SEMG Data
  Acquisition are really helpful (and are where
  lots of the figures used in this presentation are
  from)
• You can download the PDF files and keep them as
  references
• A site that will be useful for this and the next
  class is http//arts.ucsc.edu/ems/music/tech_backg
  round/TE-16/teces_16.html