Biomedical Signal Processing

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Biomedical Signal Processing
Chapter 1. Introduction
Dept. of Biomedical Engineering Yonsei
University Prof. Young Ro Yoon yoon_at_yonsei.ac.kr 0
10-2007-2440, 033-760-2440,2501
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System Theory

• Definition of system If the input is given to
  the black bock, then output is coming from the
  black bock. Then, we called the black bock as the
  system.
• Most system is the linear time-invariant system.

• linearity
• time-invariant
• causality
• stability

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• 1. linearity
• If the input is amplified by A, then output will
  be amplified by A.

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• If the input is the summation of two different
  amplified signals, then output is also the
  summation of two different amplified outputs.
• Principle of superposition

System
System
Linear System
A, B weighting factor
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• 2. time-invariant
• A time system is one whose properties do not vary
  with time. That is, When train from Seoul to
  Pusan is delayed for 20 minutes, it arrives 20
  minutes late. (time-invariant).
• The train arrives on estimated time of arrival.
  (time-variant)

System
Time- invariant System
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• 3. Causality
• Output signal depends only on present and/or
  previous values of the input.
• Output yn at time n depends only on the current
  input xn at time n and its past input sample
  values such as xn-1, xn-2..
• Otherwise, if a system output depends on the
  future input values, such as xn1, xn2, the
  system is noncausal.
• The noncausal system cannot be realized in real
  time.

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• 4. stability
• A stable system is one which produces a finite,
  or bounded, output in response to a bounded
  input.
• Every Bounded Input produce a a Bounded
  Output(BIBO).
• There are many other stability definitions.

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• Digital convolution sum is
• If all the inputs reach the maximum value M for
  the worst case,
• Using the absolute values of impulse response
  leads to
• If the absolute sum is finite number, the product
  of the absolute sum and the maximum input values
  is finite.
• Hence, we have a bounded input and a bounded
  output.

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• In terms of the impulse response, a linear system
  is stable if sum of its absolute impulse response
  coefficients is a finite number.
• If the impulse response decrease to zero in
  finite amount of time, this system is a linear
  stable system, because the summation of its
  absolute impulse response coefficients is
  guaranteed to be finite.

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Practical DSP Application

• 1. moving average filter
• Low pass filter, Smoothing the input signal.
• 2. bandstop filter or notch filter
• Electrocardiogram (EKG)

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Practical DSP Application

• 3. bandpass filter
• 4. lowpass filter
• 5. highpass filter

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Moving Average Filter

• Smoothing
• Low pass filtering

? 200 point - moving average filter
200-day moving average filter
The dollar price of gold, 1979-1983
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• Example of 3-point moving average filter

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• Example of 3-point moving average filter

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The dollar price of gold, 1979-1983
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• A widely-used technique is to estimate a moving
  average in digital signal processing field.
• For example, electronics engineers often need to
  remove unwanted interference, or noise, from a
  relatively slowly-varing signal.
• A smoothing filter used for this purpose is known
  as a low-pass filter. That is , it passes
  (transmits) low frequencies, representing slow
  fluctuations but reduces high frequency.

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• This is quite a common problem when recording
  biomedical signals, due to pick-up in electrode
  leads.
• Since biomedical signals are often stored in
  digital computers, we have the opportunity to
  reduce the interference with a digital filter.