Fundamentals of signal analysis Flashcards

1
Q

Why do we want to analyze biosignals? What is it for?

A

provide accurate information to support a clinical diagnosis by physicians.

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2
Q

What does filtering do?

A

Filter is any of various electric,
electronic,
acoustic,
digital
or optical devices used to reject signals, vibrations, or radiations of certain frequencies while allowing others to pass
⟹Goal: analyze the various types of artifacts that corrupt biomedical signals and explore filtering techniques to remove them without degrading the signal of interest
FILTERING for Artifact Removal

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3
Q

What does event detection do?

A

given a biomedical signal, identify discrete signal epochs, and correlate them with events in the related physiological process.
epoch: part of a signal related to a specific event
–>development of signal processing techniques to emphasize, detect, segment, and analyze epochs

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4
Q

What does wavelet analysis do?

A

*based on filtering using (time limited) Wavelets of a specific center frequency
*with this technique, we can analyze a signal and:
*analyze the spectral content in different places
*detect sharp changes in spectral character

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5
Q

What can we do with pattern recognition?

A
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6
Q

What is the difference between a deterministic signal and a random signal? Why is it important to know the difference?

A

The signal whose value at a given instant of time may be computed using a closed-form mathematical function of time or predicted from past values of the signal is a deterministic signal.
A signal that does not meet this condition is a non-deterministic or random signal.

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7
Q

What is the difference between a random signal and random noise?

A

Random noise refers to interference that arises from a random process such as thermal noise in electronic devices. (has the potential to corrupt the signal of interest, random noise can be a deterministic signal e.g. baseline drift
Random signal has its value at a given instant of time that can not be computed using a closed-form mathematical function of time or can not be predicted from past values of the signal.

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8
Q

How do we test for the randomness of a signal?

A
  • given a signal of N samples, the signal is random if the number of turning points > 2/3 (N - 2)
  • Non-stationary signal (signal of varying characteristic): using a running window of N samples, and the width of the window should be chosen by taking into consideration of the shortest duration over which the signal may remain in a given state.
    –> recognize the part of the signal that is random and the part that is not using the same threshold calculation formula 2/3 (N - 2)
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9
Q

What is a turning point? also called peak or trough in the signal.

A

A peak/trough/ turning point: a set of 3 consecutive samples of the signal, with the central sample being either the maximum or minimum, respectively.

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10
Q

What characterizes random noise?

A
  • PDF-probability density function of a random process: probabilities of occurrence of all possible values of a random variable
  • mean value (first-order moment of PDF)
  • mean-squared value (MS, second-order moment of PDF)
  • variance (second central moment)
  • standard deviation = square root of the variance
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11
Q

What is the signal-to-noise ratio (SNR)? What kind of SNR is expected in practice? give an example

A

A ratio between the average power of a signal and the average power of noise.
In practice: high SNR –> clearer signal for later analysis
e.g. ECG with high SNR –> sharp peaks –> better peak detection, accurate heart rate computing

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12
Q

What is the role of the Signal-to-Noise ratio (SNR)?

A

SNR helps estimate the influence of noise on measurement, and hence the maximal possible accuracy of the measurement.

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13
Q

Why do we need autocorrelation?

A

The autocorrelation function ACF indicates how the values of a signal at a particular instant of time are statistically related to values at another instant of time.
- to identify rhythmic patterns e.g. their periodicity, and frequencies.
- to quantify signal variability e.g. in EEG signal, used to measure the degree of similarity btw the signal at different instants of time –> insight into underlying neural processes.
- to detect noise and artifacts e.g. ACF shows a high degree of similarity at short delays –> presence of noise or artifacts.

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14
Q

What are time averages? Why do we need to compute it?
What is its difference from the ensemble average?

A

Time average is temporal statistics computed by integrating over time a sample observation of a random process i.e. averaging a signal over a specific window
An ensemble average is an ensemble of sample observations of the random process at a particular instant in time i.e. describe the averaging behavior over multiple observations/trials.

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15
Q

What is the difference between covariance and cross-correlation?

A

Covariance measures the linear association between two signals over time, while cross-correlation measures the similarity between two signals as they are shifted in time relative to each other.
A positive covariance indicates that the two signals tend to increase or decrease together, while a negative covariance indicates that one signal tends to increase while the other decreases.
A high cross-correlation at a particular lag indicates that the two signals are similar at that time shift.

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16
Q

What is cross-correlation function useful for?

A

CCF is useful for:
- aligning 2 signals
- detection of events by template matching (searching in a long signal for a shorter template)

17
Q

What is a structured noise? Give an example

A

is noise with typical interference waveform known in advance e.g. power line interference at 50Hz or 60Hz

18
Q

What is physiological interference? Give an example

A
  • the appearance of signals from systems/processes other than those of interest
    e.g.
  • EMG related to coughing, breathing, and squirming in ECG
  • EGG interfering with precordial ECG
  • maternal ECG getting added to fetal ECG
  • ECG interfering with the EEG
  • ongoing EEG in ERPs and SEPs
  • breath, lung, and bowel sounds in heart sounds (PCG)
  • heart sounds in breath or lung sounds
  • muscle sound (VMG) in joint sounds (VAG)
19
Q

What is the difference between stationary and non-stationary processes? Give an example

A

The stationary process stays constant over time.
The non-stationary process varies over time.

20
Q

What is the difference between stationary and non-stationary processes? Give an example

A

The stationary process stays constant over time.
The non-stationary process varies over time.
Stationary process:
- temporal statistics are independent of the sample observed and the same result is obtained for any sample observation xk(t)
- time averages are independent of k

Non-stationary process:
- statistics vary with time
e.g. quasi-stationary EMG, EEG, VMG, PCG
cyclo stationary ECG, PCG, carotid pulse

21
Q

What is the characteristic of physiological interference? How do we normally process it?

A
  • dynamic and non-stationary
  • linear bandpass filters will not be applicable
  • more advanced signal processing is needed e.g. adaptive filters with reference inputs, wavelet-based independent component analysis
22
Q

What is the characteristic of most biomedical systems? give some examples

A
  • are dynamic
  • produce non-stationary signals
  • limitations in the rate change of its characteristics e.g. heart rate
23
Q

Give some characteristics of noise in biomedical signals e.g. ECG

A

-Baseline drift: slow and gradual drift in the baseline over time
-Powerline interference from power grid (50Hz or 60Hz): sharp peaks or a sinusoidal waveform superimposed on the ECG signal
- Movement artifact: sharp peaks caused by contraction of skeletal muscles
- High-frequency noise: hf oscillations caused by electrode movement, electrical interference or poor electrode contact.
-…

24
Q

What is the ergodic process?

A

A stationary process that its the temporal statistics are independent of the sample observed and the same result is obtained for any sample observation 𝑥𝑘(𝑡)
*all ensemble statistics may be replaced by temporal statistics when analyzing ergodic processes
*ergodic processes are an important type of stationary random processes because their statistics may be computed from a single observation

25
Q

What is a quasi-stationary process?

A

a short-time analysis by segmenting the signal into temporal windows e.g. fix length moving window

26
Q

What is a cyclo stationary signal?

A

certain systems, such as the cardiac system, normally perform rhythmic operations e.g. ECG, PCG, carotid pulse
–> statistics vary within the duration of 1 cardiac cycle but repeat themselves at regular intervals
—> dynamically adapted instead of fixed-length windows