Fundamentals of signal analysis Flashcards
Why do we want to analyze biosignals? What is it for?
provide accurate information to support a clinical diagnosis by physicians.
What does filtering do?
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
What does event detection do?
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
What does wavelet analysis do?
*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
What can we do with pattern recognition?
What is the difference between a deterministic signal and a random signal? Why is it important to know the difference?
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.
What is the difference between a random signal and random noise?
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.
How do we test for the randomness of a signal?
- 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)
What is a turning point? also called peak or trough in the signal.
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.
What characterizes random noise?
- 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
What is the signal-to-noise ratio (SNR)? What kind of SNR is expected in practice? give an example
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
What is the role of the Signal-to-Noise ratio (SNR)?
SNR helps estimate the influence of noise on measurement, and hence the maximal possible accuracy of the measurement.
Why do we need autocorrelation?
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.
What are time averages? Why do we need to compute it?
What is its difference from the ensemble average?
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.
What is the difference between covariance and cross-correlation?
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.
What is cross-correlation function useful for?
CCF is useful for:
- aligning 2 signals
- detection of events by template matching (searching in a long signal for a shorter template)
What is a structured noise? Give an example
is noise with typical interference waveform known in advance e.g. power line interference at 50Hz or 60Hz
What is physiological interference? Give an example
- 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)
What is the difference between stationary and non-stationary processes? Give an example
The stationary process stays constant over time.
The non-stationary process varies over time.
What is the difference between stationary and non-stationary processes? Give an example
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
What is the characteristic of physiological interference? How do we normally process it?
- 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
What is the characteristic of most biomedical systems? give some examples
- are dynamic
- produce non-stationary signals
- limitations in the rate change of its characteristics e.g. heart rate
Give some characteristics of noise in biomedical signals e.g. ECG
-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.
-…
What is the ergodic process?
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
