Biological Signal Analysis - eBooks and textbooks from bookboon.com

Click on the ad to read more Click on the ad to read more Click on the ad to read more. In the last chapter, I have given a few examples of recently studied biological signal analysis applications from real life.

Figure 1.2: Filtered version of sinus rhythm ECG in Figure 1.1.

Examples of Common Biological Signals

Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more. These six precordial leads can be obtained by placing electrodes on the chest, as shown in Figure 1.7.

Figure 1.5: ECG waveform.

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At the end of axon (presynaptic membrane), the electrical potential causes chemicals known as neurotransmitters (released by synaptic vesicles) to diffuse across the synaptic cleft and the amount of neurotransmitters diffused at the postsynaptic membrane causes a proportional electrical potential at the dendrite of the connecting neuron causing an input signal to the connecting neuron's soma3 [5, 6]. Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more.

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Contents of this book

Methods for signal analysis will depend on the type of signal and the nature of the information carried by the signal - there are some general methodologies and some specific to particular signals. Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on ad to read more Click on ad to read more.

Figure 1.16: Arterial blood pressure signal. ABP data shown here was obtained from [1].

Discrete-time systems operate on an input signal according to some prescribed function7 and produce a different output signal. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. on the ad to read more Click on the ad to read more.

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Discrete-time signal

A discrete-time signal, x[n] is developed by uniformly sampling an analog signal x(t) as shown in Figure 2.2 below. It can be seen that the analog signal in Figure 2.4 is not correctly represented by the discrete-time version.

Figure 2.3: Sampling with high enough frequency – the signal is correctly represented.

Sequences

Basic Discrete-time System Operations

In downsampling, every Mth sample of the input sequence is kept and the M-1 samples in between are removed. Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on ad to read more Click on ad to read more Click on ad to read more Click on ad to read more Click on ad to read more.

Figure 2.5: Product operation.

Examples on sequence operations

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Bibliography

For example, frequency analysis of variable stars is the oldest application of analysis cycles [1]. Since we deal with discrete-time signals in this book, we will skip discussions of the continuous Fourier transform and move to the discrete Fourier transform (DFT).

Discrete frequency

If Fs = 6 Hz for the discrete-time signal shown in Figure 3.2, the frequency abscissa will be from 0 to 3 Hz. Ignoring the symmetric parts, we will have Figure 3.3 where the frequency number m=0.1….(N/2) (the rest of the N/2 points are not drawn due to symmetry in the frequency domain).

Figure 3.2: Example illustrating the connection between discrete-time and frequency number.

Discrete Fourier transform

The following MATLAB program can be used to calculate magnitude and phase spectra using DFT. Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more Click on the ad to read more.

Table 3.1: CPU usage

DFT computation using matrix relation

Picket fence effect

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Figure 3.7: Padded CPU usage spectra.

Effects of truncation

For example, let's apply the Hamming window to the ECG signal discussed in Chapter 1 and calculate the magnitude spectrum (shown in Figure 3.10). It can be seen that using windows gives a quieter (ie less noisy) spectrum.

Figure 3.9: Examples of common spectral windows: (a) Blackman (b) Hamming (c) Hanning (d)Triangular.

Examples of using DFT to compute magnitude spectrum

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Figure 3.11: A 10 Hz sine wave (a) for length N=200 (b) spectral magnitude.

Periodogram

The first plot is obtained using the periodogram code given earlier, while the second is obtained using the pwelch function. A note about the abscissa scale when using pwelch function in MATLAB: the frequency scale is normalized from 0 to 1 which represents the range 0 to Fs/2.

The first step in this method is to divide the data into K overlapping segments, each containing M sample points. In MATLAB, the pwelch function can be used where the percentage overlap is 50% with K=8 and the Hamming window is used by default.

Filter Specifications

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Figure 4.2: Magnitude frequency response of a LPF.

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Direct filtering in frequency domain

Due to symmetry, we also need to create mirror images of the passband and stopband, resulting in a rectangular window as shown in Figure 4.11(a). Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. per ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more. Click on the ad to read more.

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Time domain filtering

To solve the problems of direct filtering, we could filter in the time domain, and there are several methods of time domain filtering. It should be obvious from this figure that time domain filtering is computationally less complex.

Simple FIR filters

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Figure 4.15: Magnitude response of the simple sum filter.

FIR filter design using window method

But the question that may arise now is the appropriate length of the filter. The next problem is choosing a window that could be decided using the areas under the main lobe and the side lobes.

Figure 4.22: Truncated impulse response for LPF and Gibbs phenomenon.

IIR Filter design

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Figure 4.29: Magnitude and phase response of elliptic filter.

Characteristics are calculated values ​​that must be representative of the signal and reproducible at different times. Robust/improved representation of the signal (i.e., invariant to changes caused by noise, scale factors, etc.).

Simple features

Correlation

Autoregressive model

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Figure 5.1: AIC for ECG signal shown in Figure 1.2.

Spectral features – Power spectral density

Power spectral density derived features

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Figure 5.4: EEG channel location used to record the mental task EEG data [3].

Power spectral density computation using AR features

Hjorth descriptors

Time domain features

Joint time-frequency features

In summary, several feature extraction methods have been discussed in this chapter as examples, but these are by no means exhaustive, and we will look at a few more in the final chapter.

What is classification?

Nearest Neighbour classifier

It is not robust to irrelevant inputs, as irrelevant features have the same impact on classification as good features. So there are techniques to reduce the size of the training data set, where the general idea is to remove as many training samples as possible with minimal impact on the classifier output (i.e. performance).

Figure 6.2: Plot of several training patterns from two classes, A and B and one test pattern, x.

Artificial neuron

Multilayer-Perceptron neural network

MLP-BP classifier architecture

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Figure 6.11: MLP architecture for classification example.

Performance measures

Recognition rate: is the ratio of the number of patterns that are correctly classified to the total number of patterns that are validated. A total score is estimated by adding all scores from all patterns and finding the ratio to the total number of patterns.

Cross validation

Leave one out: N-fold cross-validation in the extreme case, where N equals L, the total number of patterns. If an equal class weight (with class size C) is used, the holdout method L/C times is repeated using L-C training data and C validation data, with each subset having an equal number of patterns from each class.

Figure 6.16: Ten fold cross validation.

Statistical measure to compare two methods

So we can decide to reject the null hypothesis if the probability of observing the sample result is less than the significance level. The p-value is the probability of observing the given data under the assumption that the null hypothesis is true.

A significance level relates to the degree of certainty required to reject the null hypothesis in favor of the alternative hypothesis. For this significance level, the probability of incorrectly rejecting the null hypothesis when it is actually true is 10%.

Ectopic beat detection using ECG and BP signals

Before the features could be extracted from the ECG signals, the R peak must be detected. These were the R peak amplitude, R-R interval before the beat (pre R-R interval), R-R interval after the beat (post R-R interval), Hjorth's mobility and Hjorth's complexity.

Figure 7.2: Modified Pan-Thompkins algorithm [2] for an ECG signal, from top to bottom: ECG signal, bandpass filtered, squared, moving window integrated and thresholded

EEG based brain-computer interface design

The asymmetry ratio as used in this study was useful because it provided an indication of the amount of interhemispheric difference in EEG activity. This allows subjects to focus on the sequence of mental tasks without worrying about the duration of each mental task, and is especially useful for constructing letters like 'H' or 'S', which consist of consecutive dots whether dashes exist.

Figure 7.3 shows the components that are found in a general BCI system. The EEG data is collected, normally from multiple channels (some even up to 128), during an external stimulus, which could be visual, auditory, somatosensory or internally induced th

Short-term visual memory impairment in alcohol abusers using visual evoked potential signals

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Identification of heart sounds using phonocardiogram

The Daubechies-2 wavelet was calculated as functions, where the component formed by the wavelet detail coefficients at the second decomposition level was divided into 32 sub-windows, and the energies of these windows were calculated as functions.

Figure 7.8: Peak detection for PCG signal (Normal). Figure from [16], used with permission from Elsevier.

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