introduction to matlabbenesco.ch/benesco_new/wp-content/uploads/2018/04/... · 18-09-2015 ·...

Introduction to MATLAB Importing data, down sampling, filtering, plotting signals

BENESCO Lecture Series on Signal Analysis

by Dr. Mojtaba Bandarabadi email: [email protected]

Inselspital, Bern, 18 Sept. 2015

BENESCO, Department of Neurology, Inselspital, Bern

Outline• What is MATLAB

• Importing data into MATLAB

• Downsampling

• Preprocessing

• Digital filters

• Fast Fourier Transform (FFT)

• Plotting data

• Feature extraction

• Homework

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What is MATLAB?• High level programming language and computing environment

• Mathematical functions for

• Linear algebra, statistics, differential equations, …

• Signal analysis, image processing, …

• Frequency domain analysis, Fourier transform, …

• Optimisation

• Visualising data

• Development tools

• Building applications using GUI

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MATLAB environment

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First step - Importing data to workspace• Loading data into MATLAB; supported formats by default:

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First step - Importing data to workspace• For formats not supported by default, use third-party functions

• By googling you can find out something to convert your data into MATLAB!

• MATLAB function and code to load Neuralynx data

[Timestamps, samples, Header] = Nlx2MatCSC('sampleData.ncs', [1 0 0 0 1], 1, 1); samples = samples(:);

% ADBitVolts is scaling factor, obtained from the Header ADBitVolts = char(Header(16)); ADBitVolts = str2double(ADBitVolts(13:38))*1000000; samples = samples*ADBitVolts;

% Obtain sampling rate of of raw signal from the Header sampRate = char(Header(14)); sampRate = str2double(sampRate(20:end));

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Variables in MATLAB• are in forms of matrices

• scalar (1x1)

• vectors (1xn or nx1)

• 2D (mxn), more-Dim (mxnx…)

• The class of the matrix

• identified by the data type stored in the matrix

• can be numeric, character, date and time, structure, cell array, table, …

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Fig. Different type of variables in workspace


Functions in MATLAB• You can write your own functions to use them regularly

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Function nameOutput variable Input variables

Des

crip

tion

of

func

tion

(opt

iona

l)Yo

ur a

lgor

ithm


Downsampling - why should we do it?• To reduce size of data, recorded in high sampling rates

• Recorded biosignal at 32 KHz, but we want to study frequencies up to 250 Hz.

• Computational cost of some analysis methods is very high, specifically in long-term continuous recordings.

• Two function for downsampling (DS) in MATLAB are

• y = downsample(x,n); % xis input signal and n is DS ratio

• y = decimate(x,n);

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Downsampling - aliasing problem• Downsampling by keeping nth sample may introduce aliasing

(‘downsample’ function).

• Aliasing occurs when new sampling rate is very low to capture high frequency content.

• HF contents leaks into lower frequencies (results in wrong FFT)

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Fig. Aliasing problem by downsampling


Downsampling - aliasing problem• Solution: applying a lowpass filter before downsampling, with

cutoff frequency of half of new sampling rate.

• ‘decimate’ by nature do this. Use it instead of ‘downsample’!

6.64 6.645 6.65 6.655 6.66 6.665 6.67

−200

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−50

0

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100

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time (sec)

rawDS by downsampleDS by decimate

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Fig. Raw data and its downsampled versions using ‘downsample’ and ‘decimate’ functions of MATLAB


Preprocessing - removing linear trends• A linear trend indicates a systematic increase/decrease in data.

Can result from sensor drift, for example.

• ‘detrend’ function subtracts the mean or a best-fit line (in the least-squares sense) from your data.

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Fig. Removing linear trends of a signal. Source: MATLAB help documentation


Digital filters• Why do we need filter signals?

• Obtain desired frequency components for further analysis

• Removing interferences

EEG

Delta

0.5-4 Hz

SWS

< 1 Hz

Spindle

11-16 Hz

0.2

mV

1000 ms

NREM

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Fig. Ten seconds of EEG signal recorded from mouse during non-REM sleep stage. Filtered to extract desired frequency components. SWS (Slow Wave Sleep), Delta activity and Spindling


Digital filters• Filter design is the process of creating the filter coefficients to meet

specific filtering requirements.

• Two types are IIR and FIR

• Infinite impulse response (IIR)

• Finite impulse response (IIR)

• Main advantage of IIR over FIR filters

• provide desired specifications with a much lower filter order.

• Main advantage of FIR over IIR filters

• can have exactly linear phase.

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IIR filter design in MATLAB

Filter name function in MATLAB

Butterworth [b,a] = butter(order,Wn,ftype)

Chebyshev type I [b,a] = cheby1(order,Rp,Wn,ftype)

Chebyshev type II [b,a] = cheby2(order,Rs,Wn,ftype)

Elliptic [b,a] = ellip(order,Rp,Rs,Wn,ftype)

Wn: normalized cutoff frequency ftype: type of filter; ‘low’, ‘high’, ‘stop’, or bandpass filter

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IIR filter design in MATLAB• Examples of lowpass IIR filters of order 8.

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Fig. Frequency response of different lowpass IIR filters with same order of 8.


FIR filter design in MATLAB

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Description function in MATLAB

Window-based FIR filter design b = fir1(order,Wn,ftype)

Frequency sampling-based FIR filter design b = fir2(order,Wn,ftype)

Least square linear-phase FIR filter design b = firls(n,f,a,ftype)

… …


Applying designed filters• There are several functions to apply designed filter on signal

• y = filter(b,a,x) - x: input, y: output, b and a: filter coefficients

• y = filtfilt(b,a,x) - performs zero-phase filtering by processing the input data in both the forward and reverse directions.

• ‘filtfilt’ function is preferred over ‘filter’ function, as it does not induce phase shift on the filtered signal.

• very important for accurate measuring of synchronisation between two signals

• But cannot be applied for real-time processing (rare cases)

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Comparing ‘filter’ and ‘filtfilt’

3300 3350 3400 3450 3500 3550 3600

−300

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0

100

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600

rawfilterfiltfilt

% MATLAB code % Sampling frequency of raw data is 500 Hz % Lowpass filter with cutoff frequency of 10 Hz

[b,a] = butter(4, 10/(500/2), 'low'); DeciSamplesFilt = filter(b,a, DeciSamples); DeciSamplesFiltFilt = filtfilt(b,a, DeciSamples);

plot(DeciSamples, 'k', 'LineWidth', 1.5); hold on plot(DeciSamplesFilt, 'b', 'LineWidth', 1.5); plot(DeciSamplesFiltFilt, 'r', 'LineWidth', 1.5) legend('raw', 'filter', 'filtfilt')

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Fig. Lowpass filtered signal with cutoff frequency of 10 Hz using ‘filter’ and ‘filtfilt’ functions.


Discrete Fourier Transform (DFT)• Any waveform can be expressed as a sum of sinusoidal waves!

• FT breaks a signal into its related sine waves

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The more frequencies you use – the closer you get to the original signal

! 1

! 2

! 3

! 10

Remember the relation –

An abrupt change in the time domain will demand a wide range of frequencies to be reconstructed from.

" Use the time constants of the phenomenon you’re looking for to determine your sampling rate + a factor for increased resolution

1~t

f△△

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Fig. Representing a sawtooth as sum of 10 sine waves. Source: Wikipedia


Fast Fourier Transform (FFT)• FFT is an algorithm to calculate DFT

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

3

3.5

frequency (Hz)

|P1(

f)|

rawHighpassBandpass

0 5 10 15 20 25 30 350

0.5

1

1.5

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frequency (Hz)

|P1(

f)|

rawHighpassBandpass

10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

frequency (Hz)

|P1(

f)|

rawHighpassBandpass

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Fig. FFT of raw, highpass filtered (> 30 Hz) and bandpass filtered (6-9 Hz) signals using FIR filters designed by ‘fir1’ function


Plot data in MATLAB

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Fig. Common graphic functions in MATLAB (source: MATLAB help documentation)


Feature extraction from signals• Measured signal is output of a system

• Feature extraction

• transforms raw data into more informative signatures of a system

• reduce size of raw data

• Next step: we can use machine learning algorithms

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Feature extraction from signals• Features can be categorized in different ways

• Linear or nonlinear

• Number of involved channels

• univariate (extracted from one signal)

• bivariate (two signals)

• multivariate (more than two signals simultaneously).

• Time domain, frequency domain, or time-frequency domain.

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Homework• Download the related exercise (18.09.2015) here.

• Go through the code and try to understand each part.

• Load different file formats provided. Try to load your data if any.

• Downsample data using two provided functions, and compare results.

• Filter signal using lowpass, highpass, bandpass and stopband

filters in several frequency bands, and plot the results.

• Apply Fast Fourier Transform (FFT) on the original signal and the filtered ones to see the effects of filtering in frequency domain.

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Questions?

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