Define a vector with three peaks and plot it.

data = [25 8 15 5 6 10 10 3 1 20 7];
plot(data)

Find the local maxima. The peaks are output in order of occurrence. The first sample is not included despite being the maximum. For the flat peak, the function returns only the point with lowest index.

pks = findpeaks(data)

pks = 1×3

    15    10    20

Use findpeaks without output arguments to display the peaks.

findpeaks(data)

Create a signal that consists of a sum of bell curves. Specify the location, height, and width of each curve.

x = linspace(0,1,1000);

Pos = [1 2 3 5 7 8]/10;
Hgt = [3 4 4 2 2 3];
Wdt = [2 6 3 3 4 6]/100;

for n = 1:length(Pos)
    Gauss(n,:) = Hgt(n)*exp(-((x - Pos(n))/Wdt(n)).^2);
end

PeakSig = sum(Gauss);

Plot the individual curves and their sum.

plot(x,Gauss,'--',x,PeakSig)

Use findpeaks with default settings to find the peaks of the signal and their locations.

[pks,locs] = findpeaks(PeakSig,x);

Plot the peaks using findpeaks and label them.

findpeaks(PeakSig,x)

text(locs+.02,pks,num2str((1:numel(pks))'))

Sort the peaks from tallest to shortest.

[psor,lsor] = findpeaks(PeakSig,x,'SortStr','descend');

findpeaks(PeakSig,x)

text(lsor+.02,psor,num2str((1:numel(psor))'))

Create a signal that consists of a sum of bell curves riding on a full period of a cosine. Specify the location, height, and width of each curve.

x = linspace(0,1,1000);

base = 4*cos(2*pi*x);

Pos = [1 2 3 5 7 8]/10;
Hgt = [3 7 5 5 4 5];
Wdt = [1 3 3 4 2 3]/100;

for n = 1:length(Pos)
    Gauss(n,:) =  Hgt(n)*exp(-((x - Pos(n))/Wdt(n)).^2);
end

PeakSig = sum(Gauss)+base;

Plot the individual curves and their sum.

plot(x,Gauss,'--',x,PeakSig,x,base)

Use findpeaks to locate and plot the peaks that have a prominence of at least 4.

findpeaks(PeakSig,x,'MinPeakProminence',4,'Annotate','extents')

The highest and lowest peaks are the only ones that satisfy the condition.

Display the prominences and the widths at half prominence of all the peaks.

[pks,locs,widths,proms] = findpeaks(PeakSig,x);
widths

widths = 1×6

    0.0154    0.0431    0.0377    0.0625    0.0274    0.0409

proms

proms = 1×6

    2.6816    5.5773    3.1448    4.4171    2.9191    3.6363

Sunspots are a cyclic phenomenon. Their number is known to peak roughly every 11 years.

Load the file sunspot.dat, which contains the average number of sunspots observed every year from 1700 to 1987. Find and plot the maxima.

load sunspot.dat

year = sunspot(:,1);
avSpots = sunspot(:,2);

findpeaks(avSpots,year)

Improve your estimate of the cycle duration by ignoring peaks that are very close to each other. Find and plot the peaks again, but now restrict the acceptable peak-to-peak separations to values greater than six years.

findpeaks(avSpots,year,'MinPeakDistance',6)

Use the peak locations returned by findpeaks to compute the mean interval between maxima.

[pks,locs] = findpeaks(avSpots,year,'MinPeakDistance',6);

meanCycle = mean(diff(locs))

meanCycle = 10.9600

Create a datetime array using the year data. Assume the sunspots were counted every year on March 20th, close to the vernal equinox. Find the peak sunspot years. Use the years function to specify the minimum peak separation as a duration.

ty = datetime(year,3,20);

[pk,lk] = findpeaks(avSpots,ty,'MinPeakDistance',years(6));

plot(ty,avSpots,lk,pk,'o')

Compute the mean sunspot cycle using datetime functionality.

dttmCycle = years(mean(diff(lk)))

dttmCycle = 10.9600

Create a timetable with the data. Specify the time variable in years. Plot the data. Show the last five entries of the timetable.

TT = timetable(years(year),avSpots);
plot(TT.Time,TT.Variables)

entries = TT(end-4:end,:)

entries=5×1 timetable
      Time      avSpots
    ________    _______

    1983 yrs     66.6  
    1984 yrs     45.9  
    1985 yrs     17.9  
    1986 yrs     13.4  
    1987 yrs     29.3  

Load an audio signal sampled at 7418 Hz. Select 200 samples.

load mtlb
select = mtlb(1001:1200);

Find the peaks that are separated by at least 5 ms.

To apply this constraint, findpeaks chooses the tallest peak in the signal and eliminates all peaks within 5 ms of it. The function then repeats the procedure for the tallest remaining peak and iterates until it runs out of peaks to consider.

findpeaks(select,Fs,'MinPeakDistance',0.005)

Find the peaks that have an amplitude of at least 1 V.

findpeaks(select,Fs,'MinPeakHeight',1)

Find the peaks that are at least 1 V higher than their neighboring samples.

findpeaks(select,Fs,'Threshold',1)

Find the peaks that drop at least 1 V on either side before the signal attains a higher value.

findpeaks(select,Fs,'MinPeakProminence',1)

Sensors can return clipped readings if the data are larger than a given saturation point. You can choose to disregard these peaks as meaningless or incorporate them to your analysis.

Generate a signal that consists of a product of trigonometric functions of frequencies 5 Hz and 3 Hz embedded in white Gaussian noise of variance 0.1². The signal is sampled for one second at a rate of 100 Hz. Reset the random number generator for reproducible results.

rng default

fs = 1e2;
t = 0:1/fs:1-1/fs;

s = sin(2*pi*5*t).*sin(2*pi*3*t)+randn(size(t))/10;

Simulate a saturated measurement by truncating every reading that is greater than a specified bound of 0.32. Plot the saturated signal.

bnd = 0.32;
s(s>bnd) = bnd;

plot(t,s)
xlabel('Time (s)')

Locate the peaks of the signal. findpeaks reports only the rising edge of each flat peak.

[pk,lc] = findpeaks(s,t);

hold on
plot(lc,pk,'x')

Use the 'Threshold' name-value pair to exclude the flat peaks. Require a minimum amplitude difference of $$10^{-4}$$ between a peak and its neighbors.

[pkt,lct] = findpeaks(s,t,'Threshold',1e-4);

plot(lct,pkt,'o','MarkerSize',12)

Create a signal that consists of a sum of bell curves. Specify the location, height, and width of each curve.

x = linspace(0,1,1000);

Pos = [1 2 3 5 7 8]/10;
Hgt = [4 4 2 2 2 3];
Wdt = [3 8 4 3 4 6]/100;

for n = 1:length(Pos)
    Gauss(n,:) =  Hgt(n)*exp(-((x - Pos(n))/Wdt(n)).^2);
end

PeakSig = sum(Gauss);

Plot the individual curves and their sum.

plot(x,Gauss,'--',x,PeakSig)
grid

Measure the widths of the peaks using the half prominence as reference.

findpeaks(PeakSig,x,'Annotate','extents')

Measure the widths again, this time using the half height as reference.

findpeaks(PeakSig,x,'Annotate','extents','WidthReference','halfheight')
title('Signal Peak Widths')