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# resample() - Signal Processing

exampley = resample(x,p,q) resamples
the input sequence, x, at p/q times
the original sample rate. If x is a matrix, then resample treats
each column of x as an independent channel. resample applies
an antialiasing FIR lowpass filter to x and compensates
for the delay introduced by the filter.
y = resample(x,p,q,n) uses
an antialiasing filter of order 2 × n × max(p,q).
exampley = resample(x,p,q,n,beta) specifies
the shape parameter of the Kaiser window used to design the lowpass
filter.
y = resample(x,p,q,b) filters x using
the filter coefficients specified in b.
example[y,b] = resample(x,p,q,___) also
returns the coefficients of the filter applied to x during
the resampling.

y = resample(x,tx) resamples
the values, x, of a signal sampled at the instants
specified in vector tx. The function interpolates x linearly
onto a vector of uniformly spaced instants with the same endpoints
and number of samples as tx. NaNs
are treated as missing data and are ignored.
y = resample(x,tx,fs) uses
a polyphase antialiasing filter to resample the signal at the uniform
sample rate specified in fs.
y = resample(x,tx,fs,p,q) interpolates
the input signal to a uniform grid with a sample spacing of (p/q)/fs and
then filters the result to upsample it by p and
downsample it by q. For best results, ensure that fs × q/p is
at least twice as large as the highest frequency component of x.
exampley = resample(x,tx,___,method) specifies
the interpolation method along with any of the arguments from previous
syntaxes in this group. The interpolation method can be 'linear', 'pchip',
or 'spline'.
[y,ty] =
resample(x,tx,___) returns
in ty the instants that correspond to the resampled
signal.
[y,ty,b]
= resample(x,tx,___) returns
in b the coefficients of the antialiasing filter.
Note:

If x is not slowly varying, consider using interp1 with the 'pchip' interpolation
method.

### Syntax

y = resample(x,p,q) exampley = resample(x,p,q,n)y = resample(x,p,q,n,beta) exampley = resample(x,p,q,b)[y,b] = resample(x,p,q,___) exampley = resample(x,tx)y = resample(x,tx,fs)y = resample(x,tx,fs,p,q)y = resample(x,tx,___,method) example[y,ty] =
resample(x,tx,___)[y,ty,b]
= resample(x,tx,___)

### Example

Resample Linear SequenceOpen This Example
Resample a simple linear sequence at 3/2 the original rate of 10 Hz. Plot the original and resampled signals on the same figure.
fs = 10;
t1 = 0:1/fs:1;
x = t1;
y = resample(x,3,2);
t2 = (0:(length(y)-1))*2/(3*fs);

plot(t1,x,'*',t2,y,'o')
xlabel('Time (s)')
ylabel('Signal')
legend('Original','Resampled', ...
'Location','NorthWest')

When filtering, resample assumes that the input sequence, x, is zero before and after the samples it is given. Large deviations from zero at the endpoints of x can result in unexpected values for y.Show these deviations by resampling a triangular sequence and a vertically shifted version of the sequence with nonzero endpoints.x = [1:10 9:-1:1;
10:-1:1 2:10]';
y = resample(x,3,2);

subplot(2,1,1)
plot(1:19,x(:,1),'*',(0:28)*2/3 + 1,y(:,1),'o')
title('Edge Effects Not Noticeable')
legend('Original','Resampled', ...
'Location','South')

subplot(2,1,2)
plot(1:19,x(:,2),'*',(0:28)*2/3 + 1,y(:,2),'o')
title('Edge Effects Noticeable')
legend('Original','Resampled', ...
'Location','North')

Resample Using Kaiser WindowOpen This Example
Construct a sinusoidal signal. Specify a sample rate such that 16 samples correspond to exactly one signal period. Draw a stem plot of the signal. Overlay a stairstep graph for sample-and-hold visualization.
fs = 16;
t = 0:1/fs:1-1/fs;

x = 0.75*sin(2*pi*t);

stem(t,x)
hold on
stairs(t,x)
hold off

Use resample to upsample the signal by a factor of four. Use the default settings. Plot the result alongside the original signal.ups = 4;
dns = 1;

fu = fs*ups;
tu = 0:1/fu:1-1/fu;

y = resample(x,ups,dns);

stem(tu,y)
hold on
stairs(t,x)
hold off
legend('Resampled','Original')

Repeat the calculation. Specify n = 1 so that the antialiasing filter is of order
. Specify a shape parameter
for the Kaiser window. Output the filter as well as the resampled signal.n = 1;
beta = 0;

[y,b] = resample(x,ups,dns,n,beta);

stem(tu,y)
hold on
stairs(t,x,'--')
hold off
legend('n = 1, \beta = 0')

Verify that the filter has the expected order by plotting its impulse response.impz(b)

Increase n to 5 and leave
. Verify that the filter is of order 40. Plot the resampled signal.n = 5;

[y,b] = resample(x,ups,dns,n,beta);

fo = filtord(b)

stem(tu,y)
hold on
stairs(t,x,'--')
hold off
legend('n = 5, \beta = 0')

fo =

40

Leave the filter order at
and increase the shape parameter to
.beta = 20;

y = resample(x,ups,dns,n,beta);

stem(tu,y)
hold on
stairs(t,x,'--')
hold off
legend('n = 5, \beta = 20')

Decrease the filter order back to
and leave
.n = 1;

[y,b] = resample(x,ups,dns,n,beta);

stem(tu,y)
hold on
stairs(t,x,'--')
hold off
legend('n = 1, \beta = 20')

Resample a SinusoidOpen This Example
Generate 60 samples of a sinusoid and resample it at 3/2 the original rate. Display the original and resampled signals.
tx = 0:6:360-3;
x = sin(2*pi*tx/120);

ty = 0:4:360-2;
[y,by] = resample(x,3,2);

plot(tx,x,'+-',ty,y,'o:')
legend('original','resampled')

Plot the frequency response of the anti-aliasing filter.freqz(by)

Resample the signal at 2/3 the original rate. Display the original signal and its resampling.tz = 0:9:360-9;
[z,bz] = resample(x,2,3);

plot(tx,x,'+-',tz,z,'o:')
legend('original','resampled')

Plot the impulse response of the new lowpass filter.impz(bz)

Resample a Nonuniformly Sampled Data SetOpen This Example
Use the data recorded by Galileo Galilei in 1610 to determine the orbital period of Callisto, the outermost of Jupiter's four largest satellites.
Galileo observed the satellites' motion for six weeks, starting on 15 January. The observations have several gaps because Jupiter was not visible on cloudy nights. Generate a datetime array of observation times.t = [0 2 3 7 8 9 10 11 12 17 18 19 20 24 25 26 27 28 29 31 32 33 35 37 ...
41 42 43 44 45]'+1;

yg = [10.5 11.5 10.5 -5.5 -10.0 -12.0 -11.5 -12.0 -7.5 8.5 12.5 12.5 ...
10.5 -6.0 -11.5 -12.5 -12.5 -10.5 -6.5 2.0 8.5 10.5 13.5 10.5 -8.5 ...
-10.5 -10.5 -10.0 -8.0]';

obsv = datetime(1610,1,15+t);
Resample the data onto a regular grid using a sample rate of one observation per day. Use a moderate upsampling factor of 3 to avoid overfitting.fs = 1;

[y,ty] = resample(yg,t,fs,3,1);
Plot the data and the resampled signal.plot(t,yg,'o',ty,y,'.-')
xlabel('Day')

Repeat the procedure using spline interpolation and displaying the observation dates. Express the sample rate in inverse days.fs = 1/86400;

[ys,tys] = resample(yg,obsv,fs,3,1,'spline');

plot(t,yg,'o')
hold on
plot(ys,'.-')
hold off

ax = gca;
ax.XTick = t(1:9:end);
ax.XTickLabel = char(obsv(1:9:end));

Compute the periodogram power spectrum estimate of the uniformly spaced, linearly interpolated data. Choose a DFT length of 1024. The signal peaks at the inverse of the orbital period.[pxx,f] = periodogram(ys,[],1024,1,'power');
[pk,i0] = max(pxx);

f0 = f(i0);
T0 = 1/f0

plot(f,pxx,f0,pk,'o')
xlabel('Frequency (day^{-1})')

T0 =

16.7869

Related ExamplesReconstruct a Signal from Irregularly Sampled Data