# resample

Resample uniform or nonuniform data to new fixed rate

## Syntax

• y = resample(x,p,q) example
• y = resample(x,p,q,n)
• y = resample(x,p,q,n,beta) example
• y = resample(x,p,q,b)
• [y,b] = resample(x,p,q,___) example
• y = 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,___)

## Description

example

y = 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).

example

y = 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.

example

y = 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.

## Examples

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### Resample Linear Sequence

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 Window

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 Sinusoid

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 Set

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. The observations have several gaps because Jupiter was not visible on cloudy nights.

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]'; 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]'; 

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.

[ys,tys] = resample(yg,t,fs,3,1,'spline'); plot(t,yg,'o',tys,ys,'.-') xlabel('Day') 

Compute the periodogram power spectrum estimate of the uniformly spaced, linearly interpolated data. The signal peaks at the inverse of the orbital period.

[pxx,f] = periodogram(y,[],[],fs,'power'); [pk,i0] = max(pxx); f0 = f(i0); T0 = 1/f0 plot(f,pxx,f0,pk,'o') xlabel('Frequency (day^{-1})') 
T0 = 17.0667 

## Input Arguments

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### x — Input signalvector | matrix

Input signal, specified as a vector or matrix. If x is a matrix, then its columns are treated as independent channels. x can contain NaNs. NaNs are treated as missing data and are excluded from the resampling.

Example: cos(pi/4*(0:159))+randn(1,160) is a single-channel row-vector signal.

Example: cos(pi./[4;2]*(0:159))'+randn(160,2) is a two-channel signal.

Data Types: single | double

### p,q — Resampling factorspositive integers

Resampling factors, specified as positive integers.

Data Types: single | double

### n — Neighbor term number10 (default) | positive integer

Neighbor term number, specified as a positive integer. If n = 0, resample performs nearest-neighbor interpolation. The length of the antialiasing FIR filter is proportional to n. Larger values of n provide better accuracy at the expense of more computation time.

Data Types: single | double

### beta — Shape parameter of Kaiser window5 (default) | positive real scalar

Shape parameter of Kaiser window, specified as a positive real scalar. Increasing beta widens the mainlobe of the window used to design the antialiasing filter and decreases the amplitude of the window's sidelobes.

Data Types: single | double

### b — FIR filter coefficientsvector

FIR filter coefficients, specified as a vector. By default, resample designs the filter using firls with a Kaiser window. When compensating for the delay, resample assumes b has odd length and linear phase.

Example: fir1(4,0.5) specifies a 4th-order lowpass filter with normalized cutoff frequency 0.5π rad/sample.

Data Types: single | double

### tx — Time instantsnonnegative real vector

Time instants, specified as a nonnegative real vector. tx must increase monotonically but need not be uniformly spaced. tx can contain NaNs. NaNs are treated as missing data and are excluded from the resampling.

Data Types: single | double

### fs — Sample ratepositive scalar

Sample rate, specified as a positive scalar. The sample rate is the number of samples per unit time. If the unit of time is seconds, then the sample rate is in Hz.

Data Types: single | double

### method — Interpolation method'linear' (default) | 'pchip' | 'spline'

Interpolation method, specified as one of 'linear', 'pchip', or 'spline':

• 'linear' — Linear interpolation.

• 'pchip' — Shape-preserving piecewise cubic interpolation.

• 'spline' — Spline interpolation using not-a-knot end conditions.

See the interp1 reference page for more information.

Data Types: char

## Output Arguments

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### y — Resampled signalvector | matrix

Resampled signal, returned as a vector or matrix. If x is a signal of length N and you specify p,q, then y is of length ⌈N × p/q⌉.

### b — FIR filter coefficientsvector

FIR filter coefficients, returned as a vector.

Data Types: single | double

### ty — Output instantsnonnegative real vector

Output instants, returned as a nonnegative real vector.

Data Types: single | double

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### Algorithms

resample performs an FIR design using firls, normalizes the result to account for the processing gain of the window, and then implements a rate change using upfirdn.