interpolating data to different sample rate

I have 2 data sets I want to correlate. One is sampled every second, and one is sampled at a much smaller interval (attached). I want to get them both to the same sampling rate by increasing the smaller intervalled one to 1s.

How would I go about this?

Answer 1

[Benjamin Thompson]

You can use interp1 to interpolate, or resample, one signal onto the same set of time values as another.

Answer 2

[Star Strider]

If they are signals, use resample because it includes an anti-aliasing filter, and these appear to be signals.

format longE
T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/894275/Raw%20Data.xlsx', 'VariableNamingRule','preserve')

T1 = 499×5 table
          Time (s)          Linear Acceleration x (m/s^2)    Linear Acceleration y (m/s^2)    Linear Acceleration z (m/s^2)    Absolute acceleration (m/s^2)
    ____________________    _____________________________    _____________________________    _____________________________    _____________________________

    1.86912208300000e-01        8.93268171700000e-03              8.41090908300000e-03            -1.81244389400000e-01            1.81659199800000e-01     
    1.96983208300000e-01        8.07946331800000e-03              1.19734714000000e-02            -2.56993314000000e-01            2.57398922300000e-01     
    2.07023208300000e-01        7.70330462600000e-03             -4.94139058500000e-03            -3.28702397300000e-01            3.28829780100000e-01     
    2.17063208300000e-01        1.09702536500000e-02             -2.36724525700000e-03            -3.19120565100000e-01            3.19317843800000e-01     
    2.27134208300000e-01        1.50394041100000e-02             -1.41565110900000e-02            -2.72862072600000e-01            2.73642652300000e-01     
    2.37174208300000e-01        7.19481613500000e-03             -9.09744529100000e-03            -2.18375963000000e-01            2.18683767300000e-01     
    2.47215208300000e-01        9.69910550900000e-03              1.32750067900000e-04            -1.58347862400000e-01            1.58644684100000e-01     
    2.57255208300000e-01        1.99553044900000e-02              7.00284473600000e-03            -1.93227673200000e-01            1.94381551800000e-01     
    2.67326208300000e-01        2.18355497700000e-02              8.38541887700000e-03            -2.33348928100000e-01            2.34518290800000e-01     
    2.77366208300000e-01        1.39188583200000e-02              1.63915910000000e-02            -2.64484766700000e-01            2.65357514900000e-01     
    2.87406208300000e-01        1.97226218500000e-02              1.40000798000000e-02            -3.12020875800000e-01            3.12956883600000e-01     
    2.97477208300000e-01        1.37514086800000e-02              7.38640381000000e-03            -2.80596184700000e-01            2.81030032400000e-01     
    3.07517208300000e-01        1.23518045200000e-02              1.00708239700000e-02            -2.15932411600000e-01            2.16519733300000e-01     
    3.17558208300000e-01        1.03200432700000e-02              7.87407986800000e-03            -1.92114363300000e-01            1.92552416300000e-01     
    3.27598208300000e-01        2.17892471300000e-02              7.59140353600000e-03            -1.70313019800000e-01            1.71868919200000e-01     
    3.37669208300000e-01        1.13416249300000e-02              1.17506742100000e-02            -1.91676406900000e-01            1.92370880700000e-01     

M1 = table2array(T1);
TimeStats = [mean(diff(M1(:,1))); std(diff(M1(:,1))); 1/mean(diff(M1(:,1)))]

TimeStats = 3×1

8.031238955220885e-03 4.503231238111708e-02 1.245137899115712e+02

[y,t]  = resample(M1(:,2:end), M1(:,1), 1.25E+2);                                   % Resample To Uniform 1.25 Hz Sampling Frequency
T1r = array2table([t, y], 'VariableNames',T1.Properties.VariableNames)

T1r = 500×5 table
          Time (s)          Linear Acceleration x (m/s^2)    Linear Acceleration y (m/s^2)    Linear Acceleration z (m/s^2)    Absolute acceleration (m/s^2)
    ____________________    _____________________________    _____________________________    _____________________________    _____________________________

    1.86912208300000e-01        8.93268171700000e-03              8.41090908300000e-03            -1.81244389400000e-01            1.81659199800000e-01     
    1.94912208300000e-01        8.25491911229342e-03              1.12408662407798e-02            -2.41416308454712e-01            2.41823809074154e-01     
    2.02912208300000e-01        7.85732737329203e-03              1.98460519391782e-03            -2.99340241777460e-01            2.99581547389263e-01     
    2.10912208300000e-01        8.96875928280637e-03             -3.94429385386534e-03            -3.24990868871135e-01            3.25145325889771e-01     
    2.18912208300000e-01        1.17173352904071e-02             -4.53171279003712e-03            -3.10627669396247e-01            3.10932040097935e-01     
    2.26912208300000e-01        1.49497058275931e-02             -1.38966345122097e-02            -2.73881771272922e-01            2.74649492982455e-01     
    2.34912208300000e-01        8.96219242976595e-03             -1.02372467688225e-02            -2.30651618370040e-01            2.31065938402590e-01     
    2.42912208300000e-01        8.62590989339179e-03             -3.82278530002618e-03            -1.84072483143133e-01            1.84374011359197e-01     
    2.50912208300000e-01        1.34757158309878e-02              2.66250504678105e-03            -1.71191553687610e-01            1.71803966957261e-01     
    2.58912208300000e-01        2.02646646755784e-02              7.23032218130206e-03            -1.99828896451842e-01            2.00985322679059e-01     
    2.66912208300000e-01        2.17582563983467e-02              8.32858383635121e-03            -2.31699618247096e-01            2.32868344424665e-01     
    2.74912208300000e-01        1.58538743377590e-02              1.44347039093783e-02            -2.56874473082032e-01            2.57819720483526e-01     
    2.82912208300000e-01        1.71248017998187e-02              1.50705430801594e-02            -2.90743258838307e-01            2.91650951036474e-01     
    2.90912208300000e-01        1.76438736249956e-02              1.16976720926284e-02            -3.01081051850382e-01            3.01842243513892e-01     
    2.98912208300000e-01        1.35513656551394e-02              7.77008338466134e-03            -2.71353902389393e-01            2.71809685865289e-01     
    3.06912208300000e-01        1.24361432168924e-02              9.90906359183266e-03            -2.19828983584612e-01            2.20407057100349e-01     

The data need to be resampled regardless, since the standard deviation of the sampling intervals is not near 0 as it should be, indicating irregulal sampling intervals. This is not appropriate for signal processing applications, all of which assuming regular sampling intervals.

To use these data in any signal processing application — and even for fft — they need to be resampled first to a consistent sampling frequency. I chose 125 Hz because the mean sampling frequency of the original data ia 124.514... Hz so this would likely produce the least disruptive resampling.

Resample the other signals at 125 Hz in order to compare them. Ideally, they also need to have identical sampling times (not simply the same sampling frequency) in order to do this correctly.

.

[C.G.]

Thank you for your reponse.

My other dataset has been resampled using retime as it is in a different format as its from different equipment. How would I go about getting them identical for correlation?

[Star Strider]

My pleasure!

format longE
T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/895055/S%20Raw.xlsx', 'VariableNamingRule','preserve')

T1 = 499×2 table
                Var1                         Var2        
    _____________________________    ____________________

    {''2022-02-10 18:39:01.000''}    5.12916339756230e-01
    {''2022-02-10 18:39:02.000''}    6.04788079457912e-01
    {''2022-02-10 18:39:03.000''}    6.96659819159595e-01
    {''2022-02-10 18:39:04.000''}    7.00000000000000e-01
    {''2022-02-10 18:39:05.000''}    5.44174346120565e-01
    {''2022-02-10 18:39:06.000''}    6.37207809050609e-01
    {''2022-02-10 18:39:07.000''}    4.59791541906453e-01
    {''2022-02-10 18:39:08.000''}    3.51146870578991e-01
    {''2022-02-10 18:39:09.000''}    4.41666719473181e-01
    {''2022-02-10 18:39:10.000''}    5.64390928432270e-01
    {''2022-02-10 18:39:11.000''}    7.45466810577674e-01
    {''2022-02-10 18:39:12.000''}    9.64411062348048e-01
    {''2022-02-10 18:39:13.000''}    1.39925822374150e+00
    {''2022-02-10 18:39:14.000''}    1.30740876133655e+00
    {''2022-02-10 18:39:15.000''}    1.21908190407119e+00
    {''2022-02-10 18:39:16.000''}    1.20000000000000e+00

T1.Var1 = datetime(T1.Var1, 'InputFormat','''''yyyy-MM-dd HH:mm:ss.SSS''''')

T1 = 499×2 table
            Var1                    Var2        
    ____________________    ____________________

    10-Feb-2022 18:39:01    5.12916339756230e-01
    10-Feb-2022 18:39:02    6.04788079457912e-01
    10-Feb-2022 18:39:03    6.96659819159595e-01
    10-Feb-2022 18:39:04    7.00000000000000e-01
    10-Feb-2022 18:39:05    5.44174346120565e-01
    10-Feb-2022 18:39:06    6.37207809050609e-01
    10-Feb-2022 18:39:07    4.59791541906453e-01
    10-Feb-2022 18:39:08    3.51146870578991e-01
    10-Feb-2022 18:39:09    4.41666719473181e-01
    10-Feb-2022 18:39:10    5.64390928432270e-01
    10-Feb-2022 18:39:11    7.45466810577674e-01
    10-Feb-2022 18:39:12    9.64411062348048e-01
    10-Feb-2022 18:39:13    1.39925822374150e+00
    10-Feb-2022 18:39:14    1.30740876133655e+00
    10-Feb-2022 18:39:15    1.21908190407119e+00
    10-Feb-2022 18:39:16    1.20000000000000e+00

TT1 = table2timetable(T1)

TT1 = 499×1 timetable
            Var1                    Var2        
    ____________________    ____________________

    10-Feb-2022 18:39:01    5.12916339756230e-01
    10-Feb-2022 18:39:02    6.04788079457912e-01
    10-Feb-2022 18:39:03    6.96659819159595e-01
    10-Feb-2022 18:39:04    7.00000000000000e-01
    10-Feb-2022 18:39:05    5.44174346120565e-01
    10-Feb-2022 18:39:06    6.37207809050609e-01
    10-Feb-2022 18:39:07    4.59791541906453e-01
    10-Feb-2022 18:39:08    3.51146870578991e-01
    10-Feb-2022 18:39:09    4.41666719473181e-01
    10-Feb-2022 18:39:10    5.64390928432270e-01
    10-Feb-2022 18:39:11    7.45466810577674e-01
    10-Feb-2022 18:39:12    9.64411062348048e-01
    10-Feb-2022 18:39:13    1.39925822374150e+00
    10-Feb-2022 18:39:14    1.30740876133655e+00
    10-Feb-2022 18:39:15    1.21908190407119e+00
    10-Feb-2022 18:39:16    1.20000000000000e+00

TotTime = TT1.Var1(end) - TT1.Var1(1)

TotTime = duration
   00:08:18

TT1.ssSSS = TT1.Var1;
TT1.ssSSS.Format = 'ss.SSS'                                                 % Cumulative Time In s & ms

TT1 = 499×2 timetable
            Var1                    Var2            ssSSS 
    ____________________    ____________________    ______

    10-Feb-2022 18:39:01    5.12916339756230e-01    01.000
    10-Feb-2022 18:39:02    6.04788079457912e-01    02.000
    10-Feb-2022 18:39:03    6.96659819159595e-01    03.000
    10-Feb-2022 18:39:04    7.00000000000000e-01    04.000
    10-Feb-2022 18:39:05    5.44174346120565e-01    05.000
    10-Feb-2022 18:39:06    6.37207809050609e-01    06.000
    10-Feb-2022 18:39:07    4.59791541906453e-01    07.000
    10-Feb-2022 18:39:08    3.51146870578991e-01    08.000
    10-Feb-2022 18:39:09    4.41666719473181e-01    09.000
    10-Feb-2022 18:39:10    5.64390928432270e-01    10.000
    10-Feb-2022 18:39:11    7.45466810577674e-01    11.000
    10-Feb-2022 18:39:12    9.64411062348048e-01    12.000
    10-Feb-2022 18:39:13    1.39925822374150e+00    13.000
    10-Feb-2022 18:39:14    1.30740876133655e+00    14.000
    10-Feb-2022 18:39:15    1.21908190407119e+00    15.000
    10-Feb-2022 18:39:16    1.20000000000000e+00    16.000

TssSSS = second(TT1.ssSSS);
TimeStats = [mean(diff(TssSSS)); std(diff(TssSSS)); 1/mean(diff(TssSSS))]

TimeStats = 3×1

3.614457831325301e-02 7.550946933513523e+00 2.766666666666667e+01

[y,t]  = resample(TT1.Var2, TssSSS, 1.25E+2);                                   % Resample To Uniform 1.25 Hz Sampling Frequency
T1r = array2table([t, y], 'VariableNames',{'Time (ms)','Var2'})

T1r = 7386×2 table
         Time (ms)                  Var2        
    ____________________    ____________________

    0.00000000000000e+00    5.84632575588755e+01
    8.00000000000000e-03    6.09226103576792e+01
    1.60000000000000e-02    6.29139951844163e+01
    2.40000000000000e-02    6.44317557038368e+01
    3.20000000000000e-02    6.54828195436685e+01
    4.00000000000000e-02    6.60861145277872e+01
    4.80000000000000e-02    6.62715991338979e+01
    5.60000000000000e-02    6.60789485631659e+01
    6.40000000000000e-02    6.55559499994597e+01
    7.20000000000000e-02    6.47566706063528e+01
    8.00000000000000e-02    6.37394691873600e+01
    8.80000000000000e-02    6.25649269546137e+01
    9.60000000000000e-02    6.12937743680878e+01
    1.04000000000000e-01    5.99848895005805e+01
    1.12000000000000e-01    5.86934389560559e+01
    1.20000000000000e-01    5.74665953396047e+01

Now, the previous set and this set are all sampled at the same frequency (125 Hz), so they can all be processed with the same filters or other signal processing procedures.

.