Change of frequency content after using the retime function

Hi everyone,

I am using the retime function to downsample a set of data. I was surprised when I saw that after using the function, the frequency content of the data has changed. It doesn't do that if I filter the data before retiming:

Could someone explain this phenomena to me?

Thanks!

I include the code below:

dt1 = seconds(test_table.time(2) - test_table.time(1));
dt2 = 0.01;
dt = seconds(dt2);
test_table_rt = retime(test_table,'regular','linear','TimeStep',dt);


%% Try after filtering
test_table_f = lowpass(test_table, 10); % Filter down to 10 Hz

test_table_frt = retime(test_table_f,'regular','linear','TimeStep',dt);

%% Plot the differences:

figure
plot(test_table.time, test_table.data)
hold on
plot(test_table_rt.time, test_table_rt.data)
plot(test_table_frt.time, test_table_frt.data)

%% Plot the different spectra

figure
ax = gca;
window = 1000;

    [pxx,f] = pwelch(test_table.data,window*dt2/dt1,[],[],1/dt1);
    plot(f,pxx, 'DisplayName', 'Original');
hold on
    [pxx,f] = pwelch(test_table_rt.data,window,[],[],1/dt2);
    plot(f,pxx, 'DisplayName', 'Retimed');
    [pxx,f] = pwelch(test_table_frt.data,window,[],[],1/dt2);
    plot(f,pxx, 'DisplayName', 'Filtered and retimed');
    ax.XScale = 'log';
    % ax.YScale = 'log';

grid on
grid minor
legend
xlabel('Frequency, Hz') 
ylabel('PSD, dB/Hz')
xlim([1 50])

Answer 1

[Sulaymon Eshkabilov]

Here is how to solve this issue:

load('question_data.mat')
dt1 = seconds(test_table.time(2) - test_table.time(1));
dt2 = 0.01;
dt = seconds(dt2);
% Averaging is necessary here before resampling
test_table_rt0 = retime(test_table,'secondly','mean');
% Resampling is done after averaging
test_table_rt = retime(test_table_rt0,'regular','linear','SampleRate',100);

% Try after filtering
test_table_f = lowpass(test_table, 10); % Filter down to 10 Hz

test_table_frt = retime(test_table_f,'regular','linear','TimeStep',dt);

%% Plot the differences:

figure
plot(test_table.time, test_table.data)
hold on
plot(test_table_rt.time, test_table_rt.data)
plot(test_table_frt.time, test_table_frt.data)

%% Plot the different spectra

figure
ax = gca;
window = 1000;

    [pxx,f] = pwelch(test_table.data,window*dt2/dt1,[],[],1/dt1);
    plot(f,pxx, 'DisplayName', 'Original');
hold on
    [pxx,f] = pwelch(test_table_rt.data,window,[],[],1/dt2);
    plot(f,pxx, 'DisplayName', 'Retimed');
    [pxx,f] = pwelch(test_table_frt.data,window,[],[],1/dt2);
    plot(f,pxx, 'DisplayName', 'Filtered and retimed');
    ax.XScale = 'log';
    % ax.YScale = 'log';

grid on
grid minor
legend
xlabel('Frequency, Hz') 
ylabel('PSD, dB/Hz')
xlim([1 50])

[Julius Bartasevicius]

This solution changes the frequency content as well.

Answer 2

[Peter Perkins]

Julius, I'm definitely not any kind of signal processing expert, but I think what you want is resample, from the Signal Processing Tbx.

If I replace this

%test_table_f = lowpass(test_table, 10); % Filter down to 10 Hz
%test_table_frt = retime(test_table_f,'regular','linear','TimeStep',dt);

in your code with this

test_table_frt = resample(test_table,1,10);
test_table_frt.Properties.DimensionNames(1) = "time"; % just cosmetics to make code below this work

I get this:

[Peter Perkins]

It is perhaps not clear enough in the doc for retime, but this

dt1 = <ms time step, so .001>
dt2 = 0.01;
dt = seconds(dt2);
test_table_rt = retime(test_table,'regular','linear','TimeStep',dt);

just takes every 10th point. Often when you do downsampling like that you'd want 'mean', not 'linear', but I think you are concerned with frequency content and that's what resample is all about.

I've made a note to add some more information about this to the resample doc page.