Change of frequency content after using the retime function

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Julius Bartasevicius
编辑： Peter Perkins 2023-11-17
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])

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回答（2 个）

Sulaymon Eshkabilov
Sulaymon Eshkabilov 2023-11-17
Ran in:
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])
Peter Perkins
Peter Perkins 2023-11-17
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:
  1 个评论
Peter Perkins
Peter Perkins 2023-11-17
编辑：Peter Perkins 2023-11-17
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.

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