Department of Medical Physics and Clinical Engineering

Royal Liverpool University Hospital, Liverpool, UK


The Ornstein-Uhlenbeck 3rd-order bandpass filter (OUGP) applied directly to the

un-resampled Heart Rate Variability (HRV) tachogram for detrending and low-pass filtering





.             Setting the bandwidth ... ...



Sampling Frequency (Fs)

For irregularly-sampled data, the sampling frequency does not have straight-forward meaning.

Here take a representative value as Fsmed =1/(median(RR_interval))

Nyquist frequency (Fn)

Let's call our effective Nyquist frequency Fnmed=Fsmed / 2


Intuitively 0.5*Fs .. but this will not 'cover' all frequencies as some components will be >Fsmed .

In this demo, we conservatively limit the upper bandwidth of interest to 0.45*Fnmed

Plotting the Lomb Scargle PSD

Plots are over the bandwidth [0 ... 0.45*Fnmed] Hz

Why use an upper frequency cut-off for HRV?

Bandwith limiting (anti-aliasing filter for resampling)

Why detrend the HRV?

Good point. Maybe to deal with non-stationarity? See the many references in the Literature.




.             Using the web Gui demo (with example data provided: all freq in Hz) ... ...

Gaussian noise:

This is from MatLab randn() and has been low-pass filtered at 1Hz and

sampled back onto a random irregular time axis: Fsmed is 4Hz


Set bandwidth [0.001 ... 1.0]: all the signal appears in the PSD

Set bandwidth [0.001 ... 0.5]: low-pass effect

Set bandwidth [0.01 ... 0.5]: band-pass effect


Set bandwidth [0.001 ... 0.3]: low frequencies dominate (PSD uninteresting)

Set bandwidth [0.09 ... 0.3]: typical LF HF distribution after detrending

Premature baby:

Note typical high heart rate

Set bandwidth [0.001 ... 0.8]: low frequencies dominate (PSD uninteresting)

Set bandwidth [0.03 ... 0.8]: a typical LF HF distribution after detrending: resp rate high

Synthetic sines (3-peak, 3-peak plus Brownian 'drift', textbook 2-peak LF and HF)

Frequencies of interest: <0.01 ... 0.04 ... 0.15 ... 40 Hz

Can be used to illustrate detrending and bandwidth selection





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