Envelope and pulse counter

  The envelope is a line connecting the vertices of the time waveform (or the vertices of its absolute value for negative waves). In this application, it is obtained by Hilbert transform. It is useful for determining the interval between peaks of a signal with periodic peaks. Press  Waveform  button on the analysis screen to go to the  Envelope  screen. If a filter is applied in the Waveform screen, a Hilbert transform is performed on the filtered waveform data. The default display is the absolute value of the analysis signal obtained by the Hilbert transform, smoothed by a low pass filter (LPF; 4th order) with a cutoff frequency of 20 Hz. This LPF can change the cutoff frequency with the slider that appears below.
  From the obtained envelope, the frequency of occurrence of the peaks can be determined. A horizontal line appears when the Counter button is pressed, and the points of the envelope that intersect the line upward are determined, and the frequency of peak occurrence (/sec and /min) is calculated from the average interval of the crossing points.

  Since the heart rate cannot be measured with only one heartbeat, first expand the display time range by pinch-in operation in  Waveform  mode so that several heartbeats are displayed on the screen. You can see the first (wider) and second heart sounds lined up in the figure below. Pressing the  Waveform  button here will cause the envelope of the previous waveform to appear smoothed by the LPF. Note that the LPF cutoff frequency should be changed accordingly depending on the desired signal.

Press the  Counter  button as it appears. In the left panel below, the red horizontal line that appears hangs slightly over the second as well as the first heart sound. This means that the heart rate cannot be measured. Press the  Counter button repeatedly to move the horizontal line up, stop at an appropriate point and read the value that appears. This is the heartbeat of an infant, which is measured to be 135 beats/minute.

  It is also possible to apply LPF to the original waveform in  Waveform  mode beforehand to eliminate the peaks of 2nd heart sounds (highr frequency than 1st heart sounds). The figure below shows the process of applying an LPF with a cutoff frequency of 50 Hz to the original waveform to weaken the second heart sound wave and subsequently generate an envelope. You can see that the peak of the second heart sounds have disappeared and heart rate measurement has become easier.