FIGS. 4 and 5 show the quantization of the poles for a second-order Butterworth filter with a cutoff frequency of 0.05 Hz and a sampling rate of 256 Hz.

In FIG. 4, the distribution of the poles 63 quantized on six bits is shown on a horizontal axis representing their real portion and a vertical axis representing their imaginary portion.

FIG. 5 shows the quantization of a 64-bit pole 64, before quantization, into a 32-bit pole 65, after quantization. Each of these poles is shown on a horizontal axis representing its real portion and a vertical axis representing its imaginary portion.

This coefficient quantization is likely to modify the frequency response of the filter, for example the pass-band gain as shown in FIG. 6 using the same filter as FIGS. 4 and 5. After quantization, the pass-band gain has been systematically corrected to 0 dB using equation 5.

b
n
′

=

b
n

⁢

∑

a
i

∑

b
j

(

equation
⁢

5

)

FIG. 6 shows, with a horizontal axis representing the frequencies and two vertical axes representing, on top, the amplitudes and, below, the phases, a non-quantized signal 70, a quantized signal 71 and a rectified signal 72. FIG. 6 therefore shows the effect of the quantization and rectification of the pass-band.

The stabilization time of the filters depends on the initialization. The state of the filter is generally initialized to zero: the signal is therefore causal. However, the sensor has a rest position that is known or can be estimated. In the case of the accelerometer described already, it can be assumed that it is placed flat on the mattress, which is itself horizontal: the z axis should see an offset value of approximately +1 g, i.e. 2.31 V in this setting mode. The filter is initialized by considering that the signal is 2.31 V before beginning the recording.

With regard to the elimination of the drift of the direct component, this represents an often-undesirable component of the physiological signal. This is a low-frequency component that does not allow a high-gain amplification. In ballistocardiography, the movement of the direct component is a voltage offset dependent on the position of the body and weight in the bed. For example, during a change of position by the patient, the orientation of the accelerometer and the projection of gravity on the axes of the accelerometer change. The inventors have observed that this offset value is generally located between 0.1 and 0.5 g, for which the amplifier would be saturated with G>3 dB.

Breathing, for which the frequency varies from 0.5-1.0 Hz in neonatology up to 0.1 Hz in geriatrics, can be considered either as a portion of the drift of the direct component, or as a useful component of the signal. In the embodiment described here, the breathing is not filtered, and consequently the cutoff frequency of the basic filter is set at 0.05 Hz and f is a low-pass filter (Equation 1).

In the case of the FIR, the window method is applied using a Kaiser window with a minimum attenuation of 40 dB in the pass-band and a transition band width of 0.1 Hz. The resulting FIR filter has 5716 coefficients.

In the case of the FIR, a second-order Butterworth filter, chosen because of its maximum flat response in the pass-band, is developed and repeated twice in order to accentuate the transition. In the embodiment described here, the filter chosen is a fourth-order IIR filter, because the FIR filter is costly in calculations for the microcontroller 54.

FIG. 7 shows the responses of the FIR and IIR filters developed in equivalent low-pass. They are compared to a typical first-order resistor-capacitor (RC) filter with the same cutoff frequency.

FIG. 7 shows the frequency responses of the equivalent low-pass of the FIR filter, response 75, IIR filter, response 76 and a typical analogue RC filter, response 77. Note that the axes are identical to those in FIG. 6, but with a broader frequency range.

A gain of 21 dB is set in this embodiment. Lastly, the equivalent high-pass filter has the following numerator and denominators in table 1. It is defined by equation 6, equation 7 and equation 8.

V
out

=

g
⁡
(

V
in

)

(

equation
⁢

6

)

a
n
′

=

a
n

(

equation
⁢

7

)

b
n
′

=

G
·

(

a
n

-

b
n

)

(

equation
⁢

8

)

a0
1

a1
−1.9982646

a2
0.99826604

b0
11.183295

b1
−22.3472

b2
11.163904

Numerators a0, a1 and a2 and denominators b0, b1, b2 of the equivalent high-pass filter.

With regard to the identification and filtering of noise frequencies, the frequency of the noise is identified and filtered using the built-in algorithm 80 shown in FIG. 8.

FIG. 8 shows an input 81 of the amplified signal, a vibration detection step 82, a vibration segmentation step 83, a Fast Fourier Transform (or FFT) step 84, a maximum extraction step 85 that provides the frequency of the noise 86, a notch filter selection step 87, a step 88 of updating the reaction filter, and a step 89 of outputting the filtered signal.

The step 82 of detecting vibrations is parameterized by a voltage limit value, hereinafter referred to as a “threshold”, beyond which the vibration is detected. The vibration begins when the amplified signal exceeds this voltage limit value, and has a duration considered fixed.

The power spectral density of the segmented vibration is calculated by the microcontroller. Its peak is located at the frequency of the noise, such that it is located outside the BCG range of frequencies, otherwise the heartbeats could be deformed or filtered.

Several notch filters, with quality factors Q=0.707, have been calculated first using the scipy.signal library outside the microcontroller. The notch filter whose frequency is closest to the frequency of the noise is selected, and added to the IIR basic filter.

In this section, the results of the experiment are detailed: the filtering of the drift of the direct component, the comparison of the stabilization time, and the identification and filtering of the noise are analysed. The raw signals presented are not post-processed.

Filtering the Direct Component

The IIR filter successfully filters the direct component, and this is eliminated by the amplifier. In the balance state, the maximum peak-to-peak amplitude of the impulsions is ten times higher on output than on input. FIG. 9 is an illustration of the signal before and after the amplifier with an impulsion amplitude lower than the noise level, with an amplification of 21 dB.

FIG. 9 shows a sensor output curve 90 and an amplified acceleration curve 91. The horizontal axis represents the time in seconds, and the vertical axis represents the voltage. It can be seen that a pulse, with a frequency of approximately 60 hertz, is extracted from the initial noised signal, despite the defects of the initial signal.

This filter makes it possible to generate vibrations at different constant frequencies and compare the accelerations measured before and after the filtering and the amplification by their average quadratic values. The frequency response 95 measured experimentally is compared with this filter's theoretical response 96, in FIG. 10, for the quantized IIR filter, with a gain of 21 dB.

Comparing Stabilization Times

The signals have been recorded at different levels of initialization. FIG. 11 is a superimposition of two signals at different times, with an offset initialization of 0 V, curve 101, and 2.31 V, curve 102. It can be seen that, when the filter state is initialized to 0 V, the amplifier can saturate for tens of seconds, which is not the case if the offset is well estimated.

The stabilization time, on the y-axis, depends on the initialization of the offset, on the x-axis, as shown by curve 106 in FIG. 12, with an amplification of 21 dB.

Identifying Noises

The threshold and duration have been set respectively to 1.5% and 0.25 s of the drift of the initial direct component. The noise was generated by pulsed vibrations, i.e. the simulated BCG. The frequency 112 of the noise 111 determined by the microcontroller is approximately 68 Hz, as can be seen in FIG. 13. This is the resonance frequency of the damping system.

A notch filter has then been selected by the algorithm illustrated by FIG. 8 to filter the noise frequency identified.

In conclusion, the present invention utilizes a new front-end signal conditioning circuit which identifies the resonance frequency of the system, filters the drift of the direct component and the damping noise, and amplifies the BCG signal without saturation after the patient's movement.

In the above description, the amplification gain is 21 dB for illustrating the principle of the BCG front-end circuit. However, the invention is not limited to this level of gain, especially when a specific electronic circuit with an adequate ground plane is used.

Relative to the normal BCG instruments, this front-end conditioning circuit described above has a smaller stabilization time and a sharper frequency transition. It opens up possibilities of medical applications, in real time and at low cost.

The incorporation of this front-end circuit in a BCG device is described below. It is noted that the frequencies of 0.05 Hz to 25 Hz comprise the heart and respiratory phenomena.

The aim of this device is to establish a cardio-respiratory mapping of the body surface by time-division multiplexing of an analogue filter with a digital feedback loop.

A mixed filter configuration 36 as described above replaces an analogue configuration in the feedback loop of an operational amplifier, referred to as “digital feedback”.

This “digital feedback” makes it possible to increase the constraints of the filter, to digitally initialize it so that it is more rapid, to attenuate an ambient noise whose pass-band changes over time, and to carry out high-frequency time division multiplexing of low cutoff frequency filters.

The system is a BCG imaging system that comprises the following elements:

- A surface sensor for the body pressure;
- An acquisition unit with time division multiplexing of a filter and an amplifier;
- A digital signal processing software system.

The surface sensor for the body pressure is normally used for measuring an individual's comfort in a lying or seated position, and/or the risks of pressure sores. It is generally comprised of several modules of size 35×40 cm to 50×100 cm, with resolutions ranging from 0.5 to 1 sensor/cm2, i.e. N=1024 to 4096 sensors per module. Example of “Body Pressure Measurement Systems” from Tekscan (registered trademark).