Bessel filter

The purpose of the high- and low-pass filters, shown in Figure 9.2, is to eliminate interference signals such as electrode half-cell potentials and preamplifier offset potentials and to reduce the noise amplitude by the limitation of the amplifier bandwidth. Because the biosignal should not be distorted or attenuated, higher order sharp-cutting linear-phase filters have to be used. Active Bessel filters are preferred filter types because of their smooth transfer function. Separation of biosignal and interference is in most cases incomplete because of the overlap of their spectra. 

As we have commented in Section 4.1, for wavelengths close to the central value, the filter response is very similar to the Gauss filter for wavelengths far from the central value, the filter response is similar to a 3 order Bessel filter with less out band attenuation. Both of them have a linear phase characteristic, which means a constant group delay. These simulations are in agreement with experimental measurements shown in (Parker et al.., 1998). 

Passband ripple The passband of a filter should ideally be flat. As we have seen, the Chebyshev filter sacrifices a flat passband for faster roll-off. The Butterworth filter, on the other hand, has been designed to have the shortest possible transition band while still maintaining a flat passband i.e., there is no ripple. The Bessel filter also has a flat passband however, it has the worst roll-off of the three designs. 

The data acquisition system and bipotentiostat/galvanostat of the CH series 900 SECM are microprocessor based and communicate with the PC controller via a serial data link. The bipotentiostat/galvanostat is suitable for analytical voltammetry with tip and substrate potentials up to 10 V and a compliance voltage of 12 V and potentiostat rise time of 0.6 ps. The current measurement sensitivity is in the pA range (resolution <0.01 pA). Adjustable second-order Bessel filters provide noise reduction and prevent aliasing by the ADC, which has at least 16 bits of resolution. The software for the model series 900 SECM runs on the Windows operating system and provides... 

A Bessel-Thompson filter was designed to have a delay close to 500 /us. The design procedure followed gave exact values for all of the capacitors and resistors. These values are rounded to the nearest value of capacitor available. The SPICE packages are used to determine what the implemented delay will be. Measured values of all the components used in the hardware are used. The schematic and the breadboard results are shown as Figs. 3.23 and 3.24, respectively. 

Bessel-Thompson Delay Low Pass Filter with Pulse Shaper... 

A simple pulse-shaping modification can be added to the Bessel-Thompson delay filter by using an additional operational amplifier. Resistors are used to divide down the supply voltage to half the output voltage of the delay filter, and its response is then compared with the delay filter s response, which results in a time-delayed square wave. The schematic of this circuit is shown in Fig. 3.31. This simulation also allows us to compare the operational amplifier models that came with each software package. The response of this circuit is driven from rail to rail, providing the saturation voltages of the models. Also, the slew rate of the output should be consistent with the measured and... 

Figure 3.31 Bessel-Thompson delay filter with shape reformation.

Inverted Bessel-Thompson Delay High Pass Filter... 

A quick modification to the Bessel-Thompson filter leaves us with a high pass filter. This filter does not have the built-in delay like the low pass version, but it does provide an interesting response. The schematic and the breadboard results are shown in Fig. 3.36 and Fig. 3.37, respectively. The measurements that will be made for comparison purposes are the step response height and the time until the second cross of the zero axis. 

Other window functions than the sine window have been proposed as well (see [Bosi et al., 1996b, Fielder et al., 1996]). Using Kaiser-Bessel-Derived window functions, a filter characteristic exhibiting better side-lobe suppression is possible. This is explained in [Fielder et al., 1996],... 

In actual practice, all filters have a distributed cutoff frequency so that none are infinitely sharp, and the way in which the attenuation "rolls off" with frequency affects the attainable S/N. The world of electrical engineering knows of many different filters (such as the Bessel and the Butterworth) which are characterized by different amplitude rolloff and phase characteristics near the cutoff frequency. A commonly used filter is the RC filter because of its ease of implementation. It consists simply of a capacitor C and a resistor R. It has the time constant RC (check it it has the unit of time) and this simply means that it will not respond to signals that change appreciably in times shorter than RC so it is a low pass filter. Its response to a step function in time is exponential so that the rolloff in the frequency domain, i.e., its Fourier transform, is a Lorentzian and the cutoff is very broad. 

Of the more sophisticated filters, the two most commonly used are the Butterworth and the Bessel. They can provide much sharper cutoff than the RC filter. The difference between the Butterworth and the Bessel are subtle and are usually described in terms of the rolloff characteristics, i. e.,... 

There are two demodulation techniques that are used to measure the signal arriving at the detector into and l (2a>). The first uses a lock-in amplifier and a low-pass filter [10, 69], while the second relies on the synchronous sampling demodulator (SSD) to obtain the intensity difference and average signals [65, 66]. In the first case, J2 and Jo are the second-order and zero-order Bessel functions. In the second case they are described by the following expressions ... 

---