Instrumentation & Measurement (ME342) Chapter 6: Signal Processing Dr. Hani Muhsen

6.1 Introduction Analogue and digital filters are used extensively in sensor signal processing (pre- and postprocessing of sensor signals). Analogue filters are often used to deal with the so-called aliasing phenomenon that is common in data acquisition systems. Digital filters are generally used to postprocess acquired signals and can be used in conjunction with sophisticated digital signal-processing techniques such as Fast Fourier Transform to perform spectral analysis of acquired signals. Signal filtering. consists of selectively passing or rejecting low-, medium-, and high frequency signals from the frequency spectrum of a general signal. .

6.2 Analogue Filters Analogue filters are used primarily for two reasons: To buffer and reduce the impedance of sensors for interface with data acquisition devices (DAQ devices). Eliminate high-frequency noise from the original signal so as to prevent aliasing in analogue-to-digital conversion. . Analogue filters can be constructed using passive components (namely resistors, capacitors, and, at times, inductors) or combination of passive and active components or more commonly, operational amplifiers.

6.2.1 Passive Filters They are designed with a few simple electronic components (resistors & capacitors) Low- pass filter, can be used to remove (or attenuate) high-frequency noise in the original signal. Any time function can be viewed as being a combination of sinusoidal ( infinite series of sinusoidal frequencies that are multiples of the so-called fundamental frequency). Approx. Where Vi,1,Vi,2,Vi,3, . . . are the amplitudes of the consecutively higher frequency components or harmonics of the original signal.

6.2.1 Passive Filters Higher frequency components may represent fluctuations (or, in many cases, electrical noise) that we may wish to attenuate to prevent aliasing. (present a clean signal to the DAQ system.) The filter produces an output, vo, which has the same set of components (in terms of the respective frequencies) as the original signal, vi, but at reduced amplitudes. Where Vo,1,Vo,2,Vo,3, . . . . are the amplitudes of the sinusoidal components in vo. In general, Vo,1, Vo,2,Vo,3, . . . . are smaller than their counterparts in the input signal, Vi,1,Vi,2,Vi,3, . . . . Low-pass filter attenuates each signal according to its frequency, the higher the frequency, the larger the attenuation. (( e.g. V0,1 = 98% of Vi,1 V0,2 = 70% of Vi,2 and so on ))

Low Passive Filter Circuit Kirrchoff’s voltage law (KVL): Laplace transformation. Where, Corner frequency of filter,

Low Passive Filter Circuit Signal is not attenuated in the pass band Signal completely attenuated in the stop band

Frequency Domain Analysis   Frequency Domain Analysis Partial fractions and simplification, The steady-state output would be, In more standard form,

High –Pass Passive filter

High –Pass Passive filter

6.2.2 Active Filters Using Op-amps Passive filters (resistors and capacitors) draw current from the input and will, in addition, “load” the circuit connected to the output of the filter. Thus, Op-amps can eliminate this problem. The current that in Op-amps is drawn from the input stage is very small (because op-amps have large internal resistances, of the order of 10 MΩ).

Op-Amps Often used in instrumentation to do the following: Boost the amplitude of the signal Buffer the signal Convert a signal current into a voltage Separate a difference signal from unwanted, common–mode signals

Standard Op-Amp Circuits

6.2.2 Active Filters Using Op-amps Passive filters (resistors and capacitors) draw current from the input and will, in addition, “load” the circuit connected to the output of the filter. Thus, Op-amps can eliminate this problem. The current that in Op-amps is drawn from the input stage is very small (because op-amps have large internal resistances, of the order of 10 MΩ).

6.2.2 Active Low Pass Filters Using Op-amps In negative feedback configuration,   Then Compared with low pass passive filter

6.2.2 Active High Pass Filters Using Op-amps

Differential Amplifier Solving and rearranging, we obtain:

6.3 Digital Filters Digital filtering uses discrete data points sampled at regular intervals. These data points are usually sampled from an analogue device such as the output of a sensor ( an accelerometer to measure vibration in a beam). They rely not only on the current value of the measured variable, but also on its past values The analog input signal must first be sampled and digitized using an ADC. The resulting binary numbers, representing successive sampled values of the input signal, are transferred to the processor, which carries out numerical calculations on them.

6.3.1 Input Averaging Filter The previously unfiltered values of the given signal are used in the scheme:   This is called a moving average filter, as it in effect averages past values of the input signal, each with its respective weight. Selection of these weights is often an issue and can be formalized.

6.3.2 Filter with Memory In a filter with memory, previously filtered values (outputs) are used to adjust the new output. This filter takes the form Where, the unfiltered signal is uk . And the filtered signal is yk-1  ≤1 Varying α will change the extent to which the input signal is filtered. In particular, a relatively large α weighs in the current value of the input signal, while a small α weighs in the past (filtered) signal.

Example A set of data points is measured from a continuous signal as given in Table 6.2. A simple input averaging filter with  values of 0.25, 0.5, 0.75, and 1.0 is used to filter these values as depicted later

Second Order Filters first order filters can be easily converted into second order filters simply by using an additional RC network within the input or feedback path. “two 1st- order filters cascaded together with amplification”. Most designs of second order filters are generally named after their inventor with the most common filter types being: Butterworth, Chebyshev, Bessel and Sallen-Key.