Chapter 5Signals and Noise

Signal carries information about the analyte that is of interest to us.

Noise is made up of extraneous information that is unwanted because it degrades the accuracy and precision of an analysis

Signal-to-Noise RatioS/N = (mean)/(Standard deviation) =

Signal-to-noise (S/N) is much more useful figure of merit than noise alone for describing the quality of an analytical method. The magnitude of the noise is defined as the standard deviation s of numerous measurements and signal is given by the mean x of the measurements. S/N is the reciprocal of the relative standard deviation. S/N < 2 or 3 impossible to detect a signal.

x

s RSD

1

Figure 5-1

Figure 5-2

Sources of Noise

Analysis are affected by two types of noise:

1. Chemical noise

2. Instrumental noise

Chemical noise: Arises from an uncontrollable variables that effect the chemistry of the system being analyzed. Examples are undetected variations in temperature, pressure, chemical equilibria, humidity, light intensity etc.

Instrumental Noise: Noise is associated with each component of an instrument – i.e., with the source, the input transducer, signal processing elements and output transducer. Noise is a complex composite that usually cannot be fully characterized. Certain kinds of instrumental noise are recognizable, such as:

1. Thermal or Johnson noise 2. Shot noise3. Flicker or 1/f noise 4. Environmental noise

Instrumental Noise1. Thermal Noise or Johnson Noise: Thermal noise is caused by the thermal agitation of electrons or other charge carriers in resistors, capacitors, radiation transducers, electrochemical cells and other resistive elements in an instruments. The magnitude of thermal noise is given by

where, rms = root mean square noise, f = frequency band width (Hz), k = Boltzmann constant (1.38 x 10-23 J/K), T = temperature in Kelvin, R = resistance in ohms of the resistive element.Thermal noise can be decreased by narrowing the bandwidth, by lowering the electrical resistance and by lowering the temperature of instrument components.

rm s = 4 k T R f

Instrumental Noise2. Shot Noise: Shot noise is encountered wherever electrons or other charged particles cross a junction.

Where, irms = root-mean-square current fluctuation, I = average direct current, e = charge on the electron (1.60 x 10-19 C), f = band width of frequencies.

Shot noise in a current measurement can be minimized only by reducing bandwidth.

i = 2 Ie frm s

3. Flicker Noise: Flicker noise is characterized as having a magnitude that is inversely proportional to the frequency of the signal being observed. It is sometimes termed 1/f (one-over-f) noise. The cause of flicker noise are not well understood and is recognizable by its frequency dependence. Flicker noise becomes significant at frequency lower than about 100 Hz. Flicker noise can be reduced significantly by using wire-wound or metallic film resistors rather than the more common carbon composition type.

4. Environmental Noise: Environmental noise is a composite of different forms of noise that arise from the surroundings. Much environmental noise occurs because each conductor in an instrument is potentially an antenna capable of picking up electromagnetic radiation and converting it to an electrical signal.

Figure 5-3

Signal-to-Noise Enhancement: When the need for sensitivity and accuracy increased, the signal-to-noise ratio often becomes the limiting factor in the precision of a measurement. Both hardware and software methods are available for improving the signal-to-noise ratio of an instrumental method.

Hardware method: Hardware noise reduction is accomplished by incorporating into the instrument design components such as filters, choppers, shields, modulators, and synchronous detectors. These devices remove or attenuate the noise without affecting the analytical signal significantly. Hardware devices and techniques are as follows:

1. Grounding and Shielding: Noise that arises from environmentally generated electromagnetic radiation can be substantially reduce by shielding, grounding and minimizing the length of conductors within the instrumental system.

2. Analog Filtering: By using low-pass and high-pass analog filters S/N ratio can be improved. Thermal, shot and flicker noise can be reduced by using analog filters.3. Modulation: In this process, low frequency or dc signal from transducers are often converted to a higher frequency, where 1/f noise is less troublesome. This process is called modulation. After amplification the modulated signal can be freed from amplifier 1/f noise by filtering with a high-pass filter, demodulation and filtering with a low-pass filter then produce an amplified dc signal suitable for output.

4. Signal chopping: In this device, the input signal is converted to a square-wave form by an electronic or mechanical chopper. Chopping can be performed either on the physical quantity to be measured or on the electrical signal from the transducer.

5. Lock-in-Amplifiers: Lock-in-amplifiers permit the recovery of signals even when the S/N is unity or less. It requires a reference signal that has the same frequency and phase as the signal to be amplified. A lock-in amplifier is generally relatively free of noise because only those signals that are locked-in to the reference signal are amplified. All other frequencies are rejected by the system.

Software Method: Software methods are based upon various computer algorithms that permit extraction of signals from noisy data. Hardware convert the signal from analog to digital form which is then collected by computer equipped with a data acquisition module. Software programs are as follows:

1. Ensemble Averaging: In ensemble averaging, successive sets of data stored in memory as arrays are colleted and summed point by point. After the collection and summation are complete, the data are averaged by dividing the sum for each point by the number of scans performed. The signal-to-noise ratio is proportional to the square root of the number of data collected.

Figure 5-9

2. Boxcar Averaging: Boxcar averaging is a digital procedure for smoothing irregularities and enhancing the signal-to-noise ratio. It is assumed that the analog analytical signal varies only slowly with time and the average of a small number of adjacent points is a better measure of the signal than any of the individual points. In practice 2 to 50 points are averaged to generate a final point. This averaging is performed by a computer in real time, i.e., as the data is being collected. Its utility is limited for complex signals that change rapidly as a function of time.

Figure 5-11

3. Digital filtering: Digital filtering can be accomplished by number of different well-characterized numerical procedure such as (a) Fourier transformation and (b) Least squares polynomial smoothing.

(a) Fourier transformation: In this transformation, a signal which is acquired in the time domain, is converted to a frequency domain signal in which the independent variable is frequency rather than time. This transformation is accomplished mathematically on a computer by a very fast and efficient algorithm. The frequency domain signal is then multiplied by the frequency response of a digital low pass filter which remove frequency components. The inverse Fourier transform then recovers the filtered time domain spectrum.

(b) Least squares polynomial data smoothing: This is very similar to the boxcar averaging. In this process first 5 data points are averaged and plotted. Then moved one point to the right and averaged. This process is repeated until all of the points except the last two are averaged to produce a new set of data points. The new curve should be somewhat less noisy than the original data. The signal-to-noise ratio of the data may be enhanced by increasing the width of the smoothing function or by smoothing the data multiple times.