Principles of Instrumental Analysis

1. Principles of Instrumental Analysis Chapter 5 Signals and Noise

2. Ch5 Signals and Noise P.111 FIGURE 5-1Effect of noise on a current measurement: (a) experimental strip-chart recording of a 0.9 ×10-15 A direct current. (b) mean of the fluctuations.

3. Ch5 Signals and Noise P.111 FIGURE 5-2Effect of signal-to-noise ratio on the NMR spectrum of progesterone: A, S/N = 4.3; B, S/N = 43.

4. Ch5 Signals and Noise P.113 FIGURE 5-3Some sources of environmental noise in a university laboratory. Noted the frequency dependence and regions where various types of interference occur.

5. Ch5 Signals and Noise P.114 FIGURE 5-4An instrumentation amplifier for reducing the effects of noise common to both inputs. The gain of the circuit is controlled by resistors R1/a and KR2.

6. Ch5 Signals and Noise P.115 FIGURE 5-5Use of a low-pass filter with a large time constant to remove noise from a slowly changing dc voltage.

7. Ch5 Signals and Noise P.116 FIGURE 5-6Amplification of a modulated dc signal.

8. Ch5 Signals and Noise P.116 FIGURE 5-7Mechanical choppers for modulating a light beam: (a) rotating disk chopper, (b) rotating vane chopper, (c) oscillating tuning fork design where rotational oscillation of a vane causes periodic interruptions of a light beam.

9. Ch5 Signals and Noise P.117 FIGURE 5-8Lock-in amplifier for atomic absorption spectrometric measurements. The chopper converts the source beam to an on-off signal that passes through the flame cell where absorption occurs. After wavelength selection and transduction to an electrical signal, the ac square-wave input to the lock-in amplifier is amplified and converted to a sinusoidal signal by the tuned amplifier. The synchronous demodulator is phase-locked to the ac signal and provides a half-wave rectification of the signal. The low-pass filter converts the demodulated signal to a dc signal for measurement.

10. Ch5 Signals and Noise P.118 FIGURE 5-9 Ensemble averaging of a spectrum.

11. Ch5 Signals and Noise P.119 FIGURE 5-10Effect of signal averaging. Note that the vertical scale is smaller as the number of scans increases. The signal-to-noise ratio is proportional to √n. Random fluctuations in the signal tend to cancel as the number of scans increases, but the signal itself accumulates Thus, the S/N increases with an increasing number of scans.

12. Ch5 Signals and Noise P.119 FIGURE 5-11Effect of boxcar averaging: (a) original data, (b) data after boxcar averaging.

13. Ch5 Signals and Noise P.121 FIGURE 5-12Digital filtering with the Fourier transform: (a) noisy spectral peak, (b) the frequency-domain spectrum of part (a) resulting from the Fourier transformation, (c) low-pass digital-filter function, (d) product of part (b) and part (c), the inverse Fourier transform of part (d) with most of the high-frequency noise removed.

14. Ch5 Signals and Noise P.121 FIGURE 5-13The operation of an unweighted moving average smoothing function: noisy spectral data (•), smoothed data (▲). See text for a description of the smoothing procedure.

15. Ch5 Signals and Noise P.122 FIGURE 5-14Least-squares polynomial smoothing convolution integers: (a) quadratic five-point integers, (b) first-derivative cubic five- point integers, (c) second- derivative quadratic five-point integers.

16. Ch5 Signals and Noise P.122 FIGURE 5-14(a)

17. Ch5 Signals and Noise P.122 FIGURE 5-14(b)

18. Ch5 Signals and Noise P.122 FIGURE 5-14(c)

19. Ch5 Signals and Noise P.123 FIGURE 5-15Effect of smoothing on a noisy absorption spectrum of tartrazine: (A) Raw spectrum, (B) quadratic 5-point smooth of the data in A, (C) fourth-degree 13-point smooth of the same data, (D) tenth-degree 77-point smooth of the data.

20. Ch5 Signals and Noise P.126

21. Ch5 Signals and Noise P.128 FIGURE IA1-1Components of an electronic analytical laboratory.

22. Ch5 Signals and Noise P.128 FIGURE IA1-2Library card for fictitious user.

23. Ch5 Signals and Noise P.129 FIGURE IA1-3 Laboratory notebook page showing author, witness, and validator.