1. 1.1 What is Noise? any ‘unwanted” part of the analytical signal always some noise in a signal 1.2 Signal-to-noise ratio (S/N) for a set of data (replicate measurements) for a temporal-varying signal For meaningful measurements, S/N  3, SS

2. 2.1 White Noise – amplitude invariant with respect to frequency Thermal Noise -voltage fluctuation due to random electron motions in the resistive elements k: Boltzmann’s constant T: absolute temperature R: resistance  f: frequency bandwidth,

3. Shot Noise -current fluctuations due to random motion of electrons cross a junction (e.g., PN interface, space between anode/cathode) I: average current e: charge of electron

4. 2.2 Flicker Noise – amplitude varies with 1/f, drift in instruments

5. 2.3 Environmental Noise - different forms of noise that arise from the surroundings - some occurs at known discrete frequencies - some unpredictable, and difficult to correct (e.g., TV stations, computers, motors,etc)

6. 2.4 Composite Noise Spectrum Fig. 5-3 (p.113) 2.4 Composite Noise Spectrum

7.  White Noise  reduce  f, temp, resistance, and I  Flicker Noise  make measurements at frequencies >100kHz  Shielding & Grounding  absorbing electromagnetic noise But signal  often at or near dc (low freq)  often directly proportional to resistance  often directly proportional to current  often measured with transducers having very large  f (fast response, PMT  f >10 7 Hz)

8. 3.1Reducing  f (white noise) 3.1.1Analog filtering: low-pass RC circuit Fig. 5-5 (p.115) High-frequency components rejected, and  f reduced A slow varying dc signal containing high frequencies with bandwidth extending over wide range

9. 3.1.2Digital filtering: Fourier transform/smooth -It is easy to smooth/filter signal as well as noise. Make sure that the result is not distorted - trade-off between resolution and noise. Need high point density to prevent losing information. control in the frequency domain by manipulating pass function Fig. 5-12 (p.121)

10. 3.2Increasing f (flicker noise) We need to move f to >100kHz… How? - Modulate: encode analytical signal at a high frequency, where 1/f noise is negligible - Amplify the signal at the modulation frequency, while reduce the noise. - demodulate the signal

11. Lock-in Amplifier Chopper Fig. 5-8 (p.117) 3. Demodulate 2. Amplify modulated signal 1. Modulate

12. 3.3Signal Averaging Total intensity of signal: increase linearly with the number (n) of replicate signals Noise: increase as (n) 1/2  S/N increase as (n) 1/2

13. 3.3.1An Example for Signal Averaging

14. 3.3.2Signal Averaging For a Spectrum Get S/N increased with n ½ Need good synchronization for replicate scan Fig. 5-10 (p.119)

15. 3.3.3 Boxcar Averaging A approach for smoothing irregularities A single –channel signal averager select a single delay time integrated signal over selected gate time average signal for n-replicate repeat at new delay time S/N increases with (averaging time) 1/2 Fig. 5-11 (p.119)

16. 3.3.3 Boxcar Averaging select a single delay time integrated signal over selected gate time average signal for n-replicate repeat at new delay time Fig. 5-11 (p.119)