Changing the sampling rate

Transcription

1 Noise Lecture 3

2 Finally you should be aware of the Nyquist rate when you re designing systems. First of all you must know your system and the limitations, e.g. decreasing sampling rate in the speech transfer over the phone might not be critical as compared to decreasing setting sampling rate for ECG. To really determine an appropriate sampling rate for a system, or to determine the necessary antialias and reconstruction filters for a system, you have to understand aliasing and filtering.

3 Changing the sampling rate

4 down sampling

5 down sampling: Things needed to be checked

6 Up sampling

7 Up sampling

8 That s End of Sampling. Let s focus on Noise

9 Physiological interferences In human body several physiological processes active at a given time, each one producing many signals of different types. Patient or subject not able to exercise control on all physiological processes and systems. Appearance of signals from systems or processes other than those of interest: physiological interference.

10 Physiological interferences Examples EMG related to coughing, breathing, squirming in ECG. Maternal ECG getting added to fetal ECG. ECG interfering with the EEG. Ongoing EEG in ERPs. Heart sounds in breath or lung sounds

11 Physiological interferences Physiological interference not characterized by any specific waveform or spectral content however a generalized trend can be seen. Typically dynamic and nonstationary: linear bandpass filters will not be applicable. Need adaptive filters with reference inputs.

12 Stationary versus nonstationary processes A process is stationary if its statistics are not changed with time. A random process is weakly stationary or stationary in the wide sense if its mean is a constant and ACF (autocorrelation function, phi) depends only upon the difference (or shift) in time. A stationary process is ergodic if the temporal statistics are independent of the sample observed (their statistics may be computed from a single observation as a function of time) K is an observation

13 Signals or processes that do not meet the conditions described in the last slide are nonstationary processes. A nonstationary process possesses statistics that vary with time e.g. (fluctuations in the signal statistics due to physiological perturbations such as drug infusion or pathology or recovery).

14 Is it stationary or non- stationary signal?

15 In continuation from last slide, The spectrogram is plotted on a linear scale to display better the major differences between the voiced and unvoiced sounds.

16 Is it stationary or non- stationary signal?

17 Most biomedical systems are dynamic: produce nonstationary signals Examples: EMG, EEG, PCG, speech. However, a physical or physiological system has limitations in the rate of change of its characteristics. This facilitates breaking the signal into segments of short duration over which the statistics of interest are not varying, or may be assumed to remain the same. Quasistationary process: short-time analysis.

18 Non-Physiological interferences The noise components of a signal can have different origins. Sometimes noise is human-made (e.g., artifacts from switching instruments or 50-Hz hum originating from power lines). Other noise sources are random in nature, such as thermal noise originating from resistors in the measurement chain. Random noise is intrinsically unpredictable, but it can be described by statistics.

19 Noise From a measurement point of view, we can have noise that is introduced as a result of the measurement procedure itself, either producing systematic bias or random measurement noise (e.g., thermal noise added by recording equipment).

20 Measurement Noise measurement noise is the noise introduce during the measurement. There are various factors that can cause it e.g. thermal noise added by recording equipment, or the sensitivity of the system. If we consider a measurement M as a function of the measured process x and some additive noise N, the ith measurement can be defined as Mi = xi + Ni

21 Measurement Noise Consider the equation on previous slide Suppose xi = 0.8x i plus the noise contribution drawn from a random process i.e. rand function in matlab. 34 Measurement Noise

22 Dynamic Noise When the output of a dynamical system becomes corrupted with noise, and the noisy value is used as input during the next iteration. Dynamical noise is not an independent additive term associated with the measurement but instead interacts with the process itself. For example, temperature fluctuations during the measurement of cellular membrane potential not only add unwanted variations to the voltage reading; they physically influence the actual processes that determine the potential. Any other example?

23 Dynamic Noise we can imagine the noise at one time step contributing to a change in the state at the next time step. Thus, one way to represent dynamical noise D affecting process x is xi = [0.8x i ]+D i 1 50 Dynamical + Measurement Noise It creates slower trends due to the correlation between sequential values

24 Lets compare both 34 Measurement Noise dynamical noise (due to the correlation between sequential values) creates slower trends when compared to the time series with only additive noise Dynamical + Measurement Noise

25 Noise White noise has equal power at all frequencies. It derives its name from white light, which has equal brightness at all wavelengths in the visible region. Sometimes noise has a more low-frequency-weighted character, that is, it has more power at low frequencies that high frequencies. This is often called "pink noise"

26 Noise Sources 1. 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. rms = 4kTR f where, rms = root mean square noise, f = frequency band width (Hz), k = Boltzmann constant (1.38 x J/K), T = temperature in Kelvin, R = resistance in ohms of the resistive element. Usually thermal noise is associated with a particular application, and it is rarely under direct control in a given setup. There are cases where designers have included cooling of the preamplifi er (using a Peltier element as cooling device) to reduce thermal noise from the input resistors.

27 Noise Sources 2. electromagnetic Electromagnetic noise is caused by a power line can be modeled by the effect of a magnetic flux through the surface formed between the electrodes and the capacitance between the power line and the input of the preamplifier. To reduce electromagnetic interferences, a metal box for electronic circuits, a shielded (Faraday cage principle) recording room, and guarding (driven or not) for common mode signal reduction are the efficient methods. In software it can be checked by introducing adaptive filters.

28 Noise Sources 3. electrostatic The same power line producing the electromagnetic interference also has an electrostatic effect on the input circuitry of the preamplifier. This can be represented in the AC power line as a hum source. Hum from an electrostatic noise source is usually much larger than the electromagnetic component. This electrostatic noise must be eliminated by shielding or removing the source. In software it can be eliminated by Notch filter.

29 Noise Sources 4. The discretization error made at the ADC In state-of-the-art electrophysiology equipment, quantization noise is a few microvolts or less. It is not uncommon to use at least a 12-bit converter. Taking into account amplification of 1000 with an analog ADC input range of 10 V (±5 V)

30 Noise Contribution More about giga seal at

31 Signal to noise ratio (SNR) Any (biomedical) measurement will necessarily be corrupted by some noise. Even if the process itself were noise free, the measurement chain adds noise components. To quantify this ratio between signal and noise components, one can (in some cases) determine the amplitude or the power of each component and from those calculate a signal-to-noise ratio.

32 Signal to noise ratio (SNR) Analogue Signal Digital signal or

33 Signal to noise ratio (SNR) sz=1000; SIGNAL_TRIALS=randn(sz); % a [sz x sz] matrix filled with noise NOISE_TRIALS=randn(sz)+randn(sz)+ randn(sz);%+ randn(sz); Find the SNR using digital ms and rms value.

34 Illustration of the Problem with Case studies 1. ERP: signal obtained in response to a stimulus. Response of small amplitude ( 10 μv ), buried in ambient EEG activity and noise. A single response may not be recognizable.

35 Illustration of the Problem with Case studies 2. ECG with high frequency noise. Noise could be due to instrumentation amplifiers, the recording system, pickup of ambient EM signals by cables, etc. Also powerline interference at 50 Hz and harmonics.

36 3. Low frequency artifacts and baseline drift in chest lead ECG due to coughing or breathing with large movement of the chest, or when an arm or leg is moved in the case of limb lead ECG.

37 4. Most common periodic artifact in biomedical signals: powerline interference at 50 Hz or 60 Hz + harmonics. Bandwidth of interest of ECG: Hz. Lowpass filtering not appropriate for removal of powerline interference: will smooth and blur QRS, and affect PQ and ST segments. Spectrum of ECG with 60Hz noise

38 We are done with introduction to noise Lets focus on how to improve the quality of signal.