Noise Removal and Signal Compensation

Lecture’s Date: 17 Sept 2007

Prepared by;

Pn. Saidatul Ardeenawatie, MMedPhy (UM), B.BEng (Hons)UM

Lecturer, Biomedical Electronic Engineering

School of Mechatronic Engineering

Universiti Malaysia Perlis (UniMAP)

Subtopics;

• Introduction

• Filtering in biomedical instruments:

(a) Weiner Filter

(b) DT Filter

• Properties and effects of noise in biomedical instrumentation

Introduction

• Removing noise from a signal probably is the most frequent application for signal processing.

• The distinction between noise and desired signal is an heuristic judgment that must be determined by the user.

• Biomedical applications often involve the acquisition of continuous time signals by digital sampling.

• Two choices;a) Before sampling using a continuous-time filter (analog filter)b) After sampling using a discrete-time filter (digital filter)

• Digital filters – more versatile and more convenient to modify for different applications.

• Analog filters – have certain advantages and there are pertinent reasons to employ them.

First, to prevent aliasing one always should filter a CT signal with an analog filter before sampling it.

Second, even if it is incomplete, any noise removal that one can effect with an analog filter before sampling reduces the requirements on any subsequent digital filter.

Finally, the properties of some classes of analog filters are well-studied and these filters provide a foundation for designing “equivalent” digital filters.

Introductory Example:Reducing the ECG artifact in an EMG

recording

• When an electromyogram (EMG) is recorded from muscles on the torso, the electrocardiogram (ECG) is commonly superimposed on EMG signal because of the proximity of the heart and the large electrical amplitude of the ECG compared to many EMG signals.

• To better visualize the EMG signal due to breathing, or for subsequent quantitative analysis of the signal, it is desirable to filter out the ECG artifacts.

• The power spectral density (PSD) is calculated for EMG and ECG signal.

• The ECG has much greater peak power density (amplitude and frequency) than EMG.

• Furthermore, the frequency contents of the two signals seem to overlap below about 30 Hz.

• Therefore removal of the ECG by filtering the EMG recording with highpass filter.

Power Spectral Density (PSD)

• Shows how the power of a random signal distributes with respect to frequencies

• Helps to identify dominant periodic components and to remove them

Parametric Estimation

Linear System

Time signal

PSD

Time signal

PSD

Weiner Filter

• The goal of the Wiener filter is to filter out noise that has corrupted a signal.

• Typical filters are designed for a desired frequency response. The Wiener filter approaches filtering from a different angle.

• One is assumed to have knowledge of the spectral properties of the original signal and the noise, and one seeks the LTI filter whose output would come as close to the original signal as possible.

Wiener filters are characterized by the following:

(a) Assumption: signal and (additive) noise are stationary linear stochastic processes with known spectral characteristics or known autocorrelation and cross-correlation.

(b) Requirement: the filter must be physically realizable, i.e. causal (this requirement can be dropped, resulting in a non-causal solution).

(c) Performance criteria: minimum mean-square error

DT filter

• Digital filter is any electronic filter that works by performing digital mathematical operations on an intermediate form of a signal.

• Digital filters can achieve virtually any filtering effect that can be expressed as a mathematical function or algorithm.

Limitations

• The two primary limitations of digital filters are;

a) Speed (the filter can't operate any faster than the computer at the

heart of the filter)

b) Cost

Digital filter advantages

• Digital filters can easily realize performance characteristics far beyond what are practically implementable with analog filters. e.g :

To create a 1000 Hz low-pass filter which can achieve near-perfect transmission of a 999 Hz input while entirely blocking a 1001 Hz signal.

- Practical analog filters cannot discriminate between such closely spaced signals.

• For complex multi-stage filtering operations, digital filters have the potential to attain much better signal-to-noise ratios than analog filters.

Properties & Effects of noise in biomedical instrumentations

Noise

• Every electronic component has noise– thermal noise – shot noise – distribution noise (or partition noise)

Thermal Noise

• Thermal noise due to agitation of electrons

• Present in all electronic devices and transmission media

• Cannot be eliminated

• Function of temperature

• thermal noise is caused by the thermal motion of the charge carriers; as a result the random electromotive force appears between the ends of resistor;

Johnson Noise, or Thermal Noise, or Thermal Agitation Noise

• Also referred to as white noise because of gaussian spectral density.

• (V) where

– Vn = noise Voltage – k = Boltzman’s constant

• Boltzman’s constant = 1.38 x 10 -23 Joules/Kelvin

– T = temperature in Kelvin– R = resistance in ohms (Ώ)– B = Bandwidth in Hertz (Hz)

kTRBVn 42

Example of thermal noise

– Given R = 1Kohm – Given B = 2 KHz to 3 KHz = 1 KHz– Assume: T = 290K (room Temperature)

Solution

Vn = 4KTRB units V2

• Vn2= (4) (1.38 x 10 –23 J/K) (290K) (1 Kohm) (1KHz)

= 1.6 x 10-14 V2

Vn = 1.26 x10 –7 V = 0.126 uV

Shot noise

• Shot noise appears because the current through the electron tube (diode, triode etc.) consists of the separate pulses caused by the discontinuous electrons;

– This effect is similar to the specific sound when the buckshot is poured out on the floor and the separate blows unite into the continuous noise;

• Shot Noise: noise from DC current flowing in any conductor

• where– In = noise current (amps)– q = elementary electric charge – = 1.6 x 10 -19 Coulombs– I = Current (amp)– B = Bandwidth in Hertz (Hz)

qIBIn 22 qIBIn 2

Eg: Shot noise

• Given I = 10 mA • Given B = 100 Hz to 1200 Hz = 1100 Hz

Solution• In

2= 2q I B =• = 2 (1.6 x 10 –19 Coulomb) ( 10 X10 –3 A)(1100

Hz) = 3.52 x10 –18 A2

In = (3.52 x10–18 A2) ½ = 1.88 nA

Distribution noise

• Distribution noise (or partition noise) appears in the multi-electrode devices because the distribution of the charge carriers between the electrodes bear the statistical features;

Internal and External Noise

• Internal Noise

• External Noise

• Total Noise Calculation

Internal Noise

• Internal Noise: Caused by thermal currents in semiconductor material resistances and is the difference between output noise level and input noise level

External Noise

• External Noise: Noise produced by signal sources also called source noise; cause by thermal agitation currents in signal source

Noise Reduction Strategies

• Keep source resistance and amplifier input resistance low (High resistance with increase thermal noise)

• Keep Bandwidth at a minimum but make sure you satisfy Nyquist’s Sampling Theory

• Prevent external noise with proper ground, shielding, filtering

• Use low noise at input stage (Friis Equation)• For some semiconductor circuits use the

lowest DC power supply

Noise Reduction by Signal Averaging

• Un processed SNR, Sn =20 log (Vin/Vn)

• Processed SNR Ave Sn = 20 log (Vin/Vn/ N1/2)

– where– SNR, Sn = unprocessed SNR

– SNR, Ave Sn = time averaged SNR

– N = # repetitions of signals

– Vin = Voltage of Signal

– Vn = Voltage of Noise

• Processing Gain = Ave Sn – Sn in dB

Noise Reduction by Signal Averaging

• Ex: EEG signal of 5 uV with 100 uV of random noise – Find the unprocessed SNR, processed SNR

with 1000 repetitions and the processing Gain

Solution:• Unprocessed SNR

Sn = 20 log (Vin/Vn) = 20 log (5uV/100uV) = -26dB

• Processing SNR– Ave Sn = 20 log (Vin/Vn/N1/2)

= 20 log (5uV / [100uV / (1000)1/2]) = 4 dB

• Processing gain = 4 – (- 26) = 30 dB

Thank you!!