Download Noise Removal and Signal Compensation

Lecture’s Date: 17 Sept 2007
Noise Removal and Signal
Compensation
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
Time signal
PSD
Time signal
Linear
System
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.
•V2
n
 4kTRB
(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)
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
• I n2  2qIB where
–
–
–
–
–
In = noise current (amps)
q = elementary electric charge
= 1.6 x 10 -19 Coulombs
I = Current (amp)
B = Bandwidth in Hertz (Hz)
I n  2qIB
Eg: Shot noise
• Given I = 10 mA
• Given B = 100 Hz to 1200 Hz = 1100 Hz
Solution
• In2= 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!!