Chapter 8 - Biosignal Enhancement Filtering

What are some ways to minimize data disturbances?

use better receivers, keep the channel short, reduce channel disturbance, use redundant information, use other sources for interpretation

What is the idea behind Fourier filtering?

amplify/attenuate/leave-unchanged frequencies in a signal, by multiplying the Fourier transform by a filtering function

low-pass filter

will allow low frequencies to pass, but not high

high-pass filter

will allow high frequencies to pass, but not low

band pass filter

will allow a specific range of frequencies to pass, but not others

band stop filter

will prevent a specific range of frequencies from passing, but allows anything else

impulse response, h(n)

the response of a system to a single impulse at time 0

output signal

response to the input signal

What is the meaning of convolving a signal with the function [1/3 1/3 1/3]?

average every 3 entries

What is the meaning of convolving a signal with the function [1/5 1/5 1/5 1/5 1/5]?

average every 5 entries

What is the meaning of convolving a signal with the function [1/5 3/5 1/5]?

weighted averaging, with more emphasis on the central value

What is the Fourier interpretation of convolving a signal with the function [1/3 1/3 1/3]?

multiply the Fourier transform with a wide sinc function, attenuating very high frequencies

What is the Fourier interpretation of convolving a signal with the function 0.2*[1 1 1 1 1]?

multiply the Fourier transform with a narrow sinc function, keeping only low frequencies

What are two ways we can improve the signal-to-noise ratio?

filter out noise, coherent averaging

coherent averaging

averaging across observations; the noise is additive, so when the signal is aligned and all observations are averaged, the noise has a mean of (close to) 0 and cancels out