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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
