Flashcards in Lecture Four Deck (13):

1

## What is an alternative to filters when the signal and noise are similar frequencies?

###
Signal averaging, autocorrelation and cross correlation

All carried out in the time domain

2

## What is signal averaging?

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You take several sweeps of the signal measuring several points in time each time.

A point in time is selected and averaged using the values from each sweep.

This produces a cleaner signal

3

## For signal averaging to be effective what conditions must be met?

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- The signal in each sweep must be coherent and synchronised (lined up in time)

- The noise should be uncorrelated (incoherent/ random) i.e not biological noise

4

## What is the relationship between signal averaging and improvement in the signal to noise ratio?

### Improvement in the signal to noise ratio is proportional to the square root of the number of sweeps (n).

5

## What does the relationship of signal average to S2N ratio follow?

###
Signal averaging follows the law of diminishing returns

i.e 4 sweeps = 2 factor improvement

16 sweeps is 4 times greater but only a 4 factor improvement i.e twice the gain of the 4 sweeps.

Although very noise signal might require many sweeps to extract the signal

6

## What is autocorrelation?

### Reveals the existence of repeated structure or periodicity in a signal that might not otherwise be clear.

7

## How does autocorrelation work?

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The function is evaluated by taking a copy of a signal an shifting it by t (greek letter not t for time that just represents a shift) relative to the other signal.

Therefore the autocorrelation function is at a peak when the signals most closely overlap. i.e shift = o or one period.

Shift occurs in both negative and positive directions

8

## Does the signal peak at one period of phase shift?

### No only because there are no terms in the summation equation to describe this.

9

## In plain english what does the autocorrelation function measure?

### Measures the correspondence of a function with a series of time shifted version of itself.

10

## Describe the autocorrelation of a finite and infininte sinusoid;

### decaying cosine function and non-decaying cosine function respectively

11

## What happens in an autocorrelation function of random noise?

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Large speak at t = 0 but then drops to nothing as noise is random and therefore demonstrates no periodicity.

Thus we describe noise as uncorrelated or incoherent

12

## When using the autocorrelation function what is it important to account for?

### Necessary to account for both short data lengths and non-wide band noise that will produce peaks in the autocorrelation spectrum. It is therefore necessary to use statistical techniques to access significance of autocorrelation peaks.

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