Biosignal processing and filtering Flashcards Preview

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Flashcards in Biosignal processing and filtering Deck (21)
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1
Q

Fourier Series Definition

A

A fourier series describes which frequencies are present in a signal and in which proportions
- a complex wave form can be approcimated to andy degree of accuracy with simpler functions

2
Q

Fourier Series Basics

A
  • an arbitrary periodic singal of period T can be represented as a sum of trigonometric functions
    → summing or mixing sinusoids while simulatneously adjusting their amplitudes and frequencies
3
Q

Problem with Fourier Series

A
  • Fourier Series gives the exact value of the function
  • Problem: uses an infinite number of terms
  • Solution: evaulate the partial sums of a Fourier Series by onyl evaluation a set of number of terms
4
Q

Time and Frequency domain

A
  • Fourier Series → representation of a periodic function in the time domain
  • same information can be stored in the frequency domain
  • filtering is easier in the frequency domain → mathematical benefits
5
Q

fourier transform

A

fourier transform converts fourier series to the freqeundy domain

  • can be used to decompose continuous aperiodic signal into its consituent frequency components
  • directly derived from exponential fourier series with T → ∞
6
Q

Inverse fourier transform

A

converts fourier series to the time domain

7
Q

properties of Fourier Transforms

A

linearity: F {a1x1(t) + a2x2(t)} = a1X1(w) + a2X2(w)
time shifting/delay: F = {x(t-t0)} = X(w) exp(-jwt0)
frequency shifting: F^-1 {X(w-w0)} = x(t) exp(-jw0t)

8
Q

Application of Fourier Transform

A

Variations in the frequency content of heart rate variability HRV

9
Q

discrete fourier transform

A
  • fourier transform applied to continous signals

- analysis of discrete signal in frequency domain require fourier transfrom equation

10
Q

Fast Fourier Transform

A

efficient computer algorithm for calculate discrete fourier transform

11
Q

linear systems

A
  • biological systems can be approximated by linear system models
  • characeristics: superposition (additivity) & scaling
12
Q

superposition

A

the sum of two independent inputs produces an output that is the sum of the outputs for each individual input

13
Q

scaling

A

the change in the size of the input produces a comparable change in the output

14
Q

periodic signals

A
  • expressed as a sum of cosine or complex functions with the fourier series
  • is scaled by Bm/Am and shifted by θm-ϕm
  • transfer function Hm describes how a linear system modifies the amplitue and phses of periodic input signals
15
Q

Impulse response

A

definition: relationship between the input and output of a linear system can be described by studying its behaviour in the time domain

16
Q

impulse response function

A

mathematical description of the linear system that fully characterizes its behaviour

17
Q

convolution theroem

A
  • mathematical operation between two functions producing a third function
  • can be used to filter a signal through a linear system
18
Q

Low- pass filter

A

removes high frequency noise → degrades resolution

19
Q

high pass filter

A

removal of low frequency noise → obscuring of the desired informaiton

20
Q

band-pass filter

A

remove both low an high pass frequency above or below a certain range (band)

21
Q

signal averaging application

A
  • reduce noise components of a biological signals, without removing potentially wanted parts
  • measurement error contains influence of noise and approaches 0 as number of measurment trials approaches infinity
  • if signal is measured several times, the signal parts tends to accumulate and the noise part tends to cancel itself