Biosignal processing and filtering

Question 1

Fourier Series Definition

Answer 1

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

Question 2

Fourier Series Basics

Answer 2

• 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

Question 3

Problem with Fourier Series

Answer 3

• 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

Question 4

Time and Frequency domain

Answer 4

• 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

Question 5

fourier transform

Answer 5

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 → ∞

Question 6

Inverse fourier transform

Answer 6

converts fourier series to the time domain

Question 7

properties of Fourier Transforms

Answer 7

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)

Question 8

Application of Fourier Transform

Answer 8

Variations in the frequency content of heart rate variability HRV

Question 9

discrete fourier transform

Answer 9

• fourier transform applied to continous signals

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

Question 10

Fast Fourier Transform

Answer 10

efficient computer algorithm for calculate discrete fourier transform

Question 11

linear systems

Answer 11

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

Question 12

superposition

Answer 12

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

Question 13

scaling

Answer 13

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

Question 14

periodic signals

Answer 14

• 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

Question 15

Impulse response

Answer 15

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

Question 16

impulse response function

Answer 16

mathematical description of the linear system that fully characterizes its behaviour

Question 17

convolution theroem

Answer 17

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

Question 18

Low- pass filter

Answer 18

removes high frequency noise → degrades resolution

Question 19

high pass filter

Answer 19

removal of low frequency noise → obscuring of the desired informaiton

Question 20

band-pass filter

Answer 20

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

Question 21

signal averaging application

Answer 21

• 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