Fourier Transform + 1D signal Flashcards

1
Q

What is Fourier Transform?

A

Breaks a waveform (a function or signal) into alternate representation, characterised by sine and cosines

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What does Fourier Transform show?

A

Any waveform can be written as sum of sinusoidal functions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What are all waveforms?

A

Sum of simple sinusoids of different frequencies (continuous range of frequencies)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What does Fourier Series break down?

A

A periodic function into sum of sinusoidal functions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

When a function is a periodic?

A

With fundamental period T, if the following is true for all t:
f(t+T)=f(t)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What will a function of time with period T have?

A

same value in T seconds

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is a fundamental period?

A

Value of T (>0) that is the smallest possible T for which (t+T) is always true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is Fourier Series (With Period T) and what does it include?

A

Infinite sum of sinusoidal functions (cosine+sine)
each with an integer multiple of 1/T

Includes constant

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What do coefficients of Fourier series determine?

A

Relative weight for each of sinusoids

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

When can you approximate f(t)?

A

exactly when f(t) is continuous and ‘smooth’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is am+bn?

A

How much of each frequency is included to create g(t)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

The first term in fourier series?

A

Average value of the function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

For modelling odd functions

A

Use the sine terms

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

For modelling even functions

A

Use cosine terms

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What happens when the waveform fluctates with respect to time?

A

The wave can be characterised by frequency

number of cycles passing a given point each second

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

How are spatial frequency expressed?

A

Line pairs per min

17
Q

How can square wave be constructed?

A

Adding a large number of sine waves of different frequencies and amplitude

18
Q

How can fourier series also be represented as ?

A

Frequency spectrum

19
Q

What is plotted against spatial frequency?

A

The amplitude of frequency component for square wave

20
Q

What can fourier spectrum be used to identify?

A

Frequencies and amplitide of sine wave which contribute to make up a given waveform

21
Q

Spatial domain representation

A

Plots of amplitude versus distance

22
Q

Frequency domain representation

A

Plots of amplitude vs spatial frequency

23
Q

Why is the Fourier Transform widely used throughout medical imaging?

A
  1. Determining the spatial resolution of imaging system
  2. Spatial localisation in magnetic resonance Imaging
  3. Analysis of Doppler ultrasound signal
  4. Image filtering in emission + transmission computed tomography
24
Q

What is inverse Fourier transform?

A

Mathematical technique for converting data in opposite direction
frequency domain –> spatial domain

25
What is Fourier pairs?
The transformation can go from time domain to frequency domain or opposite direction...it's reversible
26
What are known as Fourier pairs?
Two functions g(t) and G(t) | One is the fourier transform of other
27
What is fourier pairs?
Two functions | The frequency domain form and corresponding time domain form
28
What is a straight line?
The fourier transform of a delta function (mini-boxcar)
29
The more coefficients included in approximation
The closer the approximation to original signal