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Flashcards in Lecture Two Deck (25):
1

Review Trig:

X = A Cos(2piFT + Phase)
Y = A Sin (2piFT + Phase)

2

What is the wave equation?

The value at any point in a sinusoid (v) can be given by;

V(t) = C (amplitude) Cos (2piFT - phase)

3

What is fourier synthesis?

Construction of a (complex) periodic signal from summation (superposition) of two or more (simple) sinusoids

4

In fourier synthesis or transformation, what is the first frequency?

1st frequency is the fundamental frequency and is equal to the frequency of the constructed (summed) wave

5

What is unique about frequency 2 in fourier synthesis?

It is twice that of a the fundamental frequency.

BUT then the third one will be 3x the fundamental i.e increments?

6

What is fouriers theorem?

A periodic signal (waveform) can only contain ‘harmonically related' sinusoids–sinusoids that have frequencies that are integral (whole number) multiplies of the Fundamental frequency

7

In what domain is the initial analogue signal?

Time domain

8

What can a signal in the time domain be transformed into and whats it called when this is reversed?

Frequency domain


Fourier transformation

Inverse Fourier transformation to reverse this

9

What is the wave equation for a fourier series wave?

V(t) = C cos(2piFT + phase)

10

What is the wave equation that sums the entire fourier series?

The same but includes summation notation so look it up


Also includes V(o) added on the end for offset signals


V(t) = C cos(2piFT + phase) + V(o)

This is for rectangular amplitude and phase components

11

What is the equation for the value at a point in a composite complex signal in real and imaginary components?

V(t)= Acos2PiFT + B Sin (2iFT) + V(o)


Polar components

12

What is polar vs rectangular components?

Rectangular:
- Real and imaginary components


Polar:
- Phase and Amplitude

13

What is a discrete fourier transform?

Taking the time domain and converting it into the frequency domain

14

What is the sampling period?

Period that was recorded (Ts)

15

What is the sampling duration?

Total length of time spent sampling


duration of recording

16

What is sampling frequency?

1/Ts

17

How many real and imaginary components are there?

The number of real (cosine) and imaginary (sine) components is the same as in the time domain.

18

What is observed in the real and imaginary components?

Symmetry about the central frequency component.

19

Mathmatically on the frequency spectrum where are the lowest frequencies?

At 1/Ts

20

Whats the highest frequency proportional to?

Corresponds to sampling frequency

21

How many unique components are there?

(n-1)/2 unique components

22

What is the lowest frequency independent from?

Independent from sampling frequency

23

What is the resolution determined by?

Frequency res olution is determined by the lowest frequency component (the Fundamental frequency f1) which itself is determined by the period of s ampling (‘duration of recording’).

24

Does increasing the sampling frequency help?

Providing that sampling theorem is s atis fied, increasing sampling frequency does not alter the number of (useful) spectral components



there will be more components in the frequency domain but they will have an amplitude of zero

25

What does padding with zeros do?

Padding with zeros (zero amplitude components) at the centre of the real and imaginary spectrums is a convenient way of interpolating when the invers e Fourier trans form is applied


Allowing the original signal to be reconstructed at a higher sampling rate.