Lecture Two Flashcards
Review Trig:
X = A Cos(2piFT + Phase) Y = A Sin (2piFT + Phase)
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)
What is fourier synthesis?
Construction of a (complex) periodic signal from summation (superposition) of two or more (simple) sinusoids
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
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?
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
In what domain is the initial analogue signal?
Time domain
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
What is the wave equation for a fourier series wave?
V(t) = C cos(2piFT + phase)
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
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
What is polar vs rectangular components?
Rectangular:
- Real and imaginary components
Polar:
- Phase and Amplitude
What is a discrete fourier transform?
Taking the time domain and converting it into the frequency domain
What is the sampling period?
Period that was recorded (Ts)
What is the sampling duration?
Total length of time spent sampling
duration of recording
What is sampling frequency?
1/Ts
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.
What is observed in the real and imaginary components?
Symmetry about the central frequency component.
Mathmatically on the frequency spectrum where are the lowest frequencies?
At 1/Ts
Whats the highest frequency proportional to?
Corresponds to sampling frequency
How many unique components are there?
(n-1)/2 unique components
What is the lowest frequency independent from?
Independent from sampling frequency
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’).
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
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.
