Part II Flashcards
Why digital communications?
Only need to recreate the symbol, not the entire waveform
What are the differences between 1G, 2G, 3G, 4G and 5G?
1G: analog modulation no different to FM radio
2G: digitised, digital signal processing
3G:
If we have b bits per symbol, how many symbols can we have?
2^b
What are the qualities of white noise?
Additive - noise is added not multiplied
White - frequency spectrum is constant
Gaussian - probability distribution is normal
What is the conditional probability structure? P(X|Y) What does symmetric mean?
P(0|1) = probability of receiving 0 given that a 1 was sent.
Symmetric: P(1|0) = P(0|1)
What is upconversion?
Baseband signals have frequency too low, susceptible to interference. Need to be converted up to a suitable carrier frequency. The resultant signal is a passband signal.
What are the characteristics of passband signals?
They are narrowband, purely real (applied to an antenna).
It does however have reflected negative frequencies.
How does complex baseband work?
The baseband signal is complex, with real and imaginary parts. The frequency is not symmetric.
It is done by creating a digital complex signal, separating the real and imaginary parts, adding a sine and cosine to each and then adding them together.
What is a signal space?
Signals can be described as vectors in an n-dimensional vector space with basis vectors that are all orthogonal to each other. The signals are a combination of a projection along each basis vector.
What is the test for two vectors or signals to be orthogonal?
v1 . v2 = 0 (dot product)
In the time domain, integrate the product of the two functions over the time period.
What does it mean for vectors to be orthonormal?
If all vectors are orthogonal to each other and have unit norm (can be normalised to length 1)
How can you work out the length and energy of a vector in a signal space?
Length = |si| = sqrt(sum of all projections along each axis squared)
Energy = length squared = |si|^2
How can you work out the energy of a signal in the time domain?
Integrate the signal squared from time 0 to T
What is the Gram-Schmidt orthogonalisation procedure?
Start with the first waveform, s1(t)
The first basis function f1(t) is s1(t) normalised by it’s energy (divide by sqrt e1)
2nd basis fn:
Project f1(t) onto s2(t), result is coefficient c12 = int(0 to T) s2(t)*f1(t)dt
Subtract c12f1(t) from s2(t) to get f2’(t)
Normalise by the energy f2(t) = f2’(t)/sqrt(e2)
Repeat.
How is noise represented in the signal space?
Also a vector that moves the received signal away from the transmitted vector in any direction. Looks like a cloud of gaussian probability
