Midterm - Mathematical Concepts Flashcards
What do distortion, interference, and noise look like graphically?
distortion = curved edges
interference = waves
noise = niose
digital representation (“codeword”) for a number of bits
is basically a truth table style representation for all the bits from 0000… to 1111… if applicable
given a number of binary digits for something, the maximum quantity of that thing is found by doing
2^ # of digits
the base for octal digits is
- so when we need to find how many octal digits are needed to represent some number, we do 8^L = number
the base for hex is
- so when we need to find how many octal digits are needed to represent some number, we do 16^L = number
image transmission time =
(image size in bits)/(channel capacity in bits per second)
binary to hex
Group binary digits in sets of 4. viseversa
Binary to Octal
Group binary digits in sets of 3 viseversa
Binary to Decimal
Multiply each digit by its position value, and divide for viseversa
how many bi-directional links for n node bus topology?
1 backbone + n droplines
how many bi-directional links for n element ring topology?
n-1
how many bi-directional links for n node star topology?
n
how many bi-directional links for n node mesh topology?
n(n-1) /2
Using the Shannon-Hartley law, the channel capacity is given by:
𝐶 = 𝐵 ∙ 𝑙𝑜𝑔2 (1 + (𝑆/𝑁)o )
where B is the bandwidth and
(𝑆/N)o_db is the signal to noise ratio, and (𝑆/𝑁)o is linear form. the linear form is (𝑆/𝑁)o = 10^(((𝑆/N)o_db)/10)
Fourier transform of g(t) is
integral -inf to inf of g(t) e ^ (-j2pi f t) dt
Inverse Fourier transform of G(f) is
integral -inf to inf of G(f) e ^ (j2pi f t) dt
convolution in time domain is multiplication in frequency domain
convolution if frequency domain is multiplication in time domain
H(f) = Y(f)/X(f) =
|H(f)| * e ^ (j beta f)
where |H(f)| is the amplitude response
and e ^ (j beta f) is the phase response
rect(f/B1) times rect(f/B2) = ? if B1<B2
rect(f/B1)
if we have a frequency domain graph and we are asked for bandwidth, we find the distance from the origin to the first horizontal intersection.
if we have two frequency domain signals multiplied and we want to know the bandwidth of them in time domain. we know that multiplication in frequency domain in convolution in time domain, and we know that when two signals are convoluted, the total bandwidth = sum of bandwidths, so we sum the bandwidths.
the time shifting property of Fourier transform states that
a time shift t0 in time domain equals a multiplication by an complex exponential e^(-j 2 pi t0) in frequency domain
