IT IS BY MY DECREE, THAT HENCEFORTH YOU MUSK PLACE THE WORDS "HELLO MY NAME IS", IN THAT ORDER IN YOU POSTS!!!! THIS IS A HIGH SECUIRTY ZONE!!!!
------
cotocctouctHELLOspudvbpsivdbusdvbMYdlbvdkbvdlkjbvdnameduvuvibvpibivpvibpibscceninvmIS
------
------
HELLO MY NAME IS A WIZARD!!!!!
o
O /`-.__
/ \.'^I
o T l +
o _I-..-I_
O (^ '----' `)
`\-....-/^ I'M A WIZARD
O o ) "/ " ( /
_( (-) )_
O /\ ) ( /\
/ \( ) I \
o o \) ( / \
/ I( )I \
/ o \ \( / \
__.--' O \_ / .._ \
//I)\ , (_) /(((\^)'\
I I O ) ` I
I / o___ / /
/ _.-''^^__O_^^''-._ /
.' / -''^^ ^^''- \--'^
.' .`. `'''----'''^ .`. \
.' / `'--..____..--'^ \ \
/ _.-/ \ \
.::'_/^ I I `.
.-'I I `-.
_.--'` \ / `-.
/ \ / `-._
`'---..__ `. .`_.._ __ \
``'''`. .' `'^ `''---'^
`-..______..-'
------
------
HELLO MY NAME IS
------
------
hello my name is
------
HELLO MY NaME IS
<marquee>HELLO MY NAME IS JERKS.PL</marquee>
------
------
HELLO MY NAME IS DICKFACE
------
------
hhhhhhhh
------
------
hhhhhhhh
------
------
to versions of the shnnon nyquist th'm
if you've got a bandlimited signal, if you sample at twice the highest bandlimited frequency you can reconstruct completely
V.2. If x ( F^Z has a DTFT xhat, and T>0 is given, there exists a unique x_r ( F^R uith these two properties
x_r(nt) = x(n), all n ( Z [x_r "connects the dots" in x]
=x_r is bandlimited to within Pi/T (i.e. X_R(Ohm)=0, |Ohm|>= Pi/T
Terminology: Given a bandlimited continuous-time signal x_c, and given Ohm_m = "smallest bandwidth" for x_c, the Nyquist rate for x_c is 2*Ohm_m [ Ohm_m/Pi in Hz ]; Version 1 of Th'm says "sample x_c faster than Nyquist rate => can recover x_c from samples"
when constructing x_r, your brain takes the most parsimonious route, taking the solution with lowest bandwidth
44.1kHz gives some headroom over 2*20kHz
aliasing: why call it that? x_c is "posing as x_r", or you might say "assuming x_r as an alias".
time-division multiplexing (or multiple access) (i.e. CDMa, etc.)
II(t) = sum(P_a(t-n*Ts),n,-inf,inf) , t ( R
graphically, this looks like a pulse train
z(t) = x(t)*II(t)
II(t) = sum(c_k*e^(j*k*Ohm*t),k,-inf,inf)
Ohm = 2*Pi/Ts
z(t) = sum(c_k*x(t)*e^(j*k*Ohm*t),k,-inf,inf)
Suppose x <-F-> Xhat, and x is bandlimited to within Ohm_max, and Ohm_sampling > 2*Ohm_max (2x the nyquist rate)
t |--> c_k*x(t)*e^(j*k*Ohm*t) <--F--> Ohm |--> c_k*Xhat(Ohm-k*Ohm_s)
so this creates scaled and shifted versions of Xhat in the frequency domain. You can easily lowpass this signal to get just a scaled copy of X. This demonstrates that a bandlimited signal can be sampled and reconstructed perfectly.
N*T < Pi/Ohm_max or T < Pi/(n*Ohm_m).
Too sm
------
------
clean boner :OOO
------