we don't get the test back this class :/
sampling theorem
ideal sampling, ideal reconstruction
quantization, bits = log2(L)
pcm has nothing to do with sinusoids
end up with quantization noise, dependent on max range and number of levels
quan noise = Nq = mp*mp/3LL
SNR for quan is 3LL * m^2/mp^2
europe vs NA, alaw vs mulaw
levels = L = 2^n
n == bits
2nB bits/sec
max of 2B independent pieces of info per sec tx, error free over a chan of B Hz
to transmit pcm will require bw of Bt = nB Hz
digital gives you error correction, can be used for anything
analog is generally single purpose, but high BW for a given channel
for digital, snr = c(2)^(2n)
c = 2/(ln(1+mu))^2 = (alpha + 6n) dB, as you increase n, it takes more BW

digital telephony: pcm in t1
multiple channels on a single transmission path, broken up by samples in frames, 20ms ulaw, T1 has 24 tdm channels
a frame consists of 8 bits from ecah chan, 1 bit of framing for total of 193 bits
8000 frames/sec

ex 6-3:
voice sig is limited to 3.4khz, need at least 6.8khz, oversample at 8khz
quantized to 256 levels
drawn out frame, 24 chans, 1 framing bit
8000 frames/sec
193bits/frame
1.544mbit/s


resulting signal is known as DS1
for RBS, LSB from every 6th sample is robbed for signaling
in order to ID 6th frame, framing bits repeated in pattern: 100011011100
4 DS1s -> 6.312mbps DS2
7 DS2s -> 44.736mbps DS3
3 DS3s -> 139.264mbps DS4NA

DPCM: differential PCM
PCM doesn't take advantage of similarity in adjacent sigs, DPCM does
forms an est of sig determined from previous N samples of message sig, algo known on both sides
transmits difference between estimate and actual signal, estimate is a modeled version of the signal based on previous inputs
transmitting prediction error, d[k], much smaller amplitude, thus reduced amplitude and values necessary
can increase SNR for a given BW, or decrease the BW for a given SNR

Ex 6-4:
sig has dyn range of +/-2V = mp
if quan to 8b/sample
calc quan noise power: Nq = mp*mp/3LL = 4/(3*2^16) = 1/(3*2^14) = 20.234e-6
DPCM is used with a prediction alg: m&[k] = 0.75m[k-1] + 0.2m[k-2] + 0.05m[k-3]

to get same quan noise as PCM, 20.345e-6 = .25*.25/3LL -> L = 32, n = 5 instead of 8
if sig sampled at 8khz, we have reduced data rate from 64K to 40K

ADPCM: adaptive differential PCM
uses an adaptive quantizer that changes delta v based on current error amount
can halve the number of bits required to 4 bits aka 32K
G.726 is the ITU-T ADPCM codec sampled at 8Khz, uses an 8th order predictor and 4 different ADPCM rates, 16,24,32,40kbit/s, 2,3,4,5 bits
most 726 encoders use 32kbps