Hi.

Here is a simple question of transmission rates and bandwidth.

A signal source is sampled, quantified and coded in PCM. Each sample is coded into words of three impulses of information and a adicional synchronism impulse. The impulses of information can assume one of four possible levels. The transmission is made through a channel with 6KHz of bandwidth, using raised cosine impulses with roll-off factor of 50%.

Determine the maximum transmission rate of the impulses PCM, the matching transmission rate of information and the maximum bandwidth allowed for the analog source. (Solution: Rmax=8000 impulses/s; Rinformation=12 Kbps; Wmax=1KHz)

My attempt:

Raised Cosine a=0.5
Wtransmission=(Rmax/2)*(1+a)
Rmax=(2*6K)/(1+0.5)=8000 impulses/s

1 sample have 4 impulses (3 of information + 1 synchronism). Each impulse of information can assume 1 of 4 levels.
Rinformation=(3/4)*8000*4=24 Kbps

Shannon's Theorem fsampling >= 2*fmax
fsampling=(8000 impulses/s) / (4 impulses/sample) = 2000 samples/s
fmax <= fsampling/2
fmax <= 2000/2 = 1000 Hz

Can someone explain me how to solve this problem?

Thanks in advance.

 

I figured out how to solve this.

We have 3 impulses of information in 4 impulses (one sample). Each impulse of information can assume 1 of 4 levels. For example, 00 01 10 11. Well, we need 2 bits.
Rinformation=(3/4)*8000*2=12Kbps

/Solved