$5\mathrm{.}4\mathrm{.}3$ Problems

P$5-1.$ Calculate the baud rate for the given bit rate and type of modulation.

a$.2000$ bps$,$ FSK

b$.4000$ bps $,$ ASK

c$.6000$ bps $,$ QPSK

d$.36,000$ bps$,64-$QAM

P$5-2.$ Calculate the bit rate for the given baud rate and type of modulation.

a$.1000$ baud, FSK

b$.1000$ baud, ASK

c$.1000$ baud, BPSK

d$.1000$ baud, $16-$QAM

P$5-3.$ What is the number of bits per baud for the following techniques?

a$.$ ASK with four different amplitudes

b$.$ FSK with eight different frequencies

c$.$ PSK with four different phases

d$.$ QAM with a constellation of $128$ points

P$5-4.$ Draw the constellation diagram for the following:

a$.$ ASK, with peak amplitude values of $1$ and $3$

b$.$ BPSK$,$ with a peak amplitude value of $2$

c$.$ QPSK$,$ with a peak amplitude value of $3$

d$.8-$QAM with two different peak amplitude values, $1$ and $3,$ and four different phases

P$5-5.$ Draw the constellation diagram for the following cases. Find the peak amplitude value for each case and define the type of modulation $($ASK$,$ FSK$,$ PSK$,$ or QAM$).$The numbers in parentheses define the values of I and Q respectively.

a$.$ Two points at $\backslash ((2,0)\backslash )$ and $\backslash ((3,0)\backslash )$

b$.$ Two points at $\backslash ((3,0)\backslash )$ and $\backslash ((-3,0)\backslash )$

c$.$ Four points at $\backslash ((2,2),(-2,2),(-2,-2)\backslash ),$ and $\backslash ((2,-2)\backslash )$

d$.$ Two points at $\backslash ((0,2)\backslash )$ and $\backslash ((0,-2)\backslash )$

P$5-6.$ How many bits per baud can we send in each of the following cases if the signal constellation has one of the following number of points?

a$.2$

b$.4$

c$.16$

d$.1024$

P$5-7.$ What is the required bandwidth for the following cases if we need to send $4000$ bps $?$ Let d $=1.$

a$.$ ASK

b$.$ FSK with $\backslash (2\backslash$Delta $\backslash$mathrm$\{$f$\}=4\backslash$mathrm$\{$KHz$\}\backslash )$

c$.$ QPSK

d$.16-$QAM