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As we learned in class, we have an Armstrong indirect FM transmitter shown in Figure 2. According to the input of a frequency multiplier

`x(t)=A_(c)cos[2\pi f_(0)t+\phi (t)]`

, we obtain the final output

`x_(c)(t)`

with

`f_(0)=100kHz`

. Suppose we also have the peak frequency deviation of

`\phi (t)`

is

`f_(d1)=100Hz`

, the deviation ratio at the output of the narrowband FM modulator is

`D_(1)=0.1`

. The wideband output

`x_(c)(t)`

is to have a carrier frequency

`f_(c)=100MHz`

and a deviation ratio

`D_(2)=2`

. Suppose

`A_(c)`

to be a constant. (a) (5 pts) What is the bandwidth

`W`

of

`\phi (t)`

? (b) (15 pts) Assume that the input of the block "Bandpass filter" is

`e(t)`

, please give all the possible expressions of

`e(t)`

. (c) (5 pts) What is the bandwidth

`B`

of the "Bandpass filter"? (d) (5 pts) What is the center frequency of the "Bandpass filter"?