# Homework Help: Communication Problems (Filters, BW, Bit rate, FM)

1. Dec 17, 2008

### ineedmunchies

1. The problem statement, all variables and given/known data

A 1kHz analogue signal is to be encoded using 8-level Pulse Code Modulator. This specification results in a bit rate of 5.5K bits/sec. The signal is to be transmitted over a 1 km distance with a 10kHz bandwidth on a Frequency Modulated, F.M., Carrier. The carrier frequency is in the digital cellular radio frequency band (GSM Reverse Band) at 875 MHz. In this frequency band legislation permits up to 1 watt of carrier power to be transmitted and received through omnidirectional antennas. The transmit and receive antenna feeders are of low loss type and exhibit 0.1 dB maximum attenuation.

The received signal is to be passed through a matched impedance and matched bandwidth single down conversion superheterodyne receiver. This receiver should have three stages. The gain of the first and third stages are 7 dB and 27 dB respectively and the noise figure for each of these stages is 2 dB and 8 dB respectively. The mixer placed immediately after the low noise amplifier has a loss of 3 dB. The overall noise figure of the receiver should not exceed 6.2 dB.

2. Relevant equations

Step 1

The analogue input signal must pass through an anti-alias filter. In order to define the bandwidth of the system this should have………………………. Filter characteristics.
The bandwidth of this filter should be set to at least the…………………………..
which is this case is……………….kHz

Step 2

Bit rate is given as 5.5K bits/sec.

On a minimum bandwidth channel each cycle of each sinewave carries……………….. bits of information. Allowing for 1.5 times over-sampling in order to avoid aliasing, the minimum bandwidth for the systems becomes………………… Hz.

Due to the bit rate calculated above the digitally encoded signal can now be transmitted to the FM modulator via a……………… type cable.

Step 3

In order to define the modulator characteristics the FM modulator frequency deviation must now be computed. The system has narrowband FM characteristics so that the necessary frequency deviation can be obtained by an approximate technique such as…………………………….. rule. From this approximate calculation the required modulator frequency deviation is………………………………………… Hz.

3. The attempt at a solution

Ok, so for a few of the parts I'm only looking to check if I have the correct answer, and some parts I haven't a clue about.

But here goes:

Step 1:
I think the anti-aliasing filter should have low pass characteristics, and the cut-off frequency/bandwidth of the filter should be at least the maximum analogue signal frequency, which in this case is 1KHz.

Step 2:
Ok, so this is where I start to become unsure of everything.
I think that on a minimum bandwidth channel each cycle of a sinewave can contain 2 bits.
If there are 2 bits per cycle, and the sampling rate is 5.5Kbits/sec then the bandwidth is 5.5/2 = 2.25KHz?? But they want to over sample by 1.5 so this should then become 2.25*1.5 = 4.125KHz ??

I am unsure as to which type of cable it wants, I would hazard a guess at coaxial.

Step 3:
It is a narrowband system, so Carson's rule can be used to obtain the frequency deviation.
The carrier frequency is 875 Mhz, the bandwidth is 10 kHz.

This is where I really start getting lost. But anyway carsons rule is : BW = 2 * (f$$\Delta$$ + fm)

Where f$$\Delta$$ is the peak deviation of the instantaneous frequency from the center carrier frequency, and fm is the highest modulating frequency.
10 kHz = 2( ? + ?)

But the modulating/carrier frequency is given as 875 MHz so that would give a large negative frequency for f$$\Delta$$

874.995 MHz from my calculation.

There are two more parts to this question but I haven't included them here as I haven't attempted them properly yet.

Thank you, any help with any of this is greatly appreciated.