Frequency division multiplexing fdm pdf

Each transmitter sends signal of different frequency. For example, the transmitter 1 sends signal of 30 KHz, transmitter 2 sends signal of 40 KHz and transmitter sends signal of 50 KHz.

These signals of different frequencies are multiplexed or combined using a multiplexer. Multiplexer transmits multiplexed signal over a communication channel. At the receiver end the multiplexed signals are separated using a de-multiplexer and the separated signals are sent to intended receivers.

Time division multiplexing TDM is a digital multiplexing technique. All signals are operating at same frequency but within different time slots. Thus, user gets control of channel for a fixed amount of time and data is transmitted one by one. The signals are transmitted in the form of frames and frames contain a cycle of time slots and each frame contains a dedicated slot for a user. Synchronous TDM — in this technique time slots are pre-assigned to each device. Each device is given a time slot irrespective whether device had data or not to transmit.

The best application we can have is in television and radio systems where multiple signals are transmitted over a single channel with different frequency slots. In this, the 12 voice channel modulates different carriers and then these modulated carriers are added in a mixer.

The carrier frequency is modulated in the range from 4 KHz to KHz range and the spacing provided to them is of 4 KHz each. The output of balanced modulator gives upper sideband and lower sideband. The upper sidebands are selected by using bandpass filter BPF. Now the 12 USB signals are added by a linear mixer to produce a combined signal. At the receiver end, the BPF demodulators are used for demodulating the received signal so that we can have the actually transmitted signals at the output of the receiver.

To prevent the interference caused during FDM we use guard bands which is of range 0 to 4KHz and these are the unused portion of the spectrum. Your email address will not be published. The electrode setup and the liquid container are represented on the right. Each electrode injects a current at a slightly different frequency. A different filter was used for each current source and tuned appropriately for the frequency of that current source.

A more expensive but probably more convenient solution for future designs could be based on direct digital synthesis techniques. This creates some errors due to the impedance of the sample and the electrodes.

In other cases, it could be convenient to make use of current sources with much higher output impedances, for instance, based on Howland configurations [ 26 ]. A multiplexer MUX is used to select one of the current generation signals as the reference signal Ref for the demodulation. The measurements are read by a PC that is also responsible for controlling the multiplexer's signals.

In this case, however, the current source is based on a modified Howland circuit [ 26 ]. Every current in the FDM system is assigned a unique frequency.

It is usually associated with a specific electrode, but in general, several frequencies could be injected through the same electrode in parallel. In the following derivation, we assume that only a single current is injected through each electrode and thus there is a one-to-one mapping between the frequency and the electrode.

The current I p injected to electrode i p , at frequency f p , is. The odd-numbered electrodes measure the voltage in all of the frequencies simultaneously. In order to separate the signals, care must be taken that the bandwidth of each signal does not exceed the difference between two adjacent frequencies.

If the signal's frequency band extends beyond this gap, signals will mix. This is known as intersymbol interference ISI. This means that the signal we use to make the measurements the injected current cannot be shorter than one millisecond. Longer signals or demodulation time will lower the effects of ISI. When sampling the voltages, the exact duration of the signal may be modified slightly so that all of the injected signals complete an integral number of cycles.

Consider the case of a single current injection. We inject current I p to a current injection electrode i p at frequency f p. We then measure the voltage V l p on a voltage measurement electrode l :. The integrated voltage V l measured at the voltage measurement electrode l is the superposition of the voltages in all of the frequencies.

The integrated voltage is then. The signals can be separated by using a Fourier transform. Each voltage component, V l p , is used independently in the reconstruction algorithm in a similar manner to measurements that were acquired serially.

In this case, we have such measurements coming from 15 frequencies and 16 voltage measurement electrodes. However, not all these measurements are independent. Hence results are used for the reconstruction process. We have compared three cases: simulation, emulation, and real measurements. In the simulation, we have analyzed the situation theoretically, creating a mesh with an inhomogeneity and solving the forward problem to compute the voltages of the voltage measurement electrodes.

Then using these values as input, we solved the inverse problem to come up with an image of the inhomogeneity. Current was injected sequentially into the current injection electrodes, and measurements were recorded with the voltage measurement electrodes. A single frequency was used for the electrodes at each test. The most important results are these of the FDM system itself.

At the same time, measurements were made using the voltage measurement electrodes. We have tested the system with a circular saline tank 0. It can be seen that in both cases, the reconstructed image clearly shows a circular high impedance object in the center of the tank. The same test was repeated with the object placed close to the current sink electrode.

Similar results were obtained. Again, we see a clear circular object near the current sink electrode. The image quality demonstrates the ability of FDM EIT to separate the various frequencies and treat them independently. Using a single current sink means that the current density near the sink electrode is higher than in other parts of the tank. We, therefore, tested the accuracy of imaging an object that is placed near this electrode, and compared it to other locations.

We ran 32 simulations of a small circular object with lower impedance, which at each run was placed close to one of the 32 electrodes. For each inhomogeneity, the injected currents were simulated and the resulting voltage measurements were computed.

With the computed voltages as an input, the reconstruction process was run to obtain the estimated impedance inside the tank. These values were then compared to the true impedance with which we started and thus the error was obtained. We repeated the same process with the trigonometric current pattern [ 28 ] implemented using half of the electrodes for current injection and half for voltage measurement. In this current pattern, the electrodes inject a combination of sine and cosine functions at the same frequency and the process is repeated 16 times: each time changing the injected current in the electrodes.

It is worthwhile noting that the trigonometric current pattern we have used does not have a particularly high current density near any of the current electrodes. Comparing the errors of the two patterns will allow us to determine whether the FDM current pattern has any particular regions of better or worse accuracy.

Example of an inhomogeneity near any of the electrodes and its reconstruction. Both methods show comparable errors for different angles of the object's location. The odd-numbered electrodes This is probably due to the higher current density in this area, which is why it affects both current patterns. The error does not change considerably when the inhomogeneity is moved around the disk's perimeter but with FDM, it is slightly smaller than with the trigonometric pattern in front of the current sink.

It has 4 frequency bands, each of which can carry signal from 1 sender to 1 receiver. Each of the 4 senders is allocated a frequency band. The four frequency bands are multiplexed and sent via the communication channel. At the receiving end, a demultiplexer regenerates the original four signals as outputs. It allows sharing of a single transmission medium like a copper cable or a fiber optic cable, among multiple independent signals generated by multiple users.