28-12-2012, 04:39 PM
Frequency Division Multiplexing using Discrete Fourier Transform
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ABSTRACT
Frequency division multiplexing is obsolete now a days but there are still some area where it is still used. A VHDL program has been written to investigate Frequency Division Multiplexing (FDM). This program is valuable for future researchers simulating systems that are too theoretically complex to analyze.
Basic principle:-
The main principle of this project is that we use the dft transform for multiplexing the signal in frequency domain. How ever this uses the multirate signal processing concept for up sampling the signal.
Discrete fourier transform I did using fft algorithm which is amongst the fastest algorithm for dft computation. To reach up to the carrier frequency we up sample the signal and then pass that signal to LPF to remove the extra images.
Theory:-
DFT:-
In mathematics, the discrete Fourier transform (DFT) is a specific kind of discrete transform, used in Fourier analysis. It transforms one function into another, which is called the frequency domain representation, or simply the DFT, of the original function (which is often a function in the time domain).
The DFT requires an input function that is discrete. Such inputs are often created by sampling a continuous function, such as the amplitude of a person's voice over time. The discrete input function must also have a limited (finite) duration, such as one period of a periodic sequence or a windowed segment of a longer sequence. Unlike the discrete-time Fourier transform (DTFT), the DFT only evaluates enough frequency components to reconstruct the finite segment that was analyzed. The inverse DFT cannot reproduce the entire time domain, unless the input happens to be periodic.
FDM:-
In telecommunications, frequency division multiplexing (FDM) is a technique by which the total bandwidth available in a communication medium is divided into a series of non-overlapping frequency sub-bands, each of which is used to carry a separate signal. This allows a single transmission medium such as a cable or optical fiber to be shared by many signals.
An example of a system using FDM is cable television, in which many television channels are carried simultaneously on a single cable. FDM is also used by telephone systems to transmit multiple telephone calls through high capacity trunklines, communications satellites to transmit multiple channels of data on uplink and downlink radio beams, and broadband DSL modems to transmit large amounts of computer data through twisted pair telephone lines, among many other uses.
How it works:-
At the source end, for each frequency channel, an electronic oscillator generates a carrier signal, a steady oscillating waveform at a single frequency such as a sine wave, that serves to "carry" information. The carrier is much higher in frequency than the data signal. The carrier signal and the incoming data signal (called the baseband signal) are applied to a modulator circuit. The modulator alters some aspect of the carrier signal, such as its amplitude, frequency, or phase, with the data signal, "piggybacking" the data on the carrier. Multiple modulated carriers at different frequencies are sent through the transmission medium, such as a cable or optical fiber.
Each modulated carrier consists of a narrow band of frequencies, centered on the carrier frequency. The information from the data signal is carried in sidebands on either side of the carrier frequency. This band of frequencies is called the passband for the channel. As long as the carrier frequencies of separate channels are spaced far enough apart so that their passbands do not overlap, the separate signals will not interfere with one another. Thus the available bandwidth is divided into "slots" or channels, each of which can carry a data signal.
At the destination end of the cable or fiber, for each channel, an electronic filter extracts the channel's signal from all the other channels. A local oscillator generates a signal at the channel's carrier frequency. The incoming signal and the local oscillator signal are applied to a demodulator circuit. This translates the data signal in the sidebands back to its original baseband frequency. An electronic filter removes the carrier frequency, and the data signal is output for use.