The Fourier transform is an algorithmic method for the decomposition of a complex signal in sinusoidal elements. There are many forms of this Fourier transform, however, for digital signal processing, the DFT (Discrete Fourier Transform) is the most appropriate.
The DFT version that is part of the Fourier transform is applied to N discrete samples of a complex waveform, which covers an infinite period. This is an image of the sampled signal within the frequency domain.
OFDM Concept – The Fourier Transform
The result generated by the DFT will consist that containing N number complexes. Each complex number explains the frequency and amplitude of one of the sine waves, which represents an inverse of the complex waveform over the sampling period. There is also the possibility of reversing this process. In this instance, the IDFT (Inverse Fourier Transform Discrete) is employed in order to create a single complex from the set of sine waves.
It can be observed how the IDFT could be utilized to create the multi-carrier transmit signal within the OFDM system. In addition, it is possible that it is possible that the DFT could be used to distinguish the subcarrier signals that are part of a reception OFDM transmission. In the scenario of OFDM, the sample period will be set to equal the period of the modulation symbol.
It is true that the DFT along with the IDFT are significant transforms that have applications across a variety of areas that deal with digital signal processing such as, for example, the creation and deconstruction of OFDM signals. However, the amount of different calculations needed to execute DFT directly DFT directly is quite significant, which poses the issue of cost-effective implementation.
One of the most popular solutions can be found in the FFT (Fast Fourier Transform). It is a matrix-based technique that greatly reduces the number of calculations needed to create results that are comparable to DFT. In practice it is the FFT is utilized in order to compute the DFT. In the same way in practice, using the IFFT (Inverse Fast Fourier Transform) is utilized to calculate the IDFT. IDFT
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