The Fourier transform is used to convert the signals from time domain to frequency domain and the inverse Fourier transform is used to convert the signal back from the frequency domain to the time domain.The Fourier transform is a powerful tool to analyse the signals and construct them to and from their frequency components. If the signal is discrete in time that is sampled, one uses the discrete Fourier transform to convert them to the discrete frequency form DFT, and vice verse, the inverse discrete transform IDFT is used to back convert the discrete frequency form into the discrete time form.
To reduce the mathematical operations used in the calculation of DFT and IDFT one uses the fast Fourier transform algorithm FFT and IFFT which corresponds to DFT and IDFT, respectively.
In transmitters using OFDM as a multicarrier modulation technology, the OFDM symbol is constructed in the frequency domain by mapping the input bits on the I- and Q- components of the QAM symbols and then ordering them in a sequence with specific length according to the number of subcarriers in the OFDM symbol. That is by the mapping and ordering process, one constructs the frequency components of the OFDM symbol. To transmit them, the signal must be represented in time domain. This is accomplished by the inverse fast Fourier transform IFFT.
So, in summary the signal is easier synthesized in discrete frequency domain in the transmitter and to transmit it must be converted to discrte time domain by IFFT.
By using IFFT which is fast implementation of IDFT. By using IDFTwe are constructing time domain signals which can fill the desired bands of interest ( it acts like synthesizer) where FFT analyses the signal which would be used at receiver to know then informations contained in the sub bands
We use rather imprecisely the terms FFT and IFFT as though they were transforms in themselves, but in fact they are fast implementation algorithms (and there are several alternative implementations) of the Discrete Fourier Transform (DFT).
If we consider a finite length signal {x(n)}={x(0),x(1),…,x(N-1)} we can then write its z-transform as X(z)=∑from (n=0) to (N-1) of x(n) z^(-n) . The evaluation of this polynomial at specific values z(k)=exp(j2πk/N) is the Discrete Fourier Transform, usually written as
X(k)=∑from (n=0) to (N-1) of x(n) e^(-j2πkn/N)
We take as many values of k as we have elements in x(n) in order to have a simple invertible equation (ie we have a column vector X linked to the signal column vector x via square matrix which contains complex exponentials of different powers).
ie X=E*x and hence obviously x=E^(-1)*X
Thus the DFT can be seen as a simple square matrix operation on a given data vector and inversely the data vector is obtainable from the DFT vector by multiplying this by the inverse of the same matrix. It so happens that the inverse of this square matrix is the complex conjugate of the original to within a scaling constant (this has to do inter alia with orthogonality conditions, which in this simple explanation are not really essential).
The FFT is, as mentioned above, an algorithm that exploits the symmetries in the matrix E to produce computationally efficient ways of carrying out the matrix multiplications.
FFT and IFFT are transform techniques. FFT which is a technique to analyse signal in frequency domain like if we see our ecg signal in time domain and are not able to find problem then we can take FFT of this signal and find out how many frequency components are present and analyse it better. Now, if we convert it back to time domain then all frequency will be available but it will be difficult as which frequency was present at what time, so one can replace IFFT and FFT by wavelet transform i.e. DWT and IDWT.
can any body tell me how can i differentiate the two terms OFDM and FFT in simple words?
OFDM is actually a transmission system but inside OFDM there is modulation. Each subcarrier is modulated with different frequency. In OFDM IFFT makes this modulation process. and FFT makes the inverse, demodulation in each subcarrier.
Dear Sikandar,
welcome,
The OFDM in the frequency domain is a sequence of subcarriers forming the OFDM symbol. Ever carrier is QAM modulated to superpose the base band signal on the carriers. So, the OFDM symbol in the frequency domain is the FFT of the OFDM symbol provided that the number of subcarrier is 2^n with n is a positive integer.
There3fore in order to from the symbol in time domain we just inverse FFT of OFDM symbol.
Best wishes
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