Let xn be a lengthN sequence and consider the following Npoi

Let x[n] be a length-N sequence and consider the following N-point DFTs.

X[k] = DFT{x[n]}

and

y[n] = DFT{X[k]}

i.e. y[n] is the DFT of the DFT of x[n]. Express y[n] in terms of x[n] and explain how you can use this results to implement the IDFT algorithm.

Solution

DFT ALGORITHUM:

The leakage problem to a good discrete time approximate system, g(nTs) in the frequency band of interest.A simple model g(nTs) in the generated using the FIR filter with impulse response given by the inverse the DFT ie IDFT of the FRF G(jw)

       G(nTs)=IDFT(G(jwk)    the methos provides better estimates of the G(jwk) without increasing the noise sensitivity under the condition.

By the selecting the optimal length of FIR filter g(nTs) ,the systermatic errors the FIR filter is too short, are balanced with the noise sensitivity.

The algorithm is implemented in a dedicated routine ,

Other words, we can say that, we perform a search on the isbh of the document ej, in order to retrieve it in LT.IN addition we can compare the title of the returned item with the title of the document ej,and only if the two title match,we proceed to next step of the process.

After retrieving the appropriate document , we have the tag t1 in its tag cloud.If found,there is a number that follows the tag, which is the desired Uij.

Afterwards we estmate the normalized Uij as n Uij= Uij/ sigma j Uij ,where sigma j Uij is the sum of all the uij of the tags, assigned to the documents.

        Tf-idfg= nPij* idfg     and

     Tf-idf=nuij*idfL

               Idfg=log (N1/nil),

                        idfL=Log(Ng/niG)