EXP2. DISCRETE FOURIER TRANSFORM

IN this experiment ,we have implemented function in c language for  finding DFT for real valued sequency.

Here we obtained symmetric spectrum as input is real valued sequence.

DFT is frequency sampling of DTFT signal DFT and IDFT both assumes input signal to be periodic as it gives discrete spectrum(line spectrum).DFT gives approximated spectrum. Also the DFT coefficients are periodic and are defined in the range of 0 to 2𝜋

As N increases by zero padding

1.Frequency spacing decreases

2.Approximation error in spectrum representation  decreases

3. Resolution of spectrum increase.

To find one value of X[k]:

Total complex multiplication=N

Total complex Addition=N-1

To find all N value of X[k]:

Total complex multiplication=N*N

Total complex Addition=N(N-1)

In DFT, Total Real multiplication =4(N^2).

Total real Addition=4(N^2)-2N.