A1

This experiment was based on the overlap add and the overlap save method .We had taken a 13 point sequence for the overlap save method with the length of h(n) as 4.The value of L was taken as 5 and according to the formula (L+M-1) we got N=8.So the signal had to be divided into three parts of 8 blocks each.It had to be appended with a few zeroes for doing so.In the end the convolution of each of the decomposed part was fkund separately and then combined. In Overlap add method we did the same thing but in a different manner.All the signals taken were same.Just that now instead of 3,4 decompositions were made and in the end the last three columns were neglected.

Now another method to calculate the dft was using the fft formulae i.e DITFFT formulae This was our 3rd experiment .This was also done for 4pt and 8pt sequences.The flowchart of this is exactly opposite to that of the DFT whereas the results obtained are faster.The input sequence order is also different and the output is in "BIT Reverse Form". Also ,the formulae for real and complex multiplications and additions were tested. The result that was concluded was that FFT is computationally faster than DFT.

Our 2nd experiment was based on the Discrete Fourier Transform where we had to find the DFT of a 4pt and 8pt sequence using the formula method. This was implemented in C language.Two functions were used which contained arg and trignometric expressions. In the 4pt DFT ,the spectrum obtained was not that accurate as it was in 8pt sequence.The resolution was increased on appending 4 zeroes to the 4pt sequence to make it a 8pt sequence. The spectrum  obtained was Discrete in nature and was defined in the range of [0,2π). In the end the formulae for total number of complex and real addition and multiplications were tested for verification.

Our first experiment was based on linear convolution ,circular convolution and linear convolution using circular convolution. 1.In linear convolution ,the length of the output signal comes out to be L+M-1,where L and M are lengths of two signals. 2.Whereas in circular convolution,we get aliased output.In circular convolution we get the overlapped values with reference to result of linear convolution. 3.and in linear convolution using circular convolution , we select N>=L+ M-1 .