Regarding Discerete Fourier Transformation DFT

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David83

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Hi,

What does this mean, and why:

because of the periodic properties of the discrete Fourier transform (DFT), as well as the convolution process in which M inputs are converted to >= 2M - 1 outputs, zeros must be inserted into the data sequence
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Any clarification will be highly appreciate.

Thanks
 

This may help:

-Convolution of 2 signals M and N is M+N-1. So if M is convoluted with itself it is 2M-1. If doing the convolution of 2 unequal sized pieces of data you may need to pad with zeros.

-Also sometimes to get a more resolution in a DFT you will pad with zeros. something like this: **broken link removed**
 

Ok, but the two sequences do not have to be of equal size, right?

I am reading papers about single-carrier frequency domain equalization (SC-FDE), and some papers padding zeros to the to the input sequence, while others appending to the front of the sequence the last part of it (this is called cyclic prefix) to make the linear convolution circular convolution to apply DFT. If it is necessary to make the linear convolution circular, how did they apply DFT for the padding-zero case?

Thanks
 

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