Real-time digital signal processing: implementations, ... changes in the input signal is limited by its internal clock rate, so that it may be slow to
Document source : notes.ump.edu.my
n 0, y0 1 1 1 1 4
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
n 1, y1 1 1 1 3
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
Repeating the process, we obtain
yn xn hn f4, 3, 2, 2, 2, 3, 4, 5g:
This circular convolution is due to the periodicity of the DFT. In circular convolution,
the two sequences are always completely overlapping. As the end of one period is shifted
out, the beginning of the next is shifted in as shown in Figure 7.3. To eliminate the circular
effect and ensure that the DFT method results in a linear convolution, the signals must be
zero-padded so that the product terms from the end of the period being shifted out are
zero. Zero padding refers to the operation of extending a sequence of length N
1
to a length
N
2
(> N
1
) by appending (N
2
À N
1
) zero samples to the tail of the given sequence. Note
that the padding number of zeros at the end of signal has no effect on its DTFT.
DISCRETE FOURIER TRANSFORM
313
Summary :
n 0, y0 1 1 1 1 4 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 n 1, y1 1 1 1 3 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 Repeating the process, we obtain yn xn hn f4, 3, 2, 2, 2, 3, 4, 5g: This circular convolution is due to the periodicity of the DFT.
Tags :
circular,zero,conolution,end,shifted,out,padding,length,period,sequence,dft,effect,gien