Mixing
DFT zero-padding of signals starting before n=0
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If a signal starts before n=0, what part of the signal should be used to compute DFT after zero-padding? For example, x(n) = {1, 2, 3, 4, 5}, where x(-2) = 1 and x(0) = 3. If this signal is zero-padded to N=8, the new signal would be x'(n) = {1, 2, 3, 4, 5, 0, 0, 0}, where, again, x'(-2) = 1 and x'(0)=3. However, to compute the DFT of this zero-padded signal x'(0), should I use {1, 2, 3, 4, 5, 0, 0 , 0}, which starts with x'(-2), or should I use {3, 4, 5, 0, 0, 0, 1, 2}, which starts with x'(0) with the first few terms (n<0) folded over? In terms of the DFT X(k), I think its magnitude would be the same for the two approaches, but its phase would be different, right?
dft zero-padding
asked Jan 28 at 23:24
tonytony
82
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If a signal starts before n=0, what part of the signal should be used to compute DFT after zero-padding? For example, x(n) = {1, 2, 3, 4, 5}, where x(-2) = 1 and x(0) = 3. If this signal is zero-padded to N=8, the new signal would be x'(n) = {1, 2, 3, 4, 5, 0, 0, 0}, where, again, x'(-2) = 1 and x'(0)=3. However, to compute the DFT of this zero-padded signal x'(0), should I use {1, 2, 3, 4, 5, 0, 0 , 0}, which starts with x'(-2), or should I use {3, 4, 5, 0, 0, 0, 1, 2}, which starts with x'(0) with the first few terms (n<0) folded over? In terms of the DFT X(k), I think its magnitude would be the same for the two approaches, but its phase would be different, right?
dft zero-padding
asked Jan 28 at 23:24
tonytony
82
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but remember, since the DFT is circular, you can zero pad it on either end (or both ends) and the only difference in the DFT result will be a linear phase term corresponding to a rotation or circular-shift.
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– robert bristow-johnson
Jan 29 at 5:22
add a comment |
$begingroup$
If a signal starts before n=0, what part of the signal should be used to compute DFT after zero-padding? For example, x(n) = {1, 2, 3, 4, 5}, where x(-2) = 1 and x(0) = 3. If this signal is zero-padded to N=8, the new signal would be x'(n) = {1, 2, 3, 4, 5, 0, 0, 0}, where, again, x'(-2) = 1 and x'(0)=3. However, to compute the DFT of this zero-padded signal x'(0), should I use {1, 2, 3, 4, 5, 0, 0 , 0}, which starts with x'(-2), or should I use {3, 4, 5, 0, 0, 0, 1, 2}, which starts with x'(0) with the first few terms (n<0) folded over? In terms of the DFT X(k), I think its magnitude would be the same for the two approaches, but its phase would be different, right?
dft zero-padding
asked Jan 28 at 23:24
tonytony
82
$endgroup$
If a signal starts before n=0, what part of the signal should be used to compute DFT after zero-padding? For example, x(n) = {1, 2, 3, 4, 5}, where x(-2) = 1 and x(0) = 3. If this signal is zero-padded to N=8, the new signal would be x'(n) = {1, 2, 3, 4, 5, 0, 0, 0}, where, again, x'(-2) = 1 and x'(0)=3. However, to compute the DFT of this zero-padded signal x'(0), should I use {1, 2, 3, 4, 5, 0, 0 , 0}, which starts with x'(-2), or should I use {3, 4, 5, 0, 0, 0, 1, 2}, which starts with x'(0) with the first few terms (n<0) folded over? In terms of the DFT X(k), I think its magnitude would be the same for the two approaches, but its phase would be different, right?
dft zero-padding
dft zero-padding
asked Jan 28 at 23:24
tonytony
82
asked Jan 28 at 23:24
tonytony
82
asked Jan 28 at 23:24
tonytony
82
asked Jan 28 at 23:24
tonytony
82
asked Jan 28 at 23:24
tonytony
82
82
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but remember, since the DFT is circular, you can zero pad it on either end (or both ends) and the only difference in the DFT result will be a linear phase term corresponding to a rotation or circular-shift.
$endgroup$
– robert bristow-johnson
Jan 29 at 5:22
add a comment |
$begingroup$
but remember, since the DFT is circular, you can zero pad it on either end (or both ends) and the only difference in the DFT result will be a linear phase term corresponding to a rotation or circular-shift.
$endgroup$
– robert bristow-johnson
Jan 29 at 5:22
$begingroup$
but remember, since the DFT is circular, you can zero pad it on either end (or both ends) and the only difference in the DFT result will be a linear phase term corresponding to a rotation or circular-shift.
$endgroup$
– robert bristow-johnson
Jan 29 at 5:22
$begingroup$
but remember, since the DFT is circular, you can zero pad it on either end (or both ends) and the only difference in the DFT result will be a linear phase term corresponding to a rotation or circular-shift.
$endgroup$
– robert bristow-johnson
Jan 29 at 5:22
add a comment |
1 Answer
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Use the second one Tony... It yields the correct implied phase relationship.
answered Jan 28 at 23:49
Fat32Fat32
15.7k31232
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1 Answer
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$begingroup$
Use the second one Tony... It yields the correct implied phase relationship.
answered Jan 28 at 23:49
Fat32Fat32
15.7k31232
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add a comment |
$begingroup$
Use the second one Tony... It yields the correct implied phase relationship.
answered Jan 28 at 23:49
Fat32Fat32
15.7k31232
$endgroup$
add a comment |
$begingroup$
Use the second one Tony... It yields the correct implied phase relationship.
answered Jan 28 at 23:49
Fat32Fat32
15.7k31232
$endgroup$
Use the second one Tony... It yields the correct implied phase relationship.
answered Jan 28 at 23:49
Fat32Fat32
15.7k31232
answered Jan 28 at 23:49
Fat32Fat32
15.7k31232
answered Jan 28 at 23:49
Fat32Fat32
15.7k31232
answered Jan 28 at 23:49
Fat32Fat32
15.7k31232
15.7k31232
add a comment |
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but remember, since the DFT is circular, you can zero pad it on either end (or both ends) and the only difference in the DFT result will be a linear phase term corresponding to a rotation or circular-shift.
$endgroup$
– robert bristow-johnson
Jan 29 at 5:22