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From: | Daniel J Sebald |
Subject: | Re: outstanding changesets |
Date: | Sun, 01 Feb 2009 15:42:28 -0600 |
User-agent: | Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.7.3) Gecko/20041020 |
Ben Abbott wrote:
On Feb 1, 2009, at 1:56 PM, Daniel J Sebald wrote:Ben Abbott wrote:On Jan 29, 2009, at 1:50 AM, Søren Hauberg wrote:ons, 28 01 2009 kl. 22:13 -0500, skrev John W. Eaton:Does Matlab produce the same result?Matlab produces the attached pdf Søren <matlab_freqz.pdf>? ... that is not what I expected. My impression was the Matlab unwrapped the phase in such a way that only positive delays would result. However, in this example, it appears to be opposite.Any idea what they are doing?To "unwrap the phase" does not mean disallowing negative, it means to remove any 360 degree jumps from the phase which were created as a consequence of the modular arithmetic of phase angles. Note that if there are 180 degree phase shifts, those stay because they are actual phase jumps.DanHi Dan,What I've inferred is that Matlab's implementation favors unwrapping the phase so that the phase slope is negative (downward sloping), and the delay is positive.See the examples at the link below. http://hauberg.org/wiki/doku.php?id=freqz Ben
Yes, negative phase, positive delay assumes a causal system (i.e., something happens and then there is a response, not the other way around), but that is pretty conventional. The discrete-time Fourier transform is defined X(omega) = sum x[n] e^{-j omega n} such that with x[n] nonzero only for n > 0 (or more generally, a right-sided sequence) the minus sign gives negative phase. Dan
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