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## Phase shift, time delay, group delay... 7 years 4 months ago #12303

 John Ashman Offline Elite Member Posts: 226 Thank you received: 23 Hi Jim, if you have no alteration to the signal other than a time delay, you have a linear phase shift. For example, suppose you had no alteration to the signal other than a time delay of 10 ms. You would measure a phase shift of 360 deg at 100 Hz. At 50 Hz, 180 deg; at 200 Hz, 720 deg. John, if there is a pure time delay, such as the 10ms, that doesn't induce any phase shift (done properly). Phase shift occurs when the signal is delayed in proportion to the frequency. So not everything would be 10ms. The amount of time delay would vary from almost 0ms to some other figure. There is no phase shift in a time delay because all of the signals are synced up and the wave form is identical. For instance, if you do a phase delay of 180 degrees, then all of the individual frequencies would be delayed by a time factor corresponding to half a wavelengh in time, which is to say, a much longer delay for low frequencies than high requencies. Please Log in or Create an account to join the conversation. Last edit: by John Ashman.

## Phase shift, time delay, group delay... 7 years 4 months ago #12318

 john.reekie Offline Platinum Member Posts: 3775 Thank you received: 1588 Hi Jim, if you have no alteration to the signal other than a time delay, you have a linear phase shift. For example, suppose you had no alteration to the signal other than a time delay of 10 ms. You would measure a phase shift of 360 deg at 100 Hz. At 50 Hz, 180 deg; at 200 Hz, 720 deg. John, if there is a pure time delay, such as the 10ms, that doesn't induce any phase shift (done properly). You are not understanding the purpose of the example. Let me try again Phase is related to time and frequency, specifically a time delay of 1/f is a 360 phase shift. Correct? Now consider different frequencies, and compare the signal "before" the time delay and "after" the time delay. What is the relationship between the phase of the input signal and the output signal? To make it concrete, say the delay is 10 ms. At 100 Hz, the time delay delays the waveform by a full cycle, so the phase shift is 360 degrees. Right? At 50 Hz, the time delay delays the waveform by half a cycle, so the phase shift is 180 degrees. Right? As I explained, this is a linear phase shift i.e. the amount of phase shift is proportional to frequency. Yes, the shape of the waveform (any waveform) going in is the same as the shape of the waveform coming out, as you say. But still, the phase shift at different frequencies between the input and output signals is not zero. It is a linear phase shift. If you are looking just at the components of a waveform, then usually you would shift the time reference to remove the absolute time delay. The reason I started with the example of time delay and linear phase shift is to introduce the notion that time is related to phase as the slope of the phase change. So, when you have a non-linear phase shift, the slope of that curve is the frequency-dependent delay i.e. the group delay. I find that this helps to understand what group delay means in a more concrete way than just saying "group delay is the negative derivative of phase". I am not miniDSP support. "You must ask the right questions." - Dr. Alfred Lanning's hologram. -> Have you read the User Manual?? -> Have you drawn and posted a diagram? -> Have you posted a screenshot? -> Have you posted your config file? Please Log in or Create an account to join the conversation. Last edit: by john.reekie.

## Phase shift, time delay, group delay... 7 years 4 months ago #12320

 John Ashman Offline Elite Member Posts: 226 Thank you received: 23 But it's not a phase shift at all. A phase shift distorts the signal and while the ear isn't that adept at hearing it, even at extreme levels, it shows up as an obvious change in the signal shape. A delay of one cycle is simply a delay. If you delay all frequencies by one cycle, then that his a phase delay. If you delay everything by a specific time, then that is simply time delay. Phase shift is a relative thing. If you delay a pure sine wave by half a cycle, you're really not shifting phase, unless there is another frequency to which it is related. If you're using it to make the point, I just am completely misunderstanding the point you're making, unless you're trying to equate a term I've never even heard of, "linear phase shift" with "time delay", which I think entirely muddies the waters as there is no phase shift. Please Log in or Create an account to join the conversation.

## Phase shift, time delay, group delay... 7 years 4 months ago #12321

 john.reekie Offline Platinum Member Posts: 3775 Thank you received: 1588 Hi John, you would be familiar with the term "linear phase filter", though? (DEQX uses it to describe what their product does.) Here's a definition: "Linear phase is a property of a filter, where the phase response of the filter is a linear function of frequency, " (en.wikipedia.org/wiki/Linear_phase) The article continues: "Since a linear phase ... filter has constant group delay, all frequency components have equal delay times. That is, there is no distortion due to the time delay of frequencies relative to one another.." Hope that helps... (my emphasis added to quotes) I am not miniDSP support. "You must ask the right questions." - Dr. Alfred Lanning's hologram. -> Have you read the User Manual?? -> Have you drawn and posted a diagram? -> Have you posted a screenshot? -> Have you posted your config file? Please Log in or Create an account to join the conversation.

## Phase shift, time delay, group delay... 7 years 4 months ago #12323

 John Ashman Offline Elite Member Posts: 226 Thank you received: 23 Ahhhhh. You mean a "linear-phase delay". Time delay, but sure, if you put a hyphen in there, it clears it up more. I was reading it like "linear phase-delay". Now having searched it, I see that the term is used with a hyphen between linear and phase to keep it clean. This is why I was confused. As you were.....just...you know, don't forget the hyphen Please Log in or Create an account to join the conversation.

## Phase shift, time delay, group delay... 7 years 4 months ago #12336

 Jim the Oldbie Topic Author Offline Elite Member Posts: 268 Thank you received: 78 Hi John, may I butt in with a quick question or two? Just trying to keep up here... As I explained, this is a linear phase shift i.e. the amount of phase shift is proportional to frequency. Yes, the shape of the waveform (any waveform) going in is the same as the shape of the waveform coming out, as you say. But still, the phase shift at different frequencies between the input and output signals is not zero. It is a linear phase shift. I understand what you're saying, but I must admit I've always been more comfortable thinking of a time delay as just a time delay, and not as a continuously (even linearly) varying phase shift. But maybe that's part of why I haven't been fully comprehending this stuff. If you are looking just at the components of a waveform, then usually you would shift the time reference to remove the absolute time delay. The reason I started with the example of time delay and linear phase shift is to introduce the notion that time is related to phase as the slope of the phase change. So, when you have a non-linear phase shift, the slope of that curve is the frequency-dependent delay i.e. the group delay. I find that this helps to understand what group delay means in a more concrete way than just saying "group delay is the negative derivative of phase". So let me try this out: On a graph of phase angle vs linear frequency, linear (pure?) phase shift is represented as a straight, sloping line (or if you prefer, a sawtooth as the phase wraps); and any deviation from that straight line is the group delay? -- Jim, fingers crossed Please Log in or Create an account to join the conversation.

## Phase shift, time delay, group delay... 7 years 4 months ago #12337

 Jim the Oldbie Topic Author Offline Elite Member Posts: 268 Thank you received: 78 So let me try this out: On a graph of phase angle vs linear frequency, linear (pure?) phase shift is represented as a straight, sloping line (or if you prefer, a sawtooth as the phase wraps); and any deviation from that straight line is the group delay? Oops! One more detail: The above example assumes a time delay of > zero? (Otherwise no slope, heh) Please Log in or Create an account to join the conversation.

## Phase shift, time delay, group delay... 7 years 4 months ago #12341

 john.reekie Offline Platinum Member Posts: 3775 Thank you received: 1588 I need to add (sorry but it's late here...): your original quote based on my earlier statements "linear (pure?) phase shift is represented as a straight, sloping line" is fine too, it's just not very clear (my fault) I am not miniDSP support. "You must ask the right questions." - Dr. Alfred Lanning's hologram. -> Have you read the User Manual?? -> Have you drawn and posted a diagram? -> Have you posted a screenshot? -> Have you posted your config file? Please Log in or Create an account to join the conversation.