# Background:

There is delay system concept given in this link:

But, I did not understand the phase response of this dely system by diagram.
Diagram details are given in this link (crop shown below) as figure 6.2:

# The problem restated:

I tried to understand phase of a delay system by this diagram but I failed to understand how the phase is represented by the equation of a straight line with slope equal to -n in figure 6.2.

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Do you know how to convert the difference equation into a transfer function in the z domain? That would probably be the best first step to take into finding out why the phase response is what it is. –  Bitrex May 10 '11 at 3:19
sorry no.. i did not study z doamin.. yet –  Miss May 10 '11 at 3:28
To get up to speed, you may want to have a look at the first couple of parts of the following ebook section: ccrma.stanford.edu/~jos/filters/Transfer_Function_Analysis.html. Once you know how to convert a difference equation into its z domain representation, the following section: ccrma.stanford.edu/~jos/filters/… will tell you how to find the frequency and phase response. –  Bitrex May 10 '11 at 3:39
"I failed to understand" is not a question. –  markrages May 10 '11 at 5:25
You don't need the z-transform to understand phase. –  markrages May 10 '11 at 5:26
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## 1 Answer

It is important to understand what phase is.

Consider a 1 Hz sine wave. This means it goes through 360 degrees in one second. If you delay this wave by 1/2 second, that's 180 degrees phase shift.

Now consider a 2 Hz sine wave. This means it goes through 720 degrees in one second. If you delay this wave by 1/2 second, that's 360 degrees phase shift.

By these examples, see how the phase at a constant time delay depends on frequency?

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I am not sure I would have made as concise an example. Too many years with only using the z transform. I knew that was the reason, but turning the brain on is never easy. –  Kortuk May 10 '11 at 5:58
@markages: i understand he applied formula for straight line.. taninver(b/a) .. so that mean phase changes depend on frequency.. –  Miss May 10 '11 at 12:14
@Miss You don't need a transcendental function to explain it... higher frequency means things are happening faster, so more change happens in a fixed amount of time. –  markrages May 10 '11 at 14:23
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