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1

The significance is a constant time delay for all frequencies. Time delay is the derivative of phase with respect to frequency, so given a linear phase as shown, the time delay is constant. Notice that the abrupt steps in phase actually only occur when the magnitude goes through zero so does not effect the nature of it being a "linear phase" filter....


4

At the risk of blowing my own trumpet and that of my co-author, Bob Williamson, there is also this paper which shows the equivalence of three techniques referred to in the FIR link in Ben's answer and also referred to in the paper linked to from Hilmar's answer. The two results that are of particular interest are Proposition's 2 and 3 of the paper, ...


3

As Hilmar pointed out, for delays that are integer multiples of the sampling period, method 1 is far superior. Also, Method 1 is more suitable for real-time operations as you don't need to buffer the data to perform the FFT. For delays that are non-integer multiples of the sampling period you can adapt method 1 by using an FIR or IIR filter using Lagrange ...


10

Is there any trade-off in numerical precision or speed? Yes. For delays that are integer multiples of the sampling period method 1 is far superior: it's computationally efficient, it's bit-exact, it's easy to implement and it's almost fool proof. Method 2 is computationally expensive, you need to pick an FFT length (which is not trivial) it's subject to ...


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