Why does a simple delay system with $h[n]=\delta[n-n_0]$ have a linear phase?

1. What is the delay of a linear phase FIR?
2. Why do FIR filters have linear phase?
3. Why do filters cause delay?
4. What causes group delay?

What is the delay of a linear phase FIR?

2.1. 4 What is the delay of a linear-phase FIR? The formula is simple: given a FIR filter which has N taps, the delay is: (N – 1) / (2 * Fs), where Fs is the sampling frequency. So, for example, a 21 tap linear-phase FIR filter operating at a 1 kHz rate has delay: (21 – 1) / (2 * 1 kHz)=10 milliseconds.

Why do FIR filters have linear phase?

The FIR filters have a phase response that traces out a straight line. Both of these FIR filters exhibit linear phase [1][2]. This means that those sinusoidal components are given a constant phase shift and that the phase shift is constant relative to each frequency.

Why do filters cause delay?

Filters, however, also induce changes in the phases of different frequencies whose amplitude is unmodulated. These phase shifts cause time lags in the filtered signals, leading to a disruption of the timing information between different frequencies within the same signal and between different signals.

What causes group delay?

In signal processing, group delay and phase delay are delay times experienced by a signal's various frequency components when the signal passes through a linear time-invariant system (LTI), such as a microphone, coaxial cable, amplifier, loudspeaker, telecommunications system or ethernet cable.