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Expanding on that - any periodic wave consists of a series of harmonically related sinusoids. If the entire wave is delayed by t seconds, then the phase shift is of the fundamental isRusslk said:A pulse can be represented as a series of harmonicly related sine waves. If the harmonics are phase shifted relative to one another, the shape of the pulse is changed. The best result is obtained when the phase shift is linear.
I'm guessing it's a finite impulse response (FIR) digital filter. Realizing that response in an infinite impulse response filter (such as an RLC filter) is basically impossible.BTW, is that a real filter or theoritical? Such sharp cutoff in a linear phase filter is impressive.
A pulse can be represented as a series of harmonicly related sine waves. If the harmonics are phase shifted relative to one another, the shape of the pulse is changed. The best result is obtained when the phase shift is linear.
Expanding on that - any periodic wave consists of a series of harmonically related sinusoids. If the entire wave is delayed by t seconds, then the phase shift is of the fundamental is
Φ=(t/T1)*360 degrees, where T1 = 1/F1 = period of fundamental,
or
Φ1=t*F1*360 (fundamental).
Since the frequency of the 2nd harmonic =2*F1,
Φ2=t*2*F1*360 (2nd harmonic),
Φ3=t*3*F1*360 (3rd harmonic)
etc.
Note that the phase shift is a linear function of frequency.
_3iMaJ said:Thinking about this in the time domain and not discrete domain does not help your endeavor.
If you review your DSP you'll find that one of the primary advantages of a FIR filter (which is what you have shown) is they have linear phase shift. The reason for the linear phase shift is the idea of causality. Initially when the FIR filter is designed it depends on FUTURE values of time (non - causal), to solve this problem we simply shift the filter by N samples to force the filter to depend on past samples (causal). Intuitively this make sense as we cannot know future samples, but we can store past samples to use them later. This is the reason for the linear phase shift that is introduced into the system.
yes, but we also do not store past output values in an FIR Filter