文档介绍：Phase and Group Delays Phase and Group Delays
• The output y[n] of a frequency-selective the output is
jwo
LTI discrete-time system with a frequency y[n] = AH (e ) cos(won + q(wo ) + f)
response H ( e j w ) exhibits some delay
• Thus, the output lags in phase by q(wo)
relative to the input x[n] caused by the radians
nonzero phase response q(w) = arg{H (e jw)}
of the system • Rewriting the above equation we get
æ æ q(w ) ö ö
• For an input jwo o
y[n] = AH (e ) cosçwoçn + ÷ + f÷
è è wo ø ø
x[n] = Acos(won + f), ­ ¥ < n < ¥
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Copyright © 2001, S. K. Mitra Copyright © 2001, S. K. Mitra
Phase and Group Delays Phase and Group Delays
• This expression indicates a time delay, • In this case, ponent of the input
known as phase delay, at w = w o given by will go through different phase delays when
q(wo) processed by a frequency-selective LTI
tp(wo) = ­
wo discrete-time system
• Now consider the case when the input • Then, the output signal, in general, will not
signal contains many sinusoidal look like the input signal
components with different frequencies that • The signal delay now is defined using a
are not harmonically related different parameter
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Copyright © 2001, S. K. Mitra Copyright © 2001, S. K. Mitra
Phase and Group Delays Phase and Group Delays
• To develop the necessary expression, • The input can be rewritten as