| Communications Toolbox | |
Without propagation delays, both Hilbert filters and raised cosine filters are noncausal. This means that the current output depends on the system's future input. In order to design only realizable filters, the hilbiir, rcosine, and rcosflt functions delay the input signal before producing an output. This delay, known as the filter's group delay, is the time between the filter's initial response and its peak response. The group delay is defined as
where θ is the phase of the filter and ω is the frequency in radians. This delay is set so that the impulse response before time zero is negligible and can safely be ignored by the function.
For example, the Hilbert filter whose impulse is shown below uses a group delay of 1 second. Notice in the figure that the impulse response near time 0 is small and that the large impulse response values occur near time 1.
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