The Discrete Fourier Transform (DFT)
Discrete-Time Signals & Digital Filtering
Infinite Impulse Response (IIR) Filters
Steady State and Transient Response
Before a signal is applied to the input of a digital filter, the filter's internal “state” is assumed equal to zero.
Digital filters are linear systems. One property of linear systems is that a sinusoidal input will produce a sinusoidal output of the same frequency.
However, when a sinusoidal signal is first applied to the input of a digital filter, the output initially exhibits a region of transition (referred to as its
For FIR filters, this transition region (or “warm-up” period) has a duration in samples equal to the filter order.
For IIR filters, the length of the transition region is dependent on the filter order and the feedback coefficient values.
Assuming a continued application of the sinusoidal input, the filter will subsequently settle into its
If the input changes frequency or displays a discontinuity of any sort, another transient region will occur in the filter output.
The frequency response of a digital filter is understood to represent its steady-state behavior.
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Gary P. Scavone