## Developer Reference

• 2021
• 03/26/2021
• Public Content
Contents

# IIRIIR Filter Functions

The functions described in this section initialize an infinite impulse response (IIR) filter and perform a zero-phase digital filtering of input data in both forward and backward directions. The formulas below explain why the filtered signal has zero-phase distortion. Consider the following case in the frequency domain: if
x(n)
is the input sequence and
h(n)
is the IIR filter's impulse response, then the result of the forward filter pass is:
where
• X(e
)
is the Fourier transform of
x(n)
• H(e
)
is the Fourier transform of
h(n)
• Y
1
(e
)
is the Fourier transform of the forward filter pass
Backward filtering corresponds to filtering of time-reversed signal. Time reversal corresponds to replacing φ with -φ in the frequency domain, so the result of time reversal is:
When the filter is applied for the second time, the above formula is multiplied by the Fourier transform of the filter's impulse response function
H(e
)
:
The final time reversal in the frequency domain results in:
You can see from the resulting equation that:
• The filtered signal has zero-phase distortion (as the filtering was done with
|H(e
)|
2
, which is purely real-valued)
• The filter transfer function has the squared magnitude of the original filter transfer function
• The filter order is double the order of the initialized IIR filter
To initialize and use an IIRIIR filter, follow this general scheme:
1. Call
ippsIIRIIRInit
to initialize the IIRIIR filter in the external buffer. To compute the size of the buffer, use the
ippsIIRIIRGetStateSize
function.
2. Call
ippsIIRIIR
to filter a vector.
3. Call
ippsIIRIIRGetDlyLine
and
ippsIIRIIRSetDlyLine
to get and set the delay line values in the IIRIIR state structure.

#### Product and Performance Information

1

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