Automotive Engineering - May 2024 - 4

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The Inside Story on Cleaning Digital Noise
with FIR and IIR Filters
F
iltering is a " must-have " tool in digital data acquisition and digital signal processing to acquire uncorrupted data.
Anti-aliasing filtering mitigates signal corruption from frequencies above the Nyquist frequency, and AC coupling
filters remove DC offset values. However, despite the obvious advantages, filtering has some negatives. This brief
focuses on these pitfalls so that engineers can better understand how filters can distort their data. There are four
basic filter classifications: analog, digital, Infinite Impulse Response (IIR), and Finite Impulse Response (FIR). Analog filters
are electronic circuits that typically model IIR filters.
What are some examples of signal distortion
caused by filters?
There are four main types of signal distortion:
roll-off in the passband, distortion in
the passband, signal delay/phase distortion,
and distortion at the beginning of the
signal. These anomalies are created by filter
mathematics. FIR filtering is a convolution
process, and IIR uses a difference equation.
Roll-off in the passband simply means
there is no brick wall filter (or the roll-off in
the frequency domain being a vertical line).
Mathematically this is not attainable, so
filters will have a roll-off in dB/octave attenuating
the signal before the specified
cut-off frequency, typically -3 dB (aka " 3 dB down " ).
Distortion in the passband is typically a trade-off with the
filter roll-off. The sharper the roll-off, the more distortion
occurs. Filtering also creates a delay/phase distortion in
the signal proportional to the number of coefficients required.
As a result, the filtered output signal is shifted in
time. The delays from FIR filters are linear and constant
across signal frequencies. On the other hand, the delays
from IIR filters are non-linear and do change with the signal
frequency. Engineers should be aware that distortion at
the beginning of the signal is caused by a filter's settling
time. This is typically an issue with very low cut-off frequencies
or when filtering very short-duration events.
Since FIR filters have a linear delay, the
time data can be shifted to correct for the
phase distortion. IIR filters have a nonlinear
delay so there is no online correction, but
the filter can be passed through the data
forward and reversed during post-processing
to remove these nonlinear delay distortions.
This process is called phase correction
or " zero-phase filtering " or " zerophase
shift filtering. "
Dewesoft's John Hiatt
Why use an FIR vs an IIR Filter?
FIR filters are much more computationally
efficient than IIR filters. This is because
they require fewer coefficients to achieve
the same roll-off. In applications where many channels
must be filtered simultaneously at high sample rates, IIR is
the way to go. With IIR Filters, both relative phase and
time alignment may be compared between channels if the
same filters were used on both signals. If absolute time is
required online, I recommend using an FIR filter. If offline
filtering is acceptable and if phase correction is available,
IIR filters are fine.
How do you mitigate signal distortion?
Signal distortion in the passband can easily be controlled by
carefully selecting the filter type. With IIR filtering, for example,
a Bessel filter is maximally flat with the lowest roll-off per coefficient
and the most roll-off within the passband. Chebyshev
would be at the other extreme, presenting the most distortion
(ripple), the sharpest roll-off, and the least amount of attenuation
within the passband. A Butterworth filter is a great compromise
between the two and is the most widely used for that
reason. The relationship between roll-off within the passband
and distortion can be described as inverse. A steeper roll-off
results in less roll-off within the passband, while also potentially
increasing distortion. Engineers usually prioritize achieving
minimal distortion within the passband. The distortion at
the beginning of the signal can be addressed by recording a
little more data to allow the filter to settle.
4 May 2024
What is a practical example of signal distortion and how
it can lead to incorrect data interpretation?
Numerical integration that changes a signal from acceleration
to velocity can be done with a filter. This process in the
frequency domain is simply dividing by ω (omega is the
angular frequency in radians per second) and shifting the
phase. However, if an IIR filter is used and the phase distortion
is not corrected in this process, the resulting sine
waves will not have a 90-degree phase difference. When
balancing rotating equipment, there is a key-phasor, which
is a 1 PPR (pulse per revolution) signal on the rotating shaft
that indicates zero phase. The other channel is typically a
response signal from an accelerometer. These are typically
IEPE accelerometers that are AC coupled with a high-pass
filter at around 1 Hz. A " best practice " with filters is to filter
all your channels with the same filter scheme and understand
the frequency response (magnitude and phase) of
the filters in the measurement and analysis chain.
More Information on this topic can be found at this link.
https://training.dewesoft.com/online/course/filters
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Automotive Engineering - May 2024

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