If you read the accelerometer datasheet, the output signal can have a noise according with the internal frequency....or the noise from power supply
it's on page 7 on datasheet.
Quote:
For most applications, a single 0.1 μF capacitor, CDC, placed
close to the ADXL335 supply pins adequately decouples the
accelerometer from noise on the power supply. However, in
applications where noise is present at the 50 kHz internal clock
frequency (or any harmonic thereof), additional care in power
supply bypassing is required as this noise can cause errors in
acceleration measurement. If additional decoupling is needed,
a 100 Ω (or smaller) resistor or ferrite bead can be inserted in
the supply line. Additionally, a larger bulk bypass capacitor
(1 μF or greater) can be added in parallel to CDC. Ensure that
the connection from the ADXL335 ground to the power supply
ground is low impedance because noise transmitted through
ground has a similar effect as noise transmitted through VS.
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