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Use First Order Low Pass Filter


first order filter bode plot first order filter bode plot


Here, the transfer function representation of the first order filter (where \(s\) is the Laplace variable) :

\[H(s) = \dfrac{1}{1+\tau.s}\]


  • \(\tau\) is the constant time in [s].

transfer function is sampled

We show here the continuous transfer function of the function we want to implement. But calculation are sampled. Relationship to Laplace transform


Using the \(z\)-transform we get the following form:

\[ \begin{align} H(z^{-1}) = \dfrac{b_1.z^{-1}}{1+a_1.z^{-1}} \\ \\ H(z) = \dfrac{b_1}{z + a_1} \\ \end{align} \]

As there's a direct relation between \(z^{-1}\) and \(q^{-1}\) the delay operator, we can write the reccuring equations we will use in the code.

We give here the recurrence equation used to filter the \(\text{input}\) signal.

\[ out_k = b_1 . \text{in}_k - a_1 . out_{k-1} \]


\[ \begin{align} a_1 &= -exp\left(-\dfrac{Ts}{\tau}\right) \\ \\ b_1 &= 1 + a_1 \end{align} \]


3 steps to use the first order filter

    #include "filters.h"

    const float32_t tau = 1e-3;               // constant time
    const float32_t Ts = 100e-6;              // sampling time
    myfilter = LowPassFirstOrderFilter(Ts, tau);

Before to run, we advise to reset the filter, in the setup_routine() of the OwnTech Power API.


In the loop_critical_task() you can call the method calculateWithReturn().

signal_filtered = myfilter.calculateWithReturn(signal_to_filter);

It returns the data filtered.


Remind that the loop_critical_task() is called at the sampling time you define and must be equal to \(T_s\).