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Are there any types of low pass filters that preserve the amplitude and phase? The one that I am aware of, sometimes called an exponentially weighted moving average does neither.

First order Low pass filter

Y(s) = $\frac{w_c}{s+w_c}$

In discrete time form

y(n) = y(n-1) + $\alpha$ [ u(n) - y(n-1) ]

Are there others that don't require significant mathematical implementation that I could use that meet similar requirements, but without the phase lag addition, and magnitude reduction.

[Edit] To clarify, I'm looking for different types of low pass filters that don't reduce the amplitude in the low frequency range.

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    $\begingroup$ What do you mean with preserve the amplitude and phase? If you want to satisfy this the only option would be a gain of one, since any low pass filter changes the amplitude of high frequency signals. $\endgroup$ – fibonatic Jan 23 at 20:51

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