# Low pass filter preserving amplitude

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.

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

• 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. – fibonatic Jan 23 '19 at 20:51