# low pass filter with minimal ringing

I am trying to filter out some square wave signal to within a limited band (1/4 or 1/8 of the original), I realized that there's a lot of ringing in the wave when I use my filter (elliptical), I also tried Butterworth, and others (given in Matlab fir1, and classic iir filters) but the only filter that seems to give no ringing is Gaussian. So my question is, how should I go about designing a LPF with minimal ringing? (preferred characteristics: minimal pass band ripple, stop band of more than -50dB, relatively fast roll off). Also as I am trying to implement this in a DSP, low order filters such as IIR types are preferred.

Thank you for any help.

• if the poles are real, not complex-conjugate, then the impulse response (and step response) does not ring. this means, for a biquad IIR, that the Q must be no greater than 1/2. but you won't get the roll-off you want with low Q, i'm afraid. whether it's IIR or FIR, a sharp transition means ringing at the frequency of approximately that of the sharp transition. Apr 28, 2015 at 19:33
• @Robert Are there any optimal IIR filters where we can optimize for Order, Transition band, PB & SB ripples like Parks-McClellan for FIR filters? Apr 28, 2015 at 22:33
• oh i dunno. i thought Prony was a method to design the impulse response of an IIR to be what you want. as far as frequency-domain design with brick-walls and the transition band and PB and SB, i guess you might want to look into Elliptical filters. they be pretty ugly in the time-domain (like horribly non-constant group delay). oh, and there is Greg Berchin's FDLS for frequency-domain design. Apr 28, 2015 at 22:39
• ringing need not happen at high frequencies. unless you're using Planck units (or some other natural system of units), frequency is relative anyway. ringing is caused by an imaginary component in your poles. with real coefficients and real signal values in your filter, poles and zeros are either purely real or the come in complex-conjugate pairs. if the latter, your impulse response will have an exponentially-damped sinusoid in it. having as rapid step response as possible without ringing usually has real poles coincident on top of each other. Apr 29, 2015 at 23:26
• well, if your FIR is long enough, you can make your FIR $h[n]$ be whatever you want, including something that rings (as long as the FIR is, note the "F"). with an IIR, it theoretically rings forever (if the poles are complex-conjugate) hence the "I" in IIR. May 1, 2015 at 18:38

Generally the amount of ringing that you get is a function of the steepness of the filter in the frequency domain, regardless of filter type. At the same steepness an Elliptic will require a lower order but will have pretty much the same ringing as a Butterworth.

Choosing between a linear phase or minimum phase will change the character but not the extent of the ringing.

No matter how you slice it, a square wave contains a lot of high frequencies and once you filter those out, it's not a square wave any more.

• Thanks for the answer, I was wondering based on the characteristics of different phases, is it possible to find a filter which has the preferred roll off, stop band, and pass band with minimal peaks in the ringing? I would rather the ringing last longer but the amplitude of the ringing is smaller Apr 29, 2015 at 14:37