Butterworth filters are all-pole filters that generate a monotonic amplitude response with a maximally flat passband and a smooth but gradual transition-band rolloff of n*6 dB/octave, where n is the number of filter poles (or "order").  Butterworth filters have a nonlinear phase response and moderate ringing (~11% overshoot) in their step response. Butterworth filters are generally preferred in applications where amplitude preservation is important (e.g. spectral analysis).

Bessel filters are all-pole filters that generate a maximally linear phase response in the passband (~constant time delay).  Bessel filters have a monotonic amplitude response that is not maximally flat in the passband and rolls off more slowly than a Butterworth. These characteristics, along with the Bessel's sharp step response with minimal ringing, make it an appropriate choice for applications where waveform preservation and time-domain analyses are important.

PFI's custom Flat Mode filters are elliptic filters designed to improve on the most desirable characteristics of a Butterworth filter. The Flat Mode filter provides a flatter passband response and sharper transition-band rolloff than a Butterworth filter of the same order with only a negligible increase in phase nonlinearity. As with the Butterworth, the Flat Mode filter is preferred for applications requiring amplitude preservation and spectral analysis.

PFI's custom Pulse Mode filters are constant time delay filters designed to improve on the most desirable characteristics of a Bessel filter. Like the Bessel, the Pulse Mode filter has linear phase in the passband and minimal ringing in its step response, but provides a sharper transition-band rolloff than a Bessel of the same order with no deterioration in the passband response. As with the Bessel, the Pulse Mode filter is preferred for applications requiring waveform preservation and time-domain analyses.

The frequency response of a filter is defined by evaluating a filter's transfer function in the frequency domain, and thus relates filter output to input in terms of spectral amplitude and phase. The frequency defining the edge of a filter's passband - or that region of the frequency response where the input and output amplitude are equal - is known as the cutoff frequency (Fc), conventionally defined as the frequency at which the input is attenuated by 3 dB. The cutoff frequency is a key element of filter design: PFI provides filters with cutoff frequencies that are software programmable. The amplitude response, alias attenuation, phase response, phase distortion, phase delay, and group delay plots can all be displayed using either normalized frequency (i.e. frequency relative to the cutoff frequency) or an absolute frequency (Hz or kHz) set by the user.

The amplitude response represents the magnitude of the complex frequency response defined by the filter's transfer function. It is the ratio of input to output amplitude as a function of frequency and is shown in decibel (dB) units such that values > 0 represent a (+) gain and numbers less than zero represent (-) gain (commonly referred to as attenuation).

Aliases are apparent in-band spectral components in a sampled signal whose true (analog) frequency is higher. Aliases can therefore cause undetectable corruption to a sampled signal that cannot be corrected using digital techniques. Aliasing is a consequence of sampling: the choice of sample rate (Fs) determines the baseband for the sampled signal, which ranges from DC to Fs/2.  Spectral content above the baseband will alias back to the baseband if not attenuated by the low-pass filter.  For this reason, low-pass analog filters are often referred to as anti-alias filters.  PFI quantifies the anti-aliasing capability of a filter in terms of how much a principal alias - the lowest frequency outside the baseband that will alias into the sampled signal - is attenuated by the filter. It is a function of both the filter cutoff frequency (Fc) and sampling frequency (Fs). The alias attenuation plot allows the user to control the ratio of Fs to Fc to compare the anti-aliasing capability between filters.

The phase response represents the phase angle of the complex frequency response defined by the filter's transfer function. It equates to the phase shift of spectral components as a function of frequency.  The phase response can be used to evaluate how a filter will distort the input waveform (see "Phase Distortion" and "Group Delay"). 

Phase distortion is defined as the deviation of the phase response from a linear function of frequency. It provides a semi-quantitative measure of input-to-output wave shape modification, commonly referred to as phase nonlinearity (see also "Group Delay").

The phase delay is one of two time delays defined by the phase response. The phase delay converts a phase shift in angular units to a time delay for a given spectral component.

Group delay is one of two time delays defined by the phase response. The group delay quantifies the change of phase with frequency; non-constant group delay provides a measure of input-to-output wave shape modification (see also "Phase Distortion").

The step response is a measure of the filter's transient response: it shows the time-domain response of a filter to a unit step input (i.e. an instantaneous step from 0 to 1 amplitude at time zero). The step response is therefore plotted in time, either normalized by the cutoff frequency (time*Fc) or in absolute units (s or ms). The step response is used to determine how responsive a filter is to transient inputs.