Filter specifications

• Cutoff frequency (w_p/2p)

o Upper passband frequency for low-pass filters

o Lower passband frequency for high-pass filters

o Determined by the -3dB point of a filter magnitude response relative to a peak passband value

• Centre frequency (w₀/2p)
  Frequency lying at the midpoint of a bandpass filter

• Bandwidth

o Frequency width of the passband of a filter

o For a low-pass filter the bandwidth is equal to the cutoff frequency

o For a band-pass filter

• Absolute bandwidth defined as the frequency difference
  between the upper and lower -3dB points
• Relative bandwidth defined as the ratio of the absolute bandwidth and
  centre frequency

• Quality factor Q

o For low-pass and high-pass filters with Q>3 can be graphically presented as
the distance between the 0-dB line and the peak point of the filter gain response

o For a band-pass filter is defined as the reciprocal value of the relative bandwidth

• Attenuation
  Amplitude loss (usually in dB) incurred by a signal after passing through a filter

• Phase response

o Difference in phase at a particular frequency, between an input sine wave
and the filter output sine wave at that frequency

o For an ideal filter the phase response is linear with the frequency

• Group delay

o Derivative of a filter phase with respect to frequency

o Can be thought as the propagation time delay of the envelope of an amplitude modulated signal
as it passes through a filter (also called envelope delay)

o For an ideal filter the group delay is constant

• Passband ripple (R_p)

o Fluctuations or variations in the frequency magnitude response within the passband of a filter

o Measured in dB

• Stopband attenuation (R_s)
  Difference between the peak passband amplitude and the largest stopband lobe amplitude

• Rolloff
  Steepness, or slope, of the filter response in the transition region from the passband to the stopband