What is a Notch Filter?

 Notch Filter 被speex aec用作第一步处理

What is a Notch Filter? 

Problem:
What is a Notch Filter? 

Solution:
A Notch filter is a filter that passes all frequencies except those in a stop band centered on a center frequency. A closely related Knowledgebase item discusses the concept of the Q of a filter. This Knowledgebase item focuses on high Q notch filters - the type that eliminate a single frequency or narrow band of frequencies. A closely related type of filter - a band reject filter, is discussed in a separate knowledgebase item. The amplitude response of a notch filter is flat at all frequencies except for the stop band on either side of the the center frequency. The standard reference points for the roll-offs on each side of the stop band are the points where the amplitude has decreased by 3 dB, to 70.7% of its original amplitude. 

The -3 dB points and -20 dB points are determined by the size of the stop band in relation to the center frequency, in other words the Q of the filter. The Q knowledgebase item will have additional information, but it is hard to talk about the roll-off points of a notch filter without defining the Q, which is the center frequency divided by the bandwidth. In the case of the figure below:

• The -3 dB points are at about 1 kHz and 100 kHz for a Q of 0.1 and a center frequency of 10 kHz. At one tenth the bandwidth, approximately 600 Hz and 1.6 kHz, the amplitude is down 20 dB.
  
  
• The -3 dB points are at about 600 Hz and 1.6 kHz for a Q of 1 and a center frequency of 10 kHz. The -20 dB points, however, are not marked because they are so close to the center frequency.
  
  
• The response of the bandpass filter with a Q of ten is also shown. The -3 dB points, however, are not marked because they are so close to the center frequency - the same place as the -20 dB for a Q of 1.
  
  
• So - what is the ultimate limit? Does this mean that any Q is possible? Unfortunately, no. At very high Q values, the response of the circuit will begin to have overshoot and undershoot that will destroy the integrity of the notch. The frequency that was supposed to be rejected may actually be amplified.

The phase response of a notch filter shows the greatest rate of change at the center frequency. The rate of change becomes more rapid as the Q of the filter increases.

The group delay of a notch filter is greatest at the center frequency, and becomes longer as the Q of the filter increases.

A common misconception of notch filter design: Many people think that the higher the Q, the deeper the notch. This is not true. The depth of the notch depends on the matching of components. The Q affects only the location of the -3 dB points, the stop band bandwidth. If the diagram above showed Q values of 0.01 and 0.001, the - 3 dB points would move outward, and the diagram would show a characteristic -20 dB per decade slope until the vicinity of the center frequency. Near the center frequency, the response would curve downward to the center frequency. A first order band rejection frequency would be created, but the response would only be first order with a sharp notch at the center frequency. This is not very useful, the designer would be far better off designing a band reject filter.