Noise Reduction Filter

The Problem

Fighting noise is a very old problem because noise cannot be eliminated. All electronic devices, resistors and other passive components generate noise. In audio systems all these can be kept below the audible level but ambient noise may not be avoided even if the audio system is designed according to the best practices. In these cases some noise reduction technique can help. Here we discuss two types of noise reduction techniques:

  • Noise reduction filtering (NRF) is a “blind” method. A signal processing method is called “blind” if the statistical properties of the involved signals are known but the actual values of them are unknown.
  • Noise cancellation (NC) is a reference based method. In this case we have access to the noise source but its actual effect on the signal is unknown.

These two approaches work in different manners and incur significantly different costs. NRF is essentially “free” in that it is an integral part of the signal processing chain on every input channel. NC, on the other hand, is a significantly more complex method that requires additional signal processing resources to implement, therefore, it is much more expensive than NRF. See Table 1 for a more detailed comparison of the two techniques.

Since ASPEN processors apply settings immediately, the amount of NRF applied to any one or more inputs can be adjusted in real time as the system is operating by a control device connected via ethernet, USB or RS-232 ports, using macros, or directly adjusted using the command terminal interface included in the ASPEN software.

Noise Reduction Filtering

The theoretical background of this method is optimal or Wiener filtering after Norbert Wiener who researched this area in the 1940’s and published his results in 1949.[1]
The signal model of optimal filtering is shown in figure 1.



The signal of interest (X) is contaminated by an additive noise (V). In order to improve the signal integrity, the observed noisy signal (Y) is passed through a filter. The output of the filter (Z) is an estimate of the unknown signal (X). The estimation error, the difference of X and Z, has the lowest possible power if the frequency response of the filter (H) is given by:


In ASPEN we use a 30-band 1/3-octave filter bank to implement the noise reduction filter. Figures 2 and 3 on the next page show an example in which the noise (cyan) has equal power in every band, i.e. it is a pink noise and the signal (blue) concentrates its power in the mid-audio range. Figure 2a and 2b show the signal and noise before and after the filtering, respectively. Figures 2 and 3 differ in that in figure 2 the signal is plotted on the top of the noise and in figure 3 the noise is on the top.

We can clearly see the benefit of the filtering. The attenuation is negligible in those bands where the signal has much more power than the noise, i.e. the signal-to-noise ratio is high; and the attenuation is high in the bands with poor signal-to-noise ratio. The result is an improved overall signal-to-noise ratio at the cost of some linear distortion of the signal.


There are two reasons why the Wiener filter cannot be used in its original form as a noise reduction filter in audio systems:

  • The signal and noise spectra are unknown therefore the equation for the frequency response of the optimal filter cannot be evaluated.
  • We may assume the noise spectrum to be quasi stationary (changing slowly), but the audio signals (such voice signals) are highly time variant.

To implement a noise reduction filter we made some assumptions and complemented the Wiener filtering algorithm with an adaptation method that automatically separates the signal and noise spectra and continuously changes the filter  parameters (see figure 4). Proper operation of the noise reduction filters in ASPEN requires that:

  • The noise be quasi stationary but its spectral distribution can be arbitrary.
  • The audio signal changes its spectral distribution rapidly. Stationary components will be misidentified as noise hence they will greatly be attenuated.


Main features of the NRF in ASPEN:

  • Every audio channel has an NRF so it scales with the size of the system.
  • The depth of the noise reduction is adjustable in a wide range: 6 dB - 36 dB.
  • 30 frequency bands all have 1/3-octave bandwidth.
  • Zero latency, minimum phase.
  • Optimal (Wiener) filtering algorithm.
  • Fast adaptation.

Follow these simple rules to use the NRF:

  • Enable the NRF only if it is necessary (the noise is distracting).
  • Enable the NRF only for the noisiest microphones.
  • Use the minimum noise reduction depth that effectively attenuates the noise. This may greatly vary depending on the characteristics of the noise and the acoustical properties of the environment as well as on personal preference.

Noise Cancellation

Noise cancelers (NC) use an adaptive filter to reconstruct the noise that effects the original signal. In this case a reference signal is needed which usually is a microphone placed close to the noise source. In this case an adaptive filter is necessary because the relationship between the noise source and the actual noise that contaminates the audio signal is unknown. 

Note the difference between NRF and NC. While the NRF is placed directly in the signal path, the NC predicts contamination and subtracts it from the observed signal. Therefore the signal is unaltered resulting in a higher sound quality. The computation burden of NC is comparable to an acoustic echo canceler which usually requires a dedicated DSP for every one, or at least every two, audio channels.


Table 1. Comparison of FRF and NC