Multi-band noise reduction system and methodology for digital audio signals
The present invention relates to a multi-band noise reduction system for digital audio signals producing a noise reduced digital audio output signal from a digital audio signal. The digital audio signal comprises a target signal and a noise signal, i.e. a noisy digital audio signal. The multi-band noise reduction system operates on a plurality of sub-band signals derived from the digital audio signal and comprises a second or adaptive signal-to-noise ratio estimator which is configured for filtering a plurality of first signal-to-noise ratio estimates of the plurality of sub-band signals with respective time-varying low-pass filters to produce respective second signal-to-noise ratio estimates of the plurality of sub-band signals. A low-pass cut-off frequency of each of the time-varying low-pass filters is adaptable in accordance with a first signal-to-noise ratio estimate determined by a first signal-to-noise ratio estimator and/or the second signal-to-noise ratio estimate of the sub-band signal.
1. A multi-band noise reduction system for digital audio signals, comprising:
a signal input for receipt of a digital audio input signal comprising a target signal and a noise signal;
an analysis filter bank configured for dividing the digital audio input signal into a plurality of sub-band signals Y k (n);
a noise estimator configured for determining respective sub-band noise estimates {circumflex over (σ)} k 2 (n) of the plurality of sub-band signals Y k (n);
a first signal-to-noise ratio estimator configured for determining respective first signal-to-noise ratio estimates ξ k 0 (n) of the plurality of sub-band signals based on the respective sub-band noise estimation signals and the respective sub-band signals Y k (n);
a second signal-to-noise ratio estimator configured for filtering the plurality of first signal-to-noise ratio estimates ξ k 0 (n) of the plurality of sub-band signals Y k (n) with respective time-varying low-pass filters to produce respective second signal-to-noise ratio estimates ζ k (n) of the plurality of sub-band signals Y k (n) wherein a low-pass cut-off frequency of each of the time-varying low-pass filters is adaptable in accordance with the first signal-to-noise ratio estimate and/or the second signal-to-noise ratio estimate of the sub-band signal;
a gain calculator configured for applying respective time-varying gains G k (n) to the plurality of sub-band signals Y k (n) based on the respective second signal-to-noise ratio estimates ζ k (n) and respective sub-band gain laws to produce a plurality of noise compensated sub-band signals; and
a synthesis filter bank configured to combine the plurality of noise compensated sub-band signals into a noise reduced digital audio output signal at a signal output.
2. A multi-band noise reduction system according to claim 1 , wherein the second signal-to-noise ratio estimator is configured to, for each of the plurality of sub-band signals Y k (n), increase the low-pass cut-off frequency of the time-varying low-pass filter with increasing values of the first and/or second signal-to-noise ratio estimates of the sub-band signal.
3. A multi-band noise reduction system according to claim 1 , wherein each of the plurality of time-varying low-pass filters comprises an IIR filter structure wherein an input of the IIR filter structure is coupled to the first signal-to-noise ratio estimate and an output of the IIR filter structure produces the second signal-to-noise ratio estimate.
4. A multi-band noise reduction system according to claim 3 , wherein the IIR filter structure comprises:
a first input summing node configured for receipt of the first signal-to-noise ratio estimate;
an output node supplying the second signal-to-noise ratio estimate;
a unit delay function coupled to the output node and configured to supply a delayed second signal-to-noise ratio estimate to the first input summing node, the input summing node configured to combine an output signal of the first input summing node and the delayed second signal-to-noise ratio estimate to generate a first intermediate signal;
a multiplication function configured to multiply the first intermediate signal and a limited delayed second signal-to-noise ratio estimate to generate a second intermediate signal;
a first intermediate summing node configured to combine the second intermediate signal and the delayed second signal-to-noise ratio estimate;
a maximum operator configured for:
at a first input, receipt of the delayed second signal-to-noise ratio estimate and at a second input, receipt of the first signal to noise-ratio estimate or a look-ahead estimate of the first signal to noise-ratio estimate; and
generating a maximum signal-to-noise ratio estimate from the first and second inputs; and
a first feedback path configured to couple a first time-varying portion of the maximum signal-to-noise ratio estimate to the multiplication function by a time-varying transfer coefficient of a first monotonic function in accordance with the first signal-to-noise ratio estimate of the sub-band signal.
5. A multi-band noise reduction system according to claim 4 , wherein the IIR filter structure further comprises:
a second input summing node arranged in front of the first input summing node and configured for receipt of the first signal-to-noise ratio estimate and a second time-varying portion of the limited delayed second signal-to-noise ratio estimate; and
a second feedback path configured to couple the second time-varying portion of the limited delayed second signal-to-noise ratio estimate to the second input summing node by a second monotonic function in accordance with a time-varying transfer coefficient value derived from the first signal-to-noise ratio estimate of the sub-band signal.
6. A multi-band noise reduction system according to claim 1 , further comprising:
a monotonic compressive function C(x) arranged in front of the second signal-to-noise ratio estimator and configured for mapping a numerical range of each of the plurality of first signal-to-noise ratio estimates ξ k 0 (n) into a smaller output numerical range before application to the second signal-to-noise ratio estimator; and
a monotonic expansive function C −1 (x), possessing an inverse transfer characteristic of the monotonic compressive function, arranged after the second signal-to-noise ratio estimator and configured for mapping a numerical range of each of the plurality of second signal-to-noise ratio estimates ζ k (n) into a larger output numerical range before application to the gain calculator.
7. A multi-band noise reduction system according to claim 6 , wherein the monotonic compressive function C(x) comprises a logarithmic function.
8. A multi-band noise reduction system according to claim 6 , wherein the monotonic compressive function C(x) comprises a non-logarithmic function such as:
C ( x )=10 P ( x 1/P −1)/log 10,
where P>1 and is a positive real number.
9. A multi-band noise reduction system according to claim 1 , wherein the gain calculator is configured for computing the respective time-varying gains G k (n) of the plurality of sub-band signals Y k (n) according to:
G
k
(
n
)
=
max
(
G
min
′
ξ
k
(
n
)
ξ
k
(
n
)
+
1
)
;
wherein
G min is a predetermined minimum gain value between 0.01 and 0.2.
10. A method of reducing noise of a digital audio signal comprising a target signal and a noise signal, comprising steps of:
a) dividing or splitting the digital audio input signal into a plurality of sub-band signals Y k (n);
b) determining respective sub-band noise estimates {circumflex over (σ)} k 2 (n) of the plurality of sub-band signals Y k (n);
c) determining respective first signal-to-noise ratio estimates ξ k 0 (n) of the plurality of sub-band signals based on the respective sub-band noise estimation signals and the respective sub-band signals Y k (n);
d) filtering the plurality of first signal-to-noise ratio estimates ξ k 0 (n) of the plurality of sub-band signals Y k (n) with respective time-varying low-pass filters to produce respective second signal-to-noise ratio estimates ζ k (n) of the plurality of sub-band signals Y k (n) wherein a low-pass cut-off frequency of each of the time-varying filters is adapted in accordance with the first signal-to-noise ratio estimate of the sub-band signal;
e) applying respective time-varying gains G k (n) to the plurality of sub-band signals Y k (n) based on the respective second signal-to-noise ratio estimates ζ k (n) and respective sub-band gain laws to produce a plurality of noise compensated sub-band signals; and
f) combining the plurality of noise compensated sub-band signals into a noise reduced digital audio output signal at a signal output.
11. A method of reducing noise of a digital audio input signal according to claim 10 comprising further steps of:
before step d) mapping a numerical range of each of the plurality of first signal-to-noise ratio estimates ξ k 0 (n) into a smaller output numerical range in accordance with a monotonic compressive function; and
before step e) mapping a numerical range of each of the plurality of second signal-to-noise ratio estimates ζ k (n) into a larger output numerical range in accordance with a monotonic expansive function possessing an inverse transfer characteristic of the monotonic compressive function.
12. A processor-readable tangible non-transient medium storing a computer program for operating a programmable signal processor, the computer program comprising instructions for causing the programmable signal processor to execute each of the method steps a)-f) of claim 10 .