1. EE599-2 Audio Signals and Systems
Noise
Kevin D. Donohue Electrical and Computer Engineering University of Kentucky

2. Quantization Noise
Signal amplitudes take on a continuum of values. A discrete signal must be digitized (mapped to a finite set of values) to be stored and process on a computer/DSP
Digital Signal
Discrete-time Signal
Quantizer
Analog Signal
Coder

3. Quantization Noise
Signal amplitudes take on a continuum of values. A discrete signal must be digitized (mapped to a finite set of values) to be stored and process on a computer/DSP
Digital Signal
Discrete-time Signal
Quantizer
Analog Signal
Coder

4. Quantization Error and Noise
Analog
Discrete
Digital
Quantization has the same effects as adding noise to the signal:
Intervals between quantization levels are proportional to the resulting quantization noise.
For uniform quantization, the interval between signal levels is the maximum signal amplitude value divided by the number of quantization intervals.

5. Quantization Noise Original CD clip quantized at 16 bits (blue)
and quantized at 6 bits (red)

6. Quantization Noise Analysis
Assume is a uniformly distributed (amplitude), white, stationary process that is uncorrelated with the signal
Show that the signal to quantization noise ratio for a full-swing range (FSR) sinusoid, quantized with B bit words is approximately:

7. Room Noise Absorption Reflection Diffusion
For noise generated inside a room will have a frequency dependent propagation, absorption and refection. Thus the room will have a filtering effect on the sound. Sound impinging on surfaces in the room will be absorbed, reflected, or diffused.
Absorption
Direct
Sound
Reflection
Specular Reflected
Diffusion
Heat
Transmission
Direct
Sound
Diffuse Scattered
Sound
Direct
Sound

8. Reflection Absorption Effects
Reflected and reverberant sounds can become distractions and annoyances. The use of absorbers on reflective surfaces can cut down the reverberation effects in rooms.
The model for a signal received at a point in space from many reflections is given as:
where n is scaling that represents the attenuation of each reflected signal due to propagation through the air and absorption at each reflected interface and n is the time delay associated with the travel path from the source to the receiver. The signal in the frequency domain is given by:

9. Reverberant Sound Travel
The near or direct field (D)
The free or early field (EF1 and EF2)
The reverberant or diffuse field (RF1 to RF3)

10. Decay of Reverberant Sound Field
The time it takes for the reverberant sound field to decay
by 60dB has become a standard way to characterize room acoustics.

11. Room Reverberation Time
For a space with many randomly distributed reflectors (typically large rooms) reverberation time (RT60 ) is defined as the amount of time for the sound pressure in a room to decrease by 60 dB from its maximum. The time is statistically predicted from the room features with the Sabine equation:
where
V is the volume of the room in cubic meters
Si is the surface area of the ith surface in room (in square meters)
ai is the absorption coefficient of ith surface
m is the absorption coefficient of air.
Discuss: The relationship between absorption, volume, and RT.

12. Room Response to White Noise Input
Data collected and spectrogram computed by H.L. Fournier Note frequency dependence on of decay time.

13. Example
Given the simulated reverb signal compute the RT60. Find the autocorrelation function and try to estimate the delays associated with the major scatterers.
% Create reverb signal
[y,fs] = wavread('clap.wav'); % Read in Clap sound
% Apply simulated reverb signal
yout1 = mrevera(y,fs,[ ]*1e-3,[ ]);
taxis = [0:length(yout1)-1]/fs;
% Compute envelope of signal
env = abs(hilbert(yout1));
figure(1)
plot(taxis,20*log10(env+eps)) % Plot Power over time
hold on
% Create Line at 60 dB below max point and look for intersection point
mp = max(20*log10(env+eps));
mp = mp(1);
dt = mp-60;
plot(taxis,dt*ones(size(taxis)),'r'); hold off; xlabel('Seconds')
ylabel('dB'); title('Envelope of Room Impulse Response')
% Compute autocorrelation function of envelop and look for peaks % to indicate delay of major echoes
maxlag = fix(fs*.5);
[ac, lags] = xcorr(env-mean(env), maxlag);
figure(2)
plot(lags/fs,ac)
xlabel('seconds')
ylabel('AC coefficient')
% Compute autocorrelation function of raw and look for peaks to
% indicate delay of major echoes
[ac, lags] = xcorr(yout1, maxlag);
figure(3)

14. Room Modes
The air in a (small) rectangular room has natural modes of vibration given by:
where c is the speed of sound in the room p, h, and r are integers 0,1,2, …., and L, W, and H are the length, width, and height of the room.