Audio Signals and Systems Noise Kevin D Donohue Electrical and Computer Engineering University of Kentucky 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 processed on a computerDSP ID: 390152
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Slide1
EE513Audio Signals and Systems
Noise
Kevin D. Donohue
Electrical and Computer Engineering
University of KentuckySlide2
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 processed on a computer/DSP
Digital Signal
Discrete-time Signal
Quantizer
Analog Signal
Coder
11 10 01 00Slide3
Quantization Error and Noise
Quantization has the same effects as adding noise to the signal as long as the rounding error is small compare to the original signal amplitude:
11 10 01 00
Analog
Discrete
Digital
Intervals between quantization levels are proportional to the resulting quantization noise since they limit the maximum rounding or truncation error.
For uniform quantization, the quantization level interval is the maximum signal range divided by the number of quantization intervals.Slide4
Quantization Noise
Original CD clip quantized at 16 bits (blue)
Quantized at 6 bits (red)
Quantized at 3 bits (black)Slide5
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 (SNR
q
) for a full scale range (FSR) sinusoid, quantized with
B bit words is approximately:Note this is the SNR for a signal amplitude at FSR, signals with smaller amplitudes. What would be the formula for a sinusoid with an X% FSR? Slide6
Homework 4.1
Derive a formula for SNRq similar to the one on last slide (in dB) for a sinusoid that is X% of the FSR in amplitude.Slide7
Noise generated from a source inside a room will undergo frequency dependent propagation, absorption and refection before reaching the sink. Thus, the room effectively filters the sound.
Sound impinging on surfaces in the room will be absorbed, reflected, or diffused.
Room Noise
Heat
Direct
Sound
Absorption
Direct
Sound
Reflection
Specular
Reflected
Sound
Direct
Sound
Diffusion
Diffuse
Scattered
Sound
TransmissionSlide8
Reflected and reverberant sounds become particularly bad distractions because they are highly correlated with the original sound source. The use of absorbers and diffusers 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
(t) denotes 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: Reflection Absorption EffectsSlide9
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)Slide10
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 reverberation in room acoustics.Slide11
For a space with many randomly distributed reflectors (typically large rooms) reverberation time (RT
60
) 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:
whereV is the volume of the room in cubic metersS
i is the surface area of the ith
surface in room (in square meters)ai is the absorption coefficient of ith surfacem is the absorption coefficient of air. Discuss: The relationship between absorption, volume, and RT.
Room Reverberation TimeSlide12
Room Response to White Noise Input
Data collected and spectrogram computed by H.L. Fournier
Note frequency dependence on of decay time.Slide13
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,[30 44 121]*1e-3,[.6 .8 .6]);
taxis = [0:length(yout1)-1]/fs;% Compute envelope of signalenv = abs(hilbert(yout1));figure(1)plot(taxis,20*log10(env+eps)) % Plot Power over timehold 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)plot(lags/fs,ac)xlabel('seconds')ylabel('AC coefficient')Slide14
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.Slide15
Efficiency
– Output power over Input power (including that of the power supply).
Distortion – Total harmonic distortion (THD). For a sinusoidal signal input, THD is the ratio of power at all harmonic frequencies P
i (excluding the fundamental P
1) to the power at the fundamental frequency. where P
T is total signal power Fidelity – Flatness of frequency response characterized by frequency range and transfer function variation in that range.
Amplifiers and DistortionSlide16
Given the transfer characteristic for a class B amplifier below, compute the THD for a 3 volt input sinusoid.
Example
V
in
V
out
0.6v
-0.6v
7v
3v
-7v
-3vSlide17
Class A
- Low distortion, bad efficiency. Output stage with single transistor requires DC biased output (10-20% efficiency).
Class B - Crossover distortion, good efficiency. Output stage has 2 transistors so bias current is zero (~80% efficient).
Class AB – Reduced crossover distortion, good efficiency. Output stage has 2 transistors with biasing to push signal out of crossover distortion range.
Class D – Moderate distortion, high efficiency, operates in switch mode. Good for battery driven applications.
Amplifier ClassesSlide18
Center Clip Distortion
f
o
= 200 Hz
THD = 4.13%
Harmonic Peak Heights
= [-8, -23, -29, -37, -47, -55, -47, -46, -49, -57];Slide19
Given the transfer characteristic for a class AB amplifier below, compute the THD for a 3 volt input sinusoid.
Example
V
in
V
out
7v
3v
-7v
-3v
1.75v
-1.75vSlide20
Clip/Overload Distortion
f
o
= 200 Hz
THD = 4.14%
Harmonic Peak Heights =
[-7, -21, -46, -37, -44, -49, -45, -72, -49, -55];