Digital Sound & Music: Concepts, Applications, & Science, Chapter 5, last updated 6/25/2013
sound clip with a narrow dynamic range has a much smaller difference between the loud and
quiet parts. In this usage of the term dynamic range, we’re focusing on the dynamic range of a
particular occurrence of sound or music.
Figure 5.10 Music with a wide dynamic range
In another usage of
the term, the potential
dynamic range of a digital
recording refers to the
possible range of high and
low amplitude samples as a
function of the bit depth.
Choosing the bit depth for a
digital recording
automatically constrains the
dynamic range, a higher bit
depth allowing for a wider
dynamic range.
Consider how this
works. A digital recording
environment has a
maximum amplitude level
that it can record. On the
scale of n-bit samples, the
maximum amplitude (in
magnitude) would be .
The question is this: How far,
MATLAB Code for Figure 5.11 and Figure 5.12:
hold on;
f = 440;T = 1/f;
Bdepth = 3; bit depth
Drange = 2^(Bdepth-1); dynamic range
axis = [0 2*T -(Drange+1) Drange+1];
SRate = 44100; %sample rate
sample_x = (0:2*T*SRate)./SRate;
sample_y = Drange*sin(2*pi*f*sample_x);
q_y = round(sample_y); %quantization value
for i = 1:length(q_y)
if q_y(i) == Drange
q_y(i) = Drange-1;
for i = -Drange:Drange-1 %quantization level
y = num2str(i); fplot(y,axis,'k:')
legend('Sample wave','Quantization
wave','Quantization level')
y = '0'; fplot(y,axis,'k-')
ylabel('amplitude');xlabel('time in seconds');
hold off;
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