levels
Summary
Levels is a multimedia project involving the measurement of
energy found in various physical phenomena such as sound and
electromagnetic radiation (radio waves, light, etc).
Its current manifestation is a
collection of octave files
or levels000.zip
Octave
To get a feel of
Octave's
syntax, take a look at
tonetest.m.
In octave, variables can be scalars, vectors or matrices. Audio
signals are typically stored as a vector (1 dimensional
arrays of numbers) whose elements can be accessed by a
vector index. In tonetest.m the variables n and index are vectors.
Frequency dependent energy is found in sound.
Using frequency selective filters, one may apply gain or reduction on
acoustic energy over a selected range of frequencies. In addition,
this gain may be varied over time based on the analysis of
the signal. By providing a time varying gain we may make
soft passages softer and louder passages louder.
Doing so lowers the perceived noise
floor and simultaneously provides a dynamic range that
exists in real life but is lost by recording equipment.
For example, if the audio signal has
a predominance of energy at lower frequencies (like an upright bass
produces), then we can apply a filter to isolate the low frequencies
and then apply a time varying gain to just the low frequencies
the result is a 'smooth and clean' sounding bass that
sits where it should in the mix.
Using the idea of frequency selective, time varying gain, we can
effect different portions of the audible frequency range
uniquely and increase the overall perceived level in a more
pleasing way. While beauty is in the eye of the beholder,
there are some fundamentals associated with applying
frequency selective, dynamic (time varying) gain during the
mastering phase of a recording:
 Frequency band filters should be linear phase
 Dynamic processing should not impart a new 'character' to the sound
References

RC circuit on wikipedia
 excellent discussion of frequency selective filtering
using a system with a single capacitor in series with a
resistor. The frequency response across the
capacitor is defined by a transfer function with a
single pole and the voltage across the resistor
is defined by a transfer function with a pole
and a zero.

Transfer function on wikipedia
"A transfer function is a mathematical representation, in terms of spatial
or temporal frequency, of the relation between the input and
output of a linear timeinvariant system with zero initial conditions
and zeropoint equilibrium."

Laplace transform on wikipedia
"transforms f(t) to a function F(s) with complex argument s.
The
Laplace transform has the useful property
that many relationships
and operations over the original f(t) correspond
to simpler
relationships and operations over its image F(s)."
Includes sophisticated discussion about the Fourier Transform (resolves
signals into frequencies) and its relationship to the Laplace Transform
(resolves signals into moments).

Moments on wikipedia
"In mathematics, a moment is, loosely speaking, a quantitative
measure of the shape of a set of points."

Digital filter on wikipedia (not bad)
"A digital filter is characterized by its transfer function, or
equivalently, its difference equation."

Difference equation (too mathy, but good)
"a recurrence relation is an equation that recursively defines a sequence,
once one or more initial terms are given: each further term of the
sequence is defined as a function of the preceding terms."

Ztransform on wikipedia
"The Ztransform converts a time domain signal, which is a sequence of
real or complex numbers, into a complex frequency domain representation.
It can be considered as a discretetime equivalent of the Laplace transform."
Includes
Ztransform's
relationship to the Laplace transform.
Todo