Audio compression - The MPEG - page 112

and there is no evidence of the envelope modulation. However, such a measurement requires an infinite time.
When a shorter time is available, the frequency discrimination of the transform falls and the bands in which energy
is detected become broader.
Figure 4.18: (a) Result of adding two sine waves of similar frequency. (b) Spectrum of (a) to infinite accuracy. (c)
With finite accuracy only a single frequency is distinguished whose amplitude changes with the envelope of (a)
giving rise to beats.
When the frequency discrimination is too wide to distinguish the two tones as in (c), the result is that they are
registered as a single tone. The amplitude of the single tone will change from one measurement to the next
because the envelope is being measured. The rate at which the envelope amplitude changes is called a beat
frequency which is not actually present in the input signal. Beats are an artifact of finite frequency resolution
transforms. The fact that the HAS produces beats from pairs of tones proves that it has finite resolution.
Measurement of when beats occur allows measurement of critical bandwidth. Figure 4.19 shows the results of
human perception of a two- tone signal as the frequency dF difference changes. When dF is zero, described
musically as unison , only a single note is heard. As dF increases, beats are heard, yet only a single note is
perceived. The limited frequency resolution of the basilar membrane has fused the two tones together. As dF
increases further, the sensation of beats ceases at 12-15 Hz and is replaced by a sensation of roughness or
dissonance . The roughness is due to parts of the basilar membrane being unable to decide the frequency at which
to vibrate. The regenerative effect may well become confused under such conditions. The roughness which
persists until dF has reached the critical bandwidth beyond which two separate tones will be heard because there
are now two discrete basilar resonances. In fact this is the definition of critical bandwidth.
Figure 4.19: Perception of two-tone signal as frequency difference changes.
4.10 Codec level calibration
Perceptive coding relies on the principle of auditory masking. Masking causes the ear/brain combination to be less
sensitive to sound at one frequency in the presence of another at a nearby frequency. If a first tone is present in the
input, then it will mask signals of lower level at nearby frequencies. The quantizing of the first tone and of further