Loudness Example

Many high-end audio systems offer digital signal processing (DSP). A computer is used to process the audio signal in various ways, for example to add reverberation (an elaborate form of echo) or to perform frequency selective filtering.

A particularly simple function that might be performed is loudness compensation. At low volumes, the human ear is less sensitive to low frequencies (base notes) than to high frequencies. Loudness compensation boosts the low frequencies. This is done simply by implementing a filter, as described in chapter 9. Thus, there are two modes, one where the low frequencies are boosted, and one where they are not.

A simple realization of loudness compensation offers a switch on a control panel to turn on and off the compensation. This can be modeled as follows:

The hybrid system reacts to input events from this switch to select from among two modes. The upper input is simply an event indicating the position of the control switch when it is thrown. The lower input x is a discrete-time signal, probably sampled at 44.1 kHz, the CD rate. The LoudnessCompensation hybrid system has two modes. In the flat mode, the output y is simply set equal to the input x. That is, if T_flat ⊂ Integers is the time indexes during which the machine is in the flat mode, then

∀ n ∈ T_flat, y(n) = x(n).

If T_boost ⊂ Integers is the time indexes during which the machine is in the boost mode, then

∀ n ∈ T_boost, y(n) = ((H(x))(n).

Hybrid Sys.

Loudness Example