Equalizers and Filters

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We have seen how all the frequencies audible by the human ear are within the 20 Hz - 20 KHz interval. When an electric signal representing an acoustic wave enters a circuit (for example the signal that comes from a microphone placed next to a sound source), it gets manipulated and its frequency content gets modified. To have a clear picture of this, we have to consider the signals'representations both in time and in frequency [Time-Frequency representation ] . Let's consider a signal x(t) entering the electrical circuit and the signal y(t) exiting the circuit. Every instant in time, the circuit acts on the entering signal according to a behavioural pattern which is typical of the circuit in question and which is described by a time function which we will call h(t).

Now that we have our three functions x(t), y(t) and h(t), let's consider their equivalent versions in the frequency domain X(f), Y(f), H(f). In the frequency domain the following equation applies:

Equation 5.1. Transfer function of a circuit 

Transfer function of a circuit

This formula allows us to get a better picture of how filter and equalizer circuits act on the signal. We indentify H(f) as the transfer function, whilst we will call h(t) impulse response.

Note: it is important to highlight that the previous formula doesn't pertain to the time-domain, where in fact a different kind of mathematical relation between the functions x(t), y(t) and h(t) takes place which is a lot more complicated and which (luckily) we won't need in order to continue our dissertations.

In the following diagram we summarize what we have just exposed:

Equalizers and filters - Signal passing through a circuit

Signal passing through a circuit