Audio Fidelity: Frequency Response

Not all frequencies are created equal.  And they're also not generally treated equally by a digital filter.  How inequally they're treated is one of the defining characteristics of a filter.  Audio engineers have a metric for describing this behavior.  The frequency response of a filter or system tells us the relative output signal given a known input signal at a given frequency.  Frequency response is different than our other metrics, in that a measurement is not simply a number.  It's a function of frequency, and the whole metric makes a curve and not just a number.

The term "frequency response" is not actually very well defined.  In technical terms, frequency response is a complex-valued function which is made of two measurements: phase shift, and magnitude.  You might also hear the terms phase response and magnitude response, corresponding to the two parts separately.  The human ear, however, cares far more about magnitude than it does about phase.  Since most people are only concerned with the real-valued magnitude of the graph, the terms "frequency response" and "magnitude response" are often used interchangably.  I will use the more precise term wherever applicable.

In an ideal audio system, the magnitude response is a constant unity value over all audible frequencies.  This means signal amplitude is independent of frequency, and all tones have the same output level as their input level.  This is important when playing back sounds, so that you don't change the characteristic of the sound.  Of course, the real world doesn't have ideal audio systems, so designers just do their best.

So what happens when somebody messes up their frequency response?  The most common problems are dropping high or low-end sounds, and overemphasizing certain bands, and none of them sound good.  Dropping out low sounds results in a signal with all middle and high frequencies, making sounds tinny, hollow, and jarring.  Dropping high sounds destroys the harmonics that give a sound its unique timbre.  Without the high frequencies, sounds are flat, lack characteristic, and are hard to tell apart.  Overemphasizing bands results in jarring volume differences between otherwise complementary tones and destroys chords as one note overpowers the others.  If a person's speech is played with overemphasized bands, meaning is also lost because the voice inflection becomes all wrong.

But don't take my word for it.  You can try it yourself with home stereo equipment that has a graphic equalizer.  A graphic equalizer is nothing more than an audio filter with a variable magnitude response.  Moving the sliders up and down changes the shape of the magnitude response curve, and you can hear these effects for yourself.  In fact, graphic equalizers were originally created as a way to correct ("equalize") audio equipment with bad magnitude response.

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