# All About Audio Equalization: Solutions and Frontiers
## 6 Sound Reproduction Applications
### Loudspeaker Equalization  
One common use of digital equalizers in audio is the flattening of the magnitude response of loudspeakers [135; 136; 137; 138; 139]. In addition to hi-fi and studio loudspeakers, there are several special categories, such as flat panel speakers [140; 141; 142; 143; 144], PA (public address) systems [145; 146; 147], and micro speakers of mobile devices [148], which benefit from equalization. The response of the speaker is first measured, usually with the sine-sweep method, in an anechoic room or another special space in which the room effect can be deduced from the impulse response. Unless the loudspeaker under study is a monitor speaker, which is usually aimed directly at the listener, it may be of interest to average the response from a few angles in the frontal sector [149]. The measured magnitude response is usually smoothed using 1/3-octave averaging, which approximately imitates the resolution of human hearing [150]. This implies that very narrow peaks or valleys may not need to be corrected. It is also known that a local peak in the speaker's magnitude response is more noticeable than a notch [151], and this may be accounted for in the processing of the response. Loudspeaker response equalization always requires a _target response_ against which the measured and smoothed speaker response is compared [108; 138]. The target response generally cannot be constant across all frequencies. Loudspeakers are inherently highpass systems, having a low-frequency crossover point below which they cannot produce sound effectively. An attempt to boost the response beyond this point leads to increased distortion and may even destroy the speaker, if its cone is forced to exceed the maximum deviation. One easy way to obtain a target curve at low frequencies is to use the magnitude response of a Butterworth highpass filter, which is smooth and does not overshoot. A reasonable crossover frequency, in the range 30 to 100 Hz, should be selected, which is near the natural low-frequency point of the speaker. A second order Butterworth highpass filter having an approximately 12-dB per octave slope is suitable for producing the target response for regular dynamic loudspeakers, while a fourth order highpass filter with a 24-dB/oct. slope should be used for vented (bass reflex) speakers. The ratio of the measured and target responses, or the difference between the dB magnitude responses, yields the necessary correction as a function of frequency. Matched filter design methods discussed in Section 5.1 and the high-precision graphic equalizer of Section 4.3 are good candidate methods for designing the equalizer. Usually loudspeakers divide the audio band for two or three speaker elements, because a single element cannot reproduce the whole audio band with good quality [78]. The input signal is delivered to each element via a crossover network, which implements a selective filter (lowpass, bandpass, or highpass) for each element[PERSON] The most common crossover filter design is the Linkwitz-Riley network [78; 152][PERSON] Each element can be equalized separately after the crossover filtering [78; 136; 149]. One possibility is to combine the equalizers and the crossover filters, as suggested by [PERSON] and [PERSON] [153][PERSON]  
Various equalization filters and design methods have been proposed for loudspeaker equalization, including automatic adjustment of parametric equalizers [154; 155]. [PERSON] _et al._ first suggested the use of warped FIR and IIR filters for loudspeaker equalization to ease the approximation at low frequencies [138; 156]. Warped filters then became a popular method for equalizing loudspeakers [138; 157; 158; 159]. [PERSON] _et al._ have proposed to use a cascade connection of a regular and a warped FIR filter [160]. The balanced model truncation method is applied in [161]. In addition to magnitude-only equalization, also phase equalization of loudspeakers is sometimes considered, especially at low frequencies [138; 162].