Comb filter
A comb filter (English comb filter) is a filter which filters a certain frequency groups of signals. In contrast to low - and high-pass filter, it is characterized by several frequencies in the same frequency interval. The amplitude response ( level of the frequency) of the frequency response of the comb filter has a comb-like appearance, where the comb filter gets its name.
A comb filter response can be detected at a shown in the frequency domain signal ( amplitude response ) is always clearly at its zeros, but which is not necessarily about the audibility of the most undesirable effect says when he is in the listening area.
Comb filter in audio engineering
Is a signal with a time-delayed copy of the same " mixed " ( additively superimposed), results in a comb filtered signal. At frequencies whose period or multiples thereof corresponds to the delay time, you get twice the signal amplitude ( constructive interference ), while the exact intermediate frequencies wipe out (destructive interference). With a lower amount of delayed signal of the comb filter effect is correspondingly lower - the differences between maxima and minima in the amplitude response are less pronounced.
In practice, the sound, for example, often occur unintentionally overlays with delayed signals - and thus the comb filter effect: When the microphone recording appearing in the room reflections can be eye-catching with a delay 2-15 ms, cause unpleasant disruptive coloration. One should speak of " audible" comb filter effect, because only that is disturbing. There are mostly ground reflections or wall reflections. By superposition of direct sound and reflection occur, as indicated above, in the frequency response of the regular spaces, and extinction of the gain. ( The principle is, moreover, a cause of loss in multipath propagation of radio waves. ) The uniformly alternating minima and maxima with a few dB difference are similar to the construction of a harmonious sound. Our ears have adjusted the ' natural listening ' to the comb filter and the brain - hearing appears this effect largely of. Comb filter electrically generated conspicuous act of disturbing.
Musical Instruments hear with added strong reflections often " topfig " to (high frequency components are missing, dull sound ). Particularly disturbing is the audible tone color, moves the sound source, with the pitch character such as "u - u -i " or "i- u -u" changes. This effect is also electronically generated with phasing or flanging, which is often used in popular music for special effects. The coloration is particularly disturbing in language when reading, for example, on a reflective tabletop.
The use of spot microphones may result in recording music to this comb filter is discolored, if a sound source with two microphones is taken and one is closer than the other set. Even when mixing of sound effects with the dry original signal in the mixer can be caused by a signal delay in the effect unit this comb filter effects.
In order to reduce the audible comb filter effect in the sound recording with multiple microphones supporting mixed together see the three-to -one rule.
A comb filter in the optical system
Depending on the design of specific wavelengths and their multiples are especially amplified because there is a standing wave between the mirrors only certain wavelengths in an optical resonator. For the possible light wavelengths λ in a laser resonator, the relationship applies:
Where N is a natural number and L is the cavity length ( distance between the resonator mirrors ). As a result, a laser always generates a plurality of wavelengths, if no countermeasures are taken. This effect is essential for the function of a frequency comb.
Comb filter in television technology
In the television industry for a softer and clearer image is generated with the comb filter. This involves the separation of color signal and Schwarz-/Weiß-Bild in composite signals in which these two parts are mixed together; a comb filter, the fact that Schwarz-/Weiß-Informationen be repeated with the line frequency advantage, and thus reduce the disturbing dot crawl. Comb filters are used primarily in high-quality receivers, can be found in most inexpensive televisions simple low-pass filter.
A comb filter in the signal processing
Comb filters can be implemented both as a continuous-time filters and discrete-time filter. In an analogous technique, the temporal offset is provided by a delay line. In the following, only time-discrete comb filter variable order to be viewed without feedback as they see others in the field of digital signal processing application.
A digital comb filter without feedback, as shown in the illustration in the structure has, as impulse response the following function:
Where y [n] is the output sequence x [ n] is the input sequence of the measured values which are sampled and stored at regular intervals. The delay time is described by the filter order K, α is a scaling factor which, with values between -1 and 1, which is set in the simplest case, equal to 1 and sets the " waviness" of the magnitude frequency response.
The Z-transform, the discrete impulse response can be transformed into the spectral range for Y (z )
In order to obtain the transfer function H (z):
By z = ejΩ, wherein Ω is the frequency related to the sampling frequency, the frequency response of this comb filter is given by:
The magnitude frequency response formed therefrom
Is shown in the second image, with different values of α. It can be seen that, when α = 1, the ripple is maximum.
The pole-zero distribution in the complex plane shows in the illustration for a comb filter 8th order (K = 8) and α = 0.5, an eight- fold pole at the origin and 8 zeros near the unit circle. When α = 1, the zeros lie on the unit circle. The uniform location of the zeros on the unit circle at α = 1 is a characteristic comb-like transfer function results in the filters that gives its name.