In signal processing, a comb filter is a filter implemented by adding a delayed version of a signal to itself, causing constructive and destructive interference. The frequency response of a comb filter consists of a series of regularly spaced notches in between regularly spaced peaks (sometimes called teeth) giving the appearance of a comb. Applications Comb filters are employed in a variety of signal processing applications, including: Cascaded integrator–comb (CIC) filters, commonly used for anti-aliasing during interpolation and decimation operations that change the sample rate of a discrete-time system. 2D and 3D comb filters implemented in hardware (and occasionally software) in PAL and NTSC analog television decoders, reduce artifacts such as dot crawl. Audio signal processing, including delay, flanging, physical modelling synthesis and digital waveguide synthesis. If the delay is set to a few milliseconds, a comb filter can model the effect of acoustic standing waves in a cylindrical cavity or in a vibrating string. In astronomy the astro-comb promises to increase the precision of existing spectrographs by nearly a hundredfold. In acoustics, comb filtering can arise as an unwanted artifact. For instance, two loudspeakers playing the same signal at different distances from the listener, create a comb filtering effect on the audio. In any enclosed space, listeners hear a mixture of direct sound and reflected sound. The reflected sound takes a longer, delayed path compared to the direct sound, and a comb filter is created where the two mix at the listener. Implementation Comb filters exist in two forms, feedforward and feedback; which refer to the direction in which signals are delayed before they are added to the input. Comb filters may be implemented in discrete time or continuous time forms which are very similar. Feedforward form The general structure of a feedforward comb filter is described by the difference equation: where is the delay length (measured in samples), and is a scaling factor applied to the delayed signal. The transform of both sides of the equation yields: The transfer function is defined as: Frequency response The frequency response of a discrete-time system expressed in the -domain, is obtained by substitution . Therefore, for the feedforward comb filter: Using Euler's formula, the frequency response is also given by Often of interest is the magnitude response, which ignores phase. This is defined as: In the case of the feedforward comb filter, this is: The term is constant, whereas the term