Comb filter

The comb filter effect, in audio technology, denotes an effect when two successive copies of a signal are summed up together at the receiver. This can be due to multiple sources at different distances (e.g. loudspeakers) emitting the same signal, multiple-spaced microphones recording the same sound source, or room reflections arriving at the microphone. Successive perfect reflections in an impulse response (e.g. two spikes in the RIR) corresponds to a repetition of the source signal. Since the delay between two successive reflections is often shorter than the source signal, overlapping occurs, which, in the case of pure sine signals yields a battery of constructive and destructive interference. All real wideband signals can be decomposed to a sum of sine signals (using Fourier-analysis), so wideband signals will consequently show a comb-filtered response. (The series of constructive and destructive interferences, if viewed as a plot of amplitude versus frequency, will visually appear as an ordinary "hair comb", hence the term, "Comb Filter", since the overall response shows periodic peaks and dips in a range of amplitude as a function of frequency response.)

<math>Y(j\omega)= A \cdot X(j\omega) \exp({-j\omega t_{0}}) [1 + B \cdot \exp({-j\omega \Delta t})]</math>

The peak frequencies occurs at a given <math>\Delta t</math> delay at: <math>f_{max}(n) = \frac{n}{\Delta t}</math> where <math>n</math> is an arbitrary natural number.