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A comb filter is a multiplier-less filter, meaning it only uses additions when computing the impulse response. The comb filter is one of the two major building blocks in the cascaded integrator comb (CIC) filter.
This blog post will describe both the impulse response and frequency response of the comb filter and demonstrate how to analyze the comb filter in the frequency domain.
Related DSP blogs:
Comb Filter Time Domain
Comb Filter Frequency Domain
and combine like terms:
The transfer function H(z) is therefore
Substituting , the frequency response is therefore
The magnitude-squared of the the frequency response is therefore
Comb Filter Passband Analysis
The maximum values, or pass-bands, of the comb filter’s frequency response (7) occur when
Using an example to illustrate (8), a comb filter with a delay M=2 will have maxima when
therefore the maxima of the passband occur at
The values of in (13) are limited to
because it is a discrete-time filter and and correspond to the negative sampling frequency and positive sampling frequency in radians.
Comb Filter Stopband Analysis
The minimum values, or stop-bands, of the comb filter’s frequency response occur when
Using an example to illustrate (15), a comb filter with a delay M=2 will have minima when
therefore the minima of the passband occur at
Examples of Comb Filter Frequency Responses
Increasing the delay M results in more passbands and more stopbands. Figure 2 gives the magnitude of the frequency response for M=4.
Figure 3 gives the responses for three different comb filters: M=2, 3 and 4. Increasing the delay M results in more maxima and more minima, which appear as more teeth in the comb. Increasing the delay M also narrows the teeth of the comb.
The comb filter is multiplier-less filter, making it efficient to implement. The comb filter is also one half of the cascaded integrator comb (CIC) filter. The blog described both the impulse response and frequency response of the comb filter. Analysis was also performed on the passbands and stopbands of the frequency response.
Related DSP blogs:
- Minimizing Filter Length: Explaining Why
- FIR Low Pass Filter Design With Remez
- Single Pole IIR: Substitute for Moving Average Filter