Comb Filters (Digital Filter Design Toolkit)

Use the DFD IIR Notch Peak Design VI to design notch and peak filters that suppress noise or enhance a signal at one particular frequency. However, you might want to suppress noise or enhance a signal at more than one frequency. For example, you might need to cancel the AC powerline fundamental and harmonics. In that situation, you can use a comb notch/peak filter.

Comb filters also can separate two signals with different frequency harmonics. For example, in color TV systems, comb filters separate the luminance component and chrominance component from the composite video signal.

The following table lists each type of comb filter with its transfer function and magnitude response. Notice that you can create two types of comb notch/peak filters. One type has notches or peaks at the frequencies kf_s/N, while the other type has notches or peaks at the frequencies (k+1/2)f_s /N, where k is an integer in the range [0, N−1].

The following figure shows the implementation of a comb filter.

In this figure, you can see that the implementation of the comb filter requires only two adders and two multipliers, which makes the comb filter efficient in many applications.

The following figure shows a typical Type I comb notch filter in which the first notch occurs at f = 0, or equivalently, (|H(0)| = 0).

The following figure shows a typical Type II comb notch filter in which the first notch occurs at f = f ₀, or equivalently, (|H(0)| = 1).

The following figure shows a typical Type I comb peak filter in which the first peak occurs at f = 0, or equivalently, (|H(0)| = 1).

The following figure shows a typical Type II comb peak filter in which the first peak occurs at f = f ₀, or equivalently, (|H(0)| = 0).

From the previous figures, you can see that a comb filter is characterized by the parameters f ₀, A_b , and Δf. f ₀ denotes the center frequency of the notch or peak, A_b denotes a level on the magnitude squared response of the filter in decibels, and Δf denotes the frequency bandwidth at A_b . The default value of A_b is −3 dB, which represents the half maximum value of the magnitude squared response. Use the DFD IIR Comb Design VI to design a comb notch or peak filter. This VI enables you to design the comb notch or peak filter either by specifying the center frequency and the bandwidth of the notch/peak or by specifying the number of notches/peaks and the bandwidth.

For example, assume a time waveform of a noisy electrocardiogram (ECG) signal sampled at 480 Hz, as shown in the following figure:

The following figure shows the spectrum of the same noisy signal. In this figure, you can identify noise at 60 Hz, 120 Hz, and 180 Hz.

To remove the noise, you can use the By f0 and Bandwidth instance of the DFD IIR Comb Design VI to design a comb notch filter with the following specifications:

The following figure shows the magnitude response of the resulting comb filter.

The following figure shows that the filtered ECG signal is close to the original noise-free samples.