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The frequency response plot from Butterworth's 1930 paper. The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter.
Chebyshev filter, has the best approximation to the ideal response of any filter for a specified order and ripple. Butterworth filter, has a maximally flat frequency response. Bessel filter, has a maximally flat phase delay. Elliptic filter, has the steepest cutoff of any filter for a specified order and ripple.
The frequency response is characterized by the magnitude, typically in decibels (dB) or as a generic amplitude of the dependent variable, and the phase, in radians or degrees, measured against frequency, in radian/s, Hertz (Hz) or as a fraction of the sampling frequency.
The frequency response is below, showing a Chebyshev 1dB equi-ripple pass band response for < <, cutoff attenuation of -1dB at the pass band edges, -60dB / decade attenuation toward =, -20dB / decade attenuation toward =, and Chebyshev style steepened slopes near the pass band edges.
The response value of the Gaussian filter at this cut-off frequency equals exp(−0.5) ≈ 0.607. However, it is more common to define the cut-off frequency as the half power point: where the filter response is reduced to 0.5 (−3 dB) in the power spectrum, or 1/ √ 2 ≈ 0.707 in the amplitude spectrum (see e.g. Butterworth filter ).
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A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design.
In electrical engineering and control theory, a Bode plot / ˈ b oʊ d i / is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift.
Compared with other smoothing filters, e.g. convolution with a Gaussian or multi-pass moving-average filtering, Savitzky–Golay filters have an initially flatter response and sharper cutoff in the frequency domain, especially for high orders of the fit polynomial (see frequency characteristics).
A band-pass filter or bandpass filter ( BPF) is a device that passes frequencies within a certain range and rejects ( attenuates) frequencies outside that range. It's the opposite of a band-stop filter .
The 3 dB bandwidth of an electronic filter or communication channel is the part of the system's frequency response that lies within 3 dB of the response at its peak, which, in the passband filter case, is typically at or near its center frequency, and in the low-pass filter is at or near its cutoff frequency.