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A simple example of a Butterworth filter is the third-order low-pass design shown in the figure on the right, with = 4/3 F, = 1 Ω, = 3/2 H, and = 1/2 H. [3] Taking the impedance of the capacitors to be / and the impedance of the inductors to be , where = + is the complex frequency, the circuit equations yield the transfer function for this device:
Roll-off is also significant on audio loudspeaker crossover filters: here the need is not so much for a high roll-off but that the roll-offs of the high frequency and low-frequency sections are symmetrical and complementary. An interesting need for high roll-off arises in EEG machines. Here the filters mostly make do with a basic 20 dB/decade ...
The feedback gain at low frequencies and for large A OL is A FB ≈ 1 / β (look at the formula for the feedback gain at the beginning of this section for the case of large gain A OL), so an equivalent way to find f 0 dB is to look where the feedback gain intersects the open-loop gain. (Frequency f 0 dB is needed later to find the phase margin.)
The meanings of 'low' and 'high'—that is, the cutoff frequency—depend on the characteristics of the filter. The term "low-pass filter" merely refers to the shape of the filter's response; a high-pass filter could be built that cuts off at a lower frequency than any low-pass filter—it is their responses that set them apart.
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).
Main indicates that high-pass filters are commonly used for directional microphones which have a proximity effect—a low-frequency boost for very close sources. This low-frequency boost commonly causes problems up to 200 or 300 Hz, but Main notes that he has seen microphones that benefit from a 500 Hz high-pass filter setting on the console. [5]
The JND for tone is dependent on the tone's frequency content. Below 500 Hz, the JND is about 3 Hz for sine waves; above 1000 Hz, the JND for sine waves is about 0.6% (about 10 cents). [8] The JND is typically tested by playing two tones in quick succession with the listener asked if there was a difference in their pitches. [9]
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...