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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.
Hann function (left), and its frequency response (right) The Hann function is named after the Austrian meteorologist Julius von Hann. It is a window function used to perform Hann smoothing. The function, with length and amplitude /, is given by:
The frequency response plot from Butterworth's 1930 paper. [1] 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.
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design .
The gain (or amplitude) response, (), as a function of angular frequency of the th-order low-pass filter is equal to the absolute value of the transfer function evaluated at =: G n ( ω ) = | H n ( j ω ) | = 1 1 + ε 2 T n 2 ( ω / ω 0 ) {\displaystyle G_{n}(\omega )=\left|H_{n}(j\omega )\right|={\frac {1}{\sqrt {1+\varepsilon ^{2}T_{n}^{2 ...
The frequency response can be classified into a number of different bandforms describing which frequency bands the filter passes (the passband) and which it rejects (the stopband): Low-pass filter – low frequencies are passed, high frequencies are attenuated.
The effective frequency response is the continuous Fourier transform of the impulse response. H Z O H ( f ) = F { h Z O H ( t ) } = 1 − e − i 2 π f T i 2 π f T = e − i π f T s i n c ( f T ) {\displaystyle H_{\mathrm {ZOH} }(f)={\mathcal {F}}\{h_{\mathrm {ZOH} }(t)\}={\frac {1-e^{-i2\pi fT}}{i2\pi fT}}=e^{-i\pi fT}\mathrm {sinc} (fT)}
If is measured in samples, the cut-off frequency (in physical units) can be calculated with = where is the sample rate. The response value of the Gaussian filter at this cut-off frequency equals exp(−0.5) ≈ 0.607.
In an electrical network, ω is a natural angular frequency of a response function f(t) if the Laplace transform F(s) of f(t) includes the term Ke −st, where s = σ + ωi for a real σ, and K ≠ 0 is a constant. Natural frequencies depend on network topology and element values but not their input.
The essential bandwidth is defined as the portion of a signal spectrum in the frequency domain which contains most of the energy of the signal. x dB bandwidth The magnitude response of a band-pass filter illustrating the concept of −3 dB bandwidth at a gain of approximately 0.707