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Filters
Published in Afshin Samani, An Introduction to Signal Processing for Non-Engineers, 2019
The frequency response of a filter in practice can be divided into three segments, namely, a passband, a transition band and a stopband. The passband determines the interval across the frequency axis, where the filter allows the input signal within that range of the frequency passing through the filter. The magnitude of the frequency response is close to 1, considering a permissible range of oscillation around 1, which is known as the “ripples” in the passband. Conversely, the stopband is the opposite and determines the interval across the frequency axis where the filter does allow the input signal within that frequency range passing through the filter. The magnitude of the frequency response is close to zero, considering a permissible range of oscillation around zero, which is known as the ripples in the stopband. The transition band, as the name indicates, refers to the interval between the passband and the stopband. As opposed to the ideal response of a filter, the transition band cannot be squeezed into one single frequency point, and the difference between the edges of the passband and stopband is non-zero. The filter attenuation in the transition phase is between its attenuation in the passband and stopband, but it is still higher than the ripples in the passband and lower than the ripples in the stopband. Figure 8.2 shows a typical response of a low-pass filter in practice. The response of high-pass, band-pass and band-stop filters can be seen in Figure 8.2.
Continuous-Time Circuits
Published in Tertulien Ndjountche, CMOS Analog Integrated Circuits, 2017
Cauer filters: Their magnitude responses have equal ripples in both the passband and stopband. In comparison with other filter types, Cauer filters provide the sharpest transition band and are then the most efficient from the viewpoint of requiring the smallest order to realize a given magnitude specification. However, the sharp transition band is obtained at the price of a more nonlinear phase response in the passband, especially near the passband edge.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Transition band - The frequencies between a passband and stopband for which there are no filter specifications that must be met. Transition bands are necessary to allow for practical filter circuits, but it is desirable to keep transition bands as narrow as possible (i.e., a sharp transition band).
Search of Optimal s-to-z Mapping Function for IIR Filter Designing without Frequency Pre-warping
Published in IETE Journal of Research, 2021
Shalabh K. Mishra, Dharmendra K. Upadhyay, Maneesha Gupta
An existing fractional-order low pass filter is taken into consideration [28]. The transfer function of the considered fractional-order analog filter is given as In the considered example, and α = 0.9. The magnitude response of the considered fractional-order filter is given below in Figure 5. It is observed that the 3-dB bandwidth is 1.5 rad/s and 20-dB attenuation is at 3.5 rad/s. It is a general convention that pass band of any filter is considered up to 3-dB bandwidth, transition band is considered within the range of 3–20-dB attenuation and the magnitude response is ignored below the 20-dB attenuation. Therefore 20-dB attenuation frequency should be considered for computation of Nyquist sampling frequency in order to avoid aliasing.
Variant of the charged system search algorithm for the design of optimal linear phase finite impulse response filters
Published in Automatika, 2019
R. P. Meenaakshi Sundhari, S. N. Deepa
The first portion of Equation (5) pertains to a pass band with slice of transition band included and the last and second portions pertain to a stop band with the remaining slice of the transition band. The appropriate slice of the transition band is based on the edge frequencies of the pass band and stop band.