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Digital Filters
Published in Samir I. Abood, Digital Signal Processing, 2020
A filter specification is usually based on the desired magnitude response. For example, the specification for a low-pass filter illustrated in Figure 13.8. The pass-band is defined as the frequency range over which the input signal is passed with approximate unit gain. Thus, the pass-band is defined by 0 ≤ ω ≤ ω1, where wp is called the pass-band-cut-off (edge) frequency. The width of the pass-band is usually called the bandwidth of the filter. For a low-pass filter, the bandwidth is ω1. The input-signal components that lie within the stop-band are attenuated to a level that effectively eliminates them from the output signal. The stop-band is defined by ω1 ≤ ω ≤ ω2 ≤ π, where ω2 is called the stop-band-edge frequency. The transition band is defined as ω1 < ω < ω2, which is between the pass-band and the stop-band. In this region, the filter magnitude response is typically, A1=20Log101+δ1db
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.
Signal Processing
Published in Stephen Horan, Introduction to PCM Telemetering Systems, 2018
Each filter type has several features of interest, as illustrated for the low pass filter shown in Figure 5.14. The pass band is that region in the frequency domain that is to be passed without attenuation by the filter. If the attenuation is less than 3 dB, then the filter is considered to be passing the signal without attenuation. The cutoff frequency defines the edge of the pass band; that is, all frequencies lower than the cutoff are passed unattenuated while those above it suffer some form of attenuation. The stop band is that region in the frequency domain where the filter attenuates any signal to the point where it is no longer important; that is, the attenuation is at least the minimal stop band attenuation for all frequencies. The transition region is that frequency region between the end of the pass band and the beginning of the stop band. The filter roll off specifies how quickly the filter transitions between the pass band and the stop band. Filter designs usually include specifications for these regions.
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.