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Digital Filters
Published in Samir I. Abood, Digital Signal Processing, 2020
FIR-filter characteristics were introduced in this chapter and briefly compared with IIR filters. In general, IIR filters have the following features: Nonlinear phase: IIR filters have a nonlinear-phase response over the frequency of interest. Therefore, group delay varies at different frequencies and results in phase distortion.Stability issue: IIR filters are not always stable due to their recursive realization. Therefore, a careful d sign approach is needed to ensure that all of the poles of an IIR filter lie inside the unit circle to guarantee a stable filter, especially for fixed-point implementations as well as the inputs. Due to the nature of output feedback, there is an inherent one sample delay in the feedback section. The IIR filter performs two inner (or dot) products of vectors, one is for the feedforward section between vectors b and x, and the other for the feedback section between vectors a and y. The design of the IIR filter determines two sets of coefficients, {bj, i = 0,1, … , L – 1} and {am, m = 1,2, … , M – I}, to meet a given specification. Also, the IIR filter is recursive in computation, which results in an infinite-impulse-response. Therefore, the IIR filter must be designed with special care to prevent any growing or oscillation of the impulse response that can lead to an unstable filter.
Cable Transmission Mediums
Published in Mário Marques da Silva, Cable and Wireless Networks, 2018
As previously described, the maximum bandwidth supported by a cable transmission medium depends on the link distance. Shorter distances allow accommodating higher bandwidths, and vice versa. This results from the fact that different frequencies present different attenuation coefficients and different delays, whose effect is more visible at longer distances. In fact, the attenuation of a twisted pair increases approximately exponentially with the increase of the frequency. The effect that results from this impairment is known as distortion (attenuation and/or phase distortion) and, in the case of digital communications, results in intersymbol interference. Improved twisted pair quality results in longer distances for the same bandwidth, or higher bandwidth for the same distances, as compared to lower quality twisted pair. As a rule of thumb, for digital signals, there is a need to use regenerators at a distance interval of 2–3 km of twisted pair cable.
Dynamic Characteristics of Instruments
Published in Francis S. Tse, Ivan E. Morse, Measurement and Instrumentation in Engineering, 2018
An amplitude distortion is a distortion of the output waveform due to changes in the sensitivity K for different harmonic components. A phase distortion is the distortion of the output waveform due to phase angles introduced at the output. Assume that an input x = x1 + x2, shown in Fig. 4-14a, has two harmonic components x1 and x2. There is no phase distortion if the components in the output y = y1 + y2 lags the input by the same amount of time, as shown in Fig. 4-14b. A phase distortion occurs if the time lag between y1 and x1 is different from that between y2 and x2, as shown in Fig. 4-14c. Note that the same time lag does not imply the same phase angle for the components. If ω2 = 2ω1, a phase angle of π radians for y1 corresponds to 2π radians for y2, as shown in Fig. 4-14d.
Measurement, Analysis, and Understanding of the Error Vector Magnitude (EVM) of Navigation Signals
Published in IETE Journal of Research, 2018
Md. Tosicul Wara, Raghavendra M. R., Kodandaram M., Bhuvaneshwari M. S.
In the test setup, usually, the coaxial RF cable is used in the downlink path to feed the navigation signal to the VSA input. The coaxial RF cable being the wide band element will have the linear phase response. This means the absolute delay or the total group delay of the cable is constant over its entire frequency band. As a result, when a composite signal passes through such cable all the frequency components will appear at the cable end simultaneously. As a result, the phase of the composite signal will remain unchanged (no phase distortion). If the cable length increases, the operating band width of the cable will decrease and consequently the non-linearity in its phase response will increase. Therefore, when the vector signal passes through lengthy cables, this nonlinear phase response of the cable will cause the phase imbalance to the vector signal. Consequently, the EVM value of vector signal will depend on the length of the downlink cable also. However, for most of the coaxial RF cables used in the test setup, the operating frequency range is quite large (typically, DC to 18 GHz). Hence, the effect of phase non-linearity (due to the increased length of the cable) may be prominent towards the band edge of the cable but its effect at L5 band (1–2 GHz) and S band (2–3 GHz) will be negligibly small. Consequently, the EVM values of the navigational signals (at L5 band and S band) will remain practically unchanged with the length of the downlink cable between the satellite and the VSA input. This has been proved by measuring the EVM values of the navigation signals of the IRNSS-1D satellite. These results [13] are shown in Table 6.
Interdigital Capacitor Based Compact Microstrip Bandpass Filter with Wide Stopband
Published in IETE Journal of Research, 2021
Group delay can be defined as the measure of phase distortion. It is nearly proportional to the order of the filter. It is expected that any microwave filters should produce flattest group delay in the passband. Since Chebyshev bandpass filer produces equi-ripple in the passband, hence group delay is not very flat. The graphical representation of the EM simulated vs. measured group delay for the proposed BPF is shown in Figure 6 and it is calculated as, where “Φ” is the phase angle of S21 and “ω” is the angular frequency in rad/sec.
A Low-Cost Compact Low-Pass Filtering Power Divider Based on Elliptic Function with Wide Attenuation Band
Published in IETE Journal of Research, 2022
Group delay can be defined as the measure of phase distortion. It is necessary for a designed filter that it should produce flattest group delay in the passband. Since, Chebyshev filters has equiripple passband, hence group delay is not very flat. The group delay can be calculated as where “Φ” is the phase angle of S21 and “ω” is the angular frequency whose unit is rad/s. Figure 7(f) shows the group delay of the proposed FPD in “ns”. The average group delay in the passband found is 0.076 ns.