# The relationship between Frequency and phase- shift in Butterworth filters Essay

Published: 2020-04-22 08:25:56
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The phase characteristic of Butterworth filters varies with the particular frequency in the passband and also with the ratio of cut-off frequency to sampling frequency. The cut off frequency occurs at the point where the phase shift is half its maximum value. The frequency of the Butterworth filters is often flat (they have no ripples). Therefore the Butterworth has a linear phase characteristic. The function of their magnitude has monotonic changes contrary to other filters which have non-monotonic ripples (Daryanani, 1976).

The Butterworth filters have rolls off slowly and thus a particular specification of stopband needs higher order to be implemented. This is because the gain is high at higher frequency and lower at low frequency. Similarly the group delay increases with decrease in frequency. All filter options of the same order has the same phase shift. 2. How this relationship affect the waveform of a complex signal with multiple frequency components sent through it. The waveform of any complex signal that passes through a Butterworth filter shows no ripple although it rolls off at a slower rate around the cut off frequency.

Lack of ripples in the Butterworth filter enables it to have a linear phase characteristic. Any signal passing through Butterworth filters experiences slight distortion but not as extensive as it occurs in Chebyshev filters and Elliptic filters. The phase of the signal is inverted in the case of multiple frequency components. The damping ratio of Butterworth filters is approximately 1. 1414 which produces a flat response (Thomas, 1971). Questions 1. The purpose of the LPF in the demodulator . and its bandwidth

Low pass filter in the demodulator is meant to suppress the subcarrier frequencies which are contained in the FM stereo of the demodulation signal. In other words, it filters out carrier frequencies Thus the resulting magnetic distortion doesnt affect the output signal. The bandwidth of the low pass filter is determined by the number of signal sampled that need to be filtered at a given speed (the sampling frequency). The LPF also helps in preventing deterioration in the sound quality (Graeme, 1971). 2. How to calculate the bit clock of the demodulator from the carrier frequency?

The bit rate of the clock is a sub multiple of carrier frequency. This means that the bit clock frequency depends on the number of channels multiplied by the number of bits per channel ((Thomas, 1971). For instance if the CD audio has a carrier frequency of 44. 1Hz, with 32 bits per(2) stereo channel, then the bit clock frequency will be given by carrier frequency divide by the channels times the number of bits 44. 1/ (32/2) = 2. 8224 MHz Eye Diagram 1. Snapshot method allows multiplexing up to ten single nucleotide polymorphisms. It is primer extension based multiplex system.

It compares every single incoming bit to the threshold voltage and judges whether it is a zero or one. Therefore, snapshot method can put exact decision on time and voltage of every signal. However, the eye diagram is used for high speed serial interfaces. Snapshot method is also used to measures the intuitive performance of the links (at instant time) whereas the eye diagram takes substantial time to give the link performance. It makes the correct decision on whether the incoming signal is one or zero. The eye diagram requires massive knowledge in algorithms to analyze and it takes quiet along time for acquisition.

Snapshot method, on the other hand gives the performance at instant time and it is easy to analyze (Graeme, 1971). 2. The effects of differing forms of interference on the signal Interferences render the wireless systems completely unusable. The three major forms of interferences include the intermodulation, radio frequency interference, and electrical interference. The intermodulation interference occurs due to the merging of strong radio signals in a wireless network while electrical interference is caused by digital equipments and lighting system.

The radio frequency interference is caused by communication equipment. It is essential to know which type of interference has occurred so as to avoid unnecessary and unproductive solutions (Daryanani, 1976). References: Daryanani, G. (. 1976). Principles of Active Network Synthesis and Design. J. Wiley & Sons. Thomas, L. C. (1971). A Multipurpose Active Filtering System. Newnes: Elsevier Graeme, J. et al. (1971). Operational Amplifiers Design and Applications. New York: McGraw-Hill. 1971.

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