By Mikhail Cherniakov
Because the Nineteen Sixties electronic sign Processing (DSP) has been probably the most extensive fields of research in electronics. although, little has been produced in particular on linear non-adaptive time-variant electronic filters.
* the 1st ebook to be devoted to Time-Variant Filtering
* presents a whole advent to the idea and perform of 1 of the subclasses of time-varying electronic platforms, parametric electronic filters and oscillators
* offers many examples demonstrating the applying of the techniques
An imperative source for pro engineers, researchers and PhD scholars interested in electronic sign and snapshot processing, in addition to postgraduate scholars on classes in machine, electric, digital and related departments.
Read Online or Download An Introduction to Parametric Digital Filters and Oscillators PDF
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Additional info for An Introduction to Parametric Digital Filters and Oscillators
Let Y (z) and X(z) be z-transforms of the output and input signals respectively. 118). 126) In this expression, the signs of the coefficients have been reversed. 19 shows a block diagram of this filter, which is referred to in literature as a pure recursive second-order filter. 127) is an equation of the second order. Consequently, in the general case it has complex-conjugate roots. Roots of the transfer function denominator are called poles. 128) Depending on coefficient values a1 , a2 , the poles p1 , p2 can be either real (a12 ≥ 4a2 ) or complex (a12 < 4a2 ) In the first case, the filter of the second order is equivalent to the serial connection of first-order filters with real coefficients.
4 STABILITY AND CAUSALITY OF DISCRETE SYSTEMS In the previous sections, it was assumed that DLSs are causal and stable. However, it is known from the theory of differential equations that in the general case this is not obvious. In each case, the system has to be analysed from stability and causality perspectives. A DLS is causal if its impulse response is equal to zero for the negative time values m. The meaning of this criterion is obvious: if a system is operating in real time, a signal cannot reach the system output earlier than it reaches its input.
For a narrowband filtering, it is important to have accurate resonance frequency adjustment. The displacement should be usually much less than the resonator bandwidth. This example clearly demonstrates that at least for a narrowband filtering, the word length is essential. Another problem of the word length limitation follows from the rounding of arithmetical operation results to Lar bits. A reasonably good approximation of the rounding noise is a process with uniform spectrum over the frequency interval ω = 0 to π and 2 power σRN = 2−2Lar /12.