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Additional resources for Digital Logic Circuit Analysis and Design
The classical method of solving a difference equation 4. The analytical solution using the z transform. We should point out that methods 1–3 require that the DT system be modeled by a single-input, single-output equation. If we are given a large number of difference equations describing the DT system, then methods 1–3 are not suitable for ﬁnding the output response in the time domain. Method 4, using the z transform, is the only powerful and general method to solve such a problem, and hence it will be treated in greater detail and illustrated by several examples in this chapter.
15. ” Thus we obtain an analog signal yd (t) at the output of the smoothing ﬁlter as shown. 17 requires considerably more hardware or involves a lot more signal processing in order to ﬁlter out the undesirable frequencies from the analog signal x(t) and deliver an output signal yd (t). 16; if so, what are the advantages of digital signal processing instead of analog signal processing, even though digital signal processing requires more circuits compared to analog signal processing? 15 A lowpass third-order digital ﬁlter.
To understand the procedure for implementing the summation formula, we choose a graphical method in the following example. Remember that the recursive algorithm cannot be used if the DT system is described by more than one difference equation, and the convolution sum requires that we have the unit pulse response of the system. We will ﬁnd that these limitations are not present when we use the z-transform method for analyzing the DT system performance in the time domain. 4a,b. Note that the input sequence is deﬁned for −2 ≤ k ≤ 5 but h(k) is a causal sequence deﬁned for 0 ≤ k ≤ 4.