Physical systems are modeled by mathematical equations. □ Physical . Simon Haykin and Barry Van Veen, “Signals and Systems,” Wiley ,. 2nd edition. Biomedical system(biomedical signal processing) . Signals and Systems, Oppenheim & Willsky, Section 1; Signals and Systems, Haykin & Van Veen, Section. ECE Material. Contribute to unm-ieee/ECE_Material development by creating an account on GitHub.

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We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. At the same time, the rectangular pulse of unit area i. The duration of the output is longer than that of the input. June 2. In addition, the book covers Advanced Communication Systems, showing the latest developments in the industry. Have a great day!

The width of pulse g t is 2, whereas the width of pulse g1 t is 4. All three pulses, g1 t , g2 t , and g3 t , are symmetrically positioned around the origin: Hence, it follows that That is, 1. Hence the angular frequency of x[n] is m: At the same time, the rectangular pulse of unit area i.

We may thus state that in the limit: In light of the results presented in parts a , b , and c of this problem, we may now make the following statement: Hence, we may write 1 2 3 The overall system output is 4 Substituting Eqs.

It follows therefore that the system described by the operator H of Problem 1.

Consider, for example, the system illustrated below: The system has memory by virtue of the term alx[n - l]. Correspondingly, feedback implementation of the inverse operator Hinv is described in Fig. Hence, the system described in Problem 1. This circuit, consisting of the series combination of the resistor R t and capacitor C, is time variant because of R t. We therefore conclude that the time-varying circuit of Fig.

We then note that for Hence the system described by Eq. This system is both linear and time invariant.

Consider another discrete-time system described by the operator H2: The system H1 is causal, but the second system H2 is noncausal. They both involve the same number of multipliers and summer. The input-output relation of H1 is representative of a differentiating action, which by itself is memoryless.

However, the duration of the output is twice as long as that of the input. This suggests that H1 may consist of a differentiator in parallel with a storage device, followed by a combiner.

On this basis, H1 may be viewed as a time-invariant system with memory. System H2 is causal because the output does not appear before the input. The duration of the output is longer than that of the input. This suggests that H2 must have memory. It is time-invariant. System H3 is noncausal because the output appears before the input. On this basis, H3 would have to be viewed as time-varying. Hence, H4 is a causal, memoryless, and time-invariant system.

It is causal because the output does not appear before the input. It has memory because of the integrating action performed on the input. On this basis, H2 may be viewed as time-varying. H3 is causal because the output does not appear before the input. On this basis, H3 is time-invariant. Consider next the input x t depicted in Fig.

This input may be decomposed into the sum of two rectangular pulses, as shown here: Response of H1 to x t: The response of the system to these three components is given in the following table: Thus, the total response y[n] of the system is as shown here: Advanced Problems 1.

Rearranging terms: MEMS of Fig. With differentiation as the operation of interest, we may also write Clearly, the value of x t is unaffected by the value assumed by the initial condition It would therefore be wrong to say that differentiation and integration are the inverse of each other.

To illustrate the meaning of this statement, consider the two following two waveforms that differ from each other by a constant value for: Yet, , as illustrated below: These are two different input conditions. Clearly, on this basis it would be wrong to say that these two LR circuits are the inverse of each other. If the input x t is scaled by an arbitrary factor a, the output y t will be scaled by the same factor.

The corresponding value of the output is For , we clearly see that. We may then rewrite Eq. The difference equation 5 is of order 4, providing an approximate description of a second-order continuous-time system.

This doubling in order is traced to Eq.

We may avoid the need for this order doubling by adopting the alternative approximation: Recognizing that noise contains a broad band of frequencies, integration has a smoothing effect on receiver noise.

Correspondingly, differentiation has the opposite effect to integration on receiver noise. Solutions to Additional Problems 2.

A discrete-time LTI system has the impulse response h[n] depicted in Fig. Use linear- ity and time invariance to determine the system output y[n] if the input x[n] is Use the fact that: Evaluate the discrete-time convolution sums given below.

Consider the discrete-time signals depicted in Fig. Evaluate the convolution sums indi- cated below. Intervals 10 Have a great day! Kindly share this post with your friends to make this exclusive release more useful.

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