h1(t)x(t)y(t)-h2(t)Figure 1: System for applying a trend-following filter.Question 1A trend-following filter is often used in quantitative finance to evaluate a trend in a signal.A trend-following trading system is built around the idea that if the price of assets is increasingthen it is more likely to continue to increase.The filter applies two exponentially weighted movingaverage filters with different time constants and then calculates the differences of the outputs. Infinance, this is calculated on discrete-time signals. We will consider a similar filter in continuoustime.We apply two filters to the input signal x(t) to derive y1(t) and y2(t) and then subtract theoutput of one from the other, so that y(t) = yı(t) – y2(t). The filters have impulse responsesh1(t)provides a diagram of the system.I apply an input x(t) = 5u(t) exp(-3t) to the trend-following filter.2a exp(-2at)u(t) where h2(t)a exp(-at)u(t) for some positive constant a. Figure 1a) Derive X(s), the Laplace transform of this signal, using the definition of the Laplace trans-form. Specify the region of convergence.b) For this input, what is Y (s), the output of the system in the Laplace domain?c) What is the region of convergence of Y(s)?d) What is the response y(t)?e) Is the system H(s) = H1(s) – H2(s) linear? Demonstrate why or why not.f) Is the system time invariant? Demonstrate why or why not.g) Is the system causal? Explain why or why not?

A transform is a change in the mathematical description of a physical variable to computation.…

h1(t) ¤(t) y(t) -h2(t) Figure 1: System for applying a trend-following filter. 1estion 1 A trend-following filter is often used in quantitative finance to evaluate a trend in a signal. trend-following trading system is built around the idea that if the price of assets is increasing en it is more likely to continue to increase.The filter applies two exponentially weighted moving erage filters with different time constants and then calculates the differences of the outputs. In ance, this is calculated on discrete-time signals. We will consider a similar filter in continuous ne. We apply two filters to the input signal r(t) to derive yı(t) and y2(t) and then subtract the put of one from the other, so that y(t) = y1 (t) – y2(t). The filters have impulse responses (t) = 2a exp(-2at)u(t) where h2(t) = a exp(-at)u(t) for some positive constant a. Figure 1 ovides a diagram of the system. I apply an input x(t) = 5u(t) exp(-3t) to the trend-following filter. a) Derive X(s), the Laplace transform of this signal, using the definition of the Laplace trans- form. Specify the region of convergence. b) For this input, what is Y(s), the output of the system in the Laplace domain? c) What is the region of convergence of Y(s)?

h1(t) ¤(t) y(t) -h2(t) Figure 1: System for applying a trend-following filter. 1estion 1 A trend-following filter is often used in quantitative finance to evaluate a trend in a signal. trend-following trading system is built around the idea that if the price of assets is increasing en it is more likely to continue to increase.The filter applies two exponentially weighted moving erage filters with different time constants and then calculates the differences of the outputs. In ance, this is calculated on discrete-time signals. We will consider a similar filter in continuous ne. We apply two filters to the input signal r(t) to derive yı(t) and y2(t) and then subtract the put of one from the other, so that y(t) = y1 (t) – y2(t). The filters have impulse responses (t) = 2a exp(-2at)u(t) where h2(t) = a exp(-at)u(t) for some positive constant a. Figure 1 ovides a diagram of the system. I apply an input x(t) = 5u(t) exp(-3t) to the trend-following filter. a) Derive X(s), the Laplace transform of this signal, using the definition of the Laplace trans- form. Specify the region of convergence. b) For this input, what is Y(s), the output of the system in the Laplace domain? c) What is the region of convergence of Y(s)?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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