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Convolution is a mathematical operation that expresses a relationship between an input signal, the output signal, and the impulse response of a linear-time invariant system. Three systems that represented by the impulse response, ħ[n], ha[n] and ħa[n] are connected in series as shown in Figure Q2(a), where x[n] and y[n] are the input and output signals respectively. The impulse response functions of each system are represented by equation (1). (2) and (3). h,[n] = 2nu[n + 3] – 2nu[n – 3] h2[n] = 6[n – 2] ha[n] = S[n + 2] - 28[n – 2] %3D x[n] h,[n] ħ[n] h[n] →y[n] Figure Q2(a) (a) Using the convolution, sketch the output response of y[n] if the input signal is given by x[n] = 6[n].

Convolution is a mathematical operation that expresses a relationship between an input signal, the output signal, and the impulse response of a linear-time invariant system. Three systems that represented by the impulse response, ħ[n], ha[n] and ħa[n] are connected in series as shown in Figure Q2(a), where x[n] and y[n] are the input and output signals respectively. The impulse response functions of each system are represented by equation (1). (2) and (3). h,[n] = 2nu[n + 3] – 2nu[n – 3] h2[n] = 6[n – 2] ha[n] = S[n + 2] - 28[n – 2] %3D x[n] h,[n] ħ[n] h[n] →y[n] Figure Q2(a) (a) Using the convolution, sketch the output response of y[n] if the input signal is given by x[n] = 6[n].

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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QUESTION 2 Convolution is a mathematical operation that expresses a relationship between an input signal, the output signal, and the impulse response of a linear-time invariant system. Three systems that represented by the impulse response, h[n], ha[n] and ħa[n] are connected in series as shown in Figure Q2(a), where x[n] and y[n] are the input and output signals respectively. The impulse response functions of each system are represented by equation (1). (2) and (3). h,[n] = 2nu[n + 3] – 2mu[n – 3] (1) ha[n] = 8[n – 2] h[n] = 8[n + 2] – 28[n – 2] (3) x[n] h,[n] h2[n] h[n] → y[n] Figure Q2(a) (a) Using the convolution, sketch the output response of y[n] if the input signal is given by x[n] = 6[n].
Transcribed Image Text:QUESTION 2 Convolution is a mathematical operation that expresses a relationship between an input signal, the output signal, and the impulse response of a linear-time invariant system. Three systems that represented by the impulse response, h[n], ha[n] and ħa[n] are connected in series as shown in Figure Q2(a), where x[n] and y[n] are the input and output signals respectively. The impulse response functions of each system are represented by equation (1). (2) and (3). h,[n] = 2nu[n + 3] – 2mu[n – 3] (1) ha[n] = 8[n – 2] h[n] = 8[n + 2] – 28[n – 2] (3) x[n] h,[n] h2[n] h[n] → y[n] Figure Q2(a) (a) Using the convolution, sketch the output response of y[n] if the input signal is given by x[n] = 6[n].
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