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)
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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].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F592e812d-b42b-410e-b1fa-06907178f67b%2F15d6623f-e94f-4e07-b788-65f0cfbccf0f%2Fkedul6c_processed.png&w=3840&q=75)
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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