1. For the multi-tone discrete time periodic signal 1 3 [n] = sin(0.24) + cos(0.4лn) + a. Find the fundamental frequencies (F₁ and F2) and periods (N₁ and N₂) of the sine and cosine functions individually. Use these to determine the fundamental period length (N) of the multi-tone signal. b. Using the alternate representation of the multi-tone signal x[n] given below, and the period length N you found in Part (a), determine the DTFS coefficients (ck) for the signal. You do not need to write out any zero-valued Ck coefficients. 1 5n π π 2 치[n]=ee-1(품)on-e-He/(품)3n + Lex()sm + He-1()sn 1 + 2 c. Calculate the complex values of each non-zero Ck coefficient you found in Part (b) in the form k = a + jb (you may round your answers to four decimal places).
1. For the multi-tone discrete time periodic signal 1 3 [n] = sin(0.24) + cos(0.4лn) + a. Find the fundamental frequencies (F₁ and F2) and periods (N₁ and N₂) of the sine and cosine functions individually. Use these to determine the fundamental period length (N) of the multi-tone signal. b. Using the alternate representation of the multi-tone signal x[n] given below, and the period length N you found in Part (a), determine the DTFS coefficients (ck) for the signal. You do not need to write out any zero-valued Ck coefficients. 1 5n π π 2 치[n]=ee-1(품)on-e-He/(품)3n + Lex()sm + He-1()sn 1 + 2 c. Calculate the complex values of each non-zero Ck coefficient you found in Part (b) in the form k = a + jb (you may round your answers to four decimal places).
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![1.
a.
For the multi-tone discrete time periodic signal
[n]=sin(0.24лn) + cos(0.4лn) +
1
3
Find the fundamental frequencies (F₁ and F2) and periods (N₁ and N₂) of the
sine and cosine functions individually. Use these to determine the fundamental
period length (N) of the multi-tone signal.
b. Using the alternate representation of the multi-tone signal x[n] given below, and
the period length N you found in Part (a), determine the DTFS coefficients (Ck)
for the signal. You do not need to write out any zero-valued C coefficients.
jn
2π
3n
3n
x[n]
= e 2 e
- e
2 e
×
1 2π
j(2) 5n
2'
1
+ e
1
5n
+
2
3
c. Calculate the complex values of each non-zero ck coefficient you found in Part
(b) in the form C₁ = a + jb (you may round your answers to four decimal places).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F670cd716-78ea-4bd2-aa02-b6fca7de8b87%2F33e5d79e-a657-4bb7-a8e3-0c554dccc619%2F61kefxp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
a.
For the multi-tone discrete time periodic signal
[n]=sin(0.24лn) + cos(0.4лn) +
1
3
Find the fundamental frequencies (F₁ and F2) and periods (N₁ and N₂) of the
sine and cosine functions individually. Use these to determine the fundamental
period length (N) of the multi-tone signal.
b. Using the alternate representation of the multi-tone signal x[n] given below, and
the period length N you found in Part (a), determine the DTFS coefficients (Ck)
for the signal. You do not need to write out any zero-valued C coefficients.
jn
2π
3n
3n
x[n]
= e 2 e
- e
2 e
×
1 2π
j(2) 5n
2'
1
+ e
1
5n
+
2
3
c. Calculate the complex values of each non-zero ck coefficient you found in Part
(b) in the form C₁ = a + jb (you may round your answers to four decimal places).
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Step 1: what is given and what to do:
VIEWStep 2: a) Fundamental frequencies and periods of sine and cosine functions individually and overall signal:
VIEWStep 3: b) Representing the signal x[n] in complex exponential form and determining DTFS coefficients:
VIEWStep 4: c) Representing the DTFS coefficients, found in part (b), in the form of a+jb:
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