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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Author: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).
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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