Answer:
a) it is periodic
N = (20/3)k = 20 { for K =3}
b) it is Non-Periodic.
N = ∞
c) x(n) is periodic
N = LCM ( 5, 20 )
Explanation:
We know that In Discrete time system, complex exponentials and sinusoidal signals are periodic only when ( 2π/w₀) ratio is a rational number.
then the period of the signal is given as
N = ( 2π/w₀)K
k is least integer for which N is also integer
Now, if x(n) = x1(n) + x2(n) and if x1(n) and x2(n) are periodic then x(n) will also be periodic; given N = LCM of N1 and N2
now
a) cos(2π(0.15)n)
w₀ = 2π(0.15)
Now, 2π/w₀ = 2π/2π(0.15) = 1/(0.15) = 1×20 / ( 0.15×20) = 20/3
so, it is periodic
N = (20/3)k = 20 { for K =3}
b) cos(2n);
w₀ = 2
Now, 2π/w₀ = 2π/2) = π
so, it is Non-Periodic.
N = ∞
c) cos(π0.3n) + cos(π0.4n)
x(n) = x1(n) + x2(n)
x1(n) = cos(π0.3n)
x2(n) = cos(π0.4n)
so
w₀ = π0.3
2π/w₀ = 2π/π0.3 = 2/0.3 = ( 2×10)/(0.3×10) = 20/3
∴ N1 = 20
AND
w₀ = π0.4
2π/w₀ = 2π/π0. = 2/0.4 = ( 2×10)/(0.4×10) = 20/4 = 5
∴ N² = 5
so, x(n) is periodic
N = LCM ( 5, 20 )
Journalism
CURRENT CATEGORIES
Public Service (1917-present)
Breaking News Reporting (1998-present)
Investigative Reporting (1985-present)
Explanatory Reporting (1998-present)
Local Reporting (1948-1952, 2007-present)
National Reporting (1948-present)
International Reporting (1948-present)
Feature Writing (1979-present)
Commentary (1973-present)
Criticism (1973-present)
Editorial Writing (1917-present)
Editorial Cartooning (1922-present)
Breaking News Photography (2000-present)
Feature Photography (1968-present)
+ SHOW PAST CATEGORIES (17)
Letters, Drama & Music
CURRENT CATEGORIES
Fiction (1948-present)
Drama (1917-present)
History (1917-present)
Biography (1917-present)
Poetry (1922-present)
General Nonfiction (1962-present)
Music (1943-present)