Answered

Explore IDNLearn.com to discover insightful answers from experts and enthusiasts alike. Find the answers you need quickly and accurately with help from our knowledgeable and dedicated community members.

We are given the discrete-time sinusoidal segment {6.2 cos(0.75 pi n + 1), n = 0, . . . , (N - 1)}. For what values of N will the spectrum computed using the DFT have no spectral leakage?

Sagot :

Nuhulawal20idn

Answer:

the values of N for which there will be no spectral leakage are;

N = Integers multiple by 8

Step-by-step explanation:

Given that;

discrete-time sinusoidal segment x[n] = 6.2cos(0.75πn + 1)

Using DFT to compute the spectrum

The spectral leakage will not be present in the spectrum if the product f₀Td is an integer.

Here, f₀ is sinusoid's frequency and Td is the segment duration

Now we calculate the period of the signal

2π/ω = 2π/0.75π

ω =  2 / 0.75

( × 4 )

ω =  8 / 3

Here, the numerator value is the period of the signal

T₀ = 8

The spectral leakage will not be present in the spectrum if N is  the Integer multiple of period T₀.

Therefore, the values of N for which there will be no spectral leakage are;

N = Integers multiple by 8

We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.