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?

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

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.  

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation: