1. How many complex numbers z are there such that z3 = 1? 2. Translate x(t)...

1. How many complex numbers z are there such that z³ = 1?

2. Translate x(t) = -cos(πt + π/3) into standard form A⋅sin(2πft + φ) (There are multiple correct answers)

3. If f_s = 100 Hz, what are three aliasing frequencies for f = 80 Hz?

4. A signal x is delayed by one sample and scaled by −1/2, producing a new signal y[n] = −1 2 x[n − 1]. (a) How does Y[m] relate to X[m]? (b) What about |Y[m]| and |X[m]|?

5. If a signal x’s DFT has entirely real coefficients X[m] (has no imaginary component), what can you deduce about x? Consider the phase for each analysis frequency.

6. Let x[n] be a signal with N = 5000 samples. (a) If you compute an STFT with a frame length of K = 1000 and hop length h = 250, what will be the shape of the resulting spectrogram? (b) How would it change if you set K = 2000? (c) What if you set h = 100?

Expert Solution

Manojponduru answered 8 months ago

how many irreducible polynomials of degree 2 in Z3 [x]

Let α be a root of x^2 +1 ∈ Z3[x]. Show that Z3(α) = {a+bα :...

Let α be a root of x^2 +1 ∈ Z3[x]. Show that Z3(α) = {a+bα : a, b ∈ Z3} is isomorphic to Z3[x]/(x^2 + 1).

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Velocity field for this system is: V=[X^2-(yz^1/2/t)]i-[zy^3+(x^1/3z^2/t^1/2)j+[-x^1/3t^2/z*y^1/2]k find the components of acceleration for the system.

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Complex Numbers: What's the difference between Log(z), log(z) and ln(z)? where z is a complex number,...

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1. Express the following complex numbers in cartesian form x + jy: 1/2 e jπ ,...

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