# Mathematics

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Solution Library **

#### Fourier Series Expansion of a Real Periodic Signal

Question The Fourier series expansion of a real periodic signal is in the form of f(t) = ao + an cos(nωot) + bn sin(nωot) Find the Hilbert-transform pair. Find the average power of the Hilbert-transform pair. Evaluate the inner product of the Hilbert-transform pair. Summa ... Read More

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#### Lowpass Highpass Frequency Transformation Technique

Question Show that the z → -z-1 frequency transformation coverts a lowpass filter HL(z) to a highpass filter HH(z) = HL(-z-1) The speech scrambler utilizes the modulation sequence [+1, -1, +1, -1, +1, -1, +1, -1,…] for the redistribution of frequency components. The z → -z- ... Read More

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#### Interpolation Techniques to Interpolate the Subsequences

Question Below, two data sequences were used for the interpolation experiments. Consider a simple single-mode 128-point sequence x(n) = sin(πn/64) for&n ... Read More

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#### Differentiation of a Polynomial Equation

Question Differentiate the following, using the correct notation. Y = x3 + 4x2 – 5 Summary: This question belongs to differentiation in mathematics and discusses about differentiation of the given equation. Answer is in image format ... Read More

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#### Differentiation of a Polynomial Equation

Question Differentiate the following, using the correct notation. Y = 12x3 + 8x2 +2x -7 Summary: This question belongs to differentiation in mathematics and discusses about differentiation of the given equation. Answer is in image format ... Read More

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#### Differentiation of a Polynomial Equation

Question Differentiate the following, using the correct notation. F(x) = x5 + - - 2 Summary: This question belongs to differentiation in mathematics and discusses about differentiation of the given equation. Answer is in image format ... Read More

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#### Differentiation of a Polynomial Equation

Question Differentiate the following, using the correct notation. Y = x (x+3)(x-4) Summary: This question belongs to differentiation in mathematics and discusses about differentiation of the given equation. Answer is in image format ... Read More

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#### Differentiation of a Polynomial Equation

Question Differentiate the following, using the correct notation. F(x) = Summary: This question belongs to differentiation in mathematics and discusses about differentiation of the given equation. Answer is in image format ... Read More

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#### Differentiation of a Polynomial Equation

Question Differentiate the following, using the correct notation. F(x) = x3 – 3x2 + + 7 Summary: This question belongs to differentiation in mathematics and discusses about differentiation of the given equation. Answer is in image format ... Read More

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#### Find Gradient of Given Curves at the Given Points

Question Find the gradient of these curves at the given points. F(x) = 2x2+2 when X =2 and X = -1. Summary: This question belongs to differentiation in mathematics and discusses about to find gr ... Read More

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#### Find Gradient of Given Curves at the Given Points

Question Find the gradient of these curves at the given points. Y = 2e3x +2x when X = -2 and X = 4. Summary: This question belongs to differentiation in mathematics and discusses about to find gradient of given curves at the ... Read More

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#### Equation of the Normal to Curves at Given Points

Question Find the equation of the normal to these curves at the given points. Y = x2 -8x + 10 at X = 2. Summary: This question belongs to differentiation in mathematics and discusses about finding the equation of the normal to given curves at the given points. Answer is in image format ... Read More

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