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Discrete Time Fourier Transform Properties

February 2, 2019 by 3200 Creative

Discrete Time Fourier Transform Properties

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  1. Question 1 of 4
    1. Question

    If signals x[n] and y[n] have discrete-time Fourier transforms (DTFTs) X(e^{j\omega}) = \frac{1}{1- 0.5e^{j\omega}} and Y(e^{j\omega}) = \frac{1}{1+ 0.25e^{j\omega}}, what is the DTFT of z[n] = -x[n] + 2y[n]??

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  2. Question 2 of 4
    2. Question

    A signal x[n] = 0.5^n u[n] is applied to a linear time-invariant system with impulse response  h[n] = 0.25^n u[n]. What is the DTFT of the output y[n] = x[n]*h[n]? Hint: recall that a^n u[n] has DTFT \frac{1}{1- ae^{-j\omega}}.

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  3. Question 3 of 4
    3. Question

    A signal x[n] = 0.8^n u[n] has DTFT  X(e^{j\omega}) = \frac{1}{1-0.8e^{-j\omega}}. Use the properties of the DTFT to find the signal z[n] with DTFT  Z(e^{j\omega}) = \frac{e^{j4\omega}}{1-0.8e^{-j\omega}}.

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  4. Question 4 of 4
    4. Question

    A signal x[n] = 0.8^n u[n] has DTFT  X(e^{j\omega}) = \frac{1}{1- 0.8e^{-j\omega}}. Use the properties of the DTFT to find the DTFT of the signal z[n] = e^{j\pi n/8} 0.8^n u[n].

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