For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h( (2024)

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Design and Analysis of Analog Filters: A Signal Processing Perspective Paarmann L.D. 1st Edition

Chapter 2, Problem 14

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    Problem 14 For the following magnitude frequency response:$…

    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (2)

    Question

    Answered step-by-step

    For the following magnitude frequency response:
    $$
    |H(j \omega)|=e^{-k|\omega|},
    $$
    where $k$ is a positive real number,
    (a) Show that this function is square-integrable,
    (b) Show that there is no $H(j \omega)$ with the given magnitude frequency response that has a corresponding $h(\mathrm{t})$ that is causal. That is, show that the Paley-Wiener Theorem is not satisfied.
    (c) Determine the half-power frequency, i.e., the frequency where $|H(j \omega)|=|H(0)| / \sqrt{2}$, in terms of $k$.
    (d) Using MATLAB, generate 1000 equally-spaced samples of $|H(j \omega)|$ with $k=\ln (2) / 200$, for $0 \leq \omega \leq 2000$. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a $d B$ vertical scale.

    See Also
    Control Tutorials for MATLAB and SimulinkControl Tutorials for MATLAB and SimulinkThe BOD Toolbox – Digital Magnitude Optimum (various inputs)Using the MATLAB functions cheb2ap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles and zeros, of a Chebyshev Type II filter with =1, Ap=1.2  dB, and N=6. (b) Determine the impulse response

    Video Answer

    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (3) For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (4) For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (5)

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (6)

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (7)

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    For the following magnitude frequency response:$$|H(j \omega)|=e^{-k|\omega|},$$where $k$ is a positive real number,(a) Show that this function is square-integrable,(b) Show that there is no $H(j \omega)$ with the given magnitude frequency response that has a corresponding $h(\mathrm{t})$ that is causal. That is, show that the Paley-Wiener Theorem is not satisfied.(c) Determine the half-power frequency, i.e., the frequency where $|H(j \omega)|=|H(0)| / \sqrt{2}$, in terms of $k$.(d) Using MATLAB, generate 1000 equally-spaced samples of $|H(j \omega)|$ with $k=\ln (2) / 200$, for $0 \leq \omega \leq 2000$. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a $d B$ vertical scale.

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (8)

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (9)

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (10)Ace Chat

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (11)Ask Our Educators

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (12)Notes & Exams

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (13)

    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (14)

    Design and Analysis of Analog Filters: A Signal Processing Perspective

    Paarmann L.D. 1st Edition

    Chapter 2

    ​ Chapter 1

    ​ Chapter 2

    ​ Chapter 3

    ​ Chapter 4

    ​ Chapter 5

    ​ Chapter 6

    ​ Chapter 7

    ​ Chapter 8

    ​ Chapter 9

    ​ Chapter 10

    ​ Chapter 11

    Sections

    Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h(t) that is causal. That is, show that the Paley-Wiener Theorem is not satisfied. (c) Determine the half-power frequency, i.e., the frequency where |H(j ω)|=|H(0)| / √(2), in terms of k. (d) Using MATLAB, generate 1000 equally-spaced samples of |H(j ω)| with k=ln(2) / 200, for 0 ≤ω≤2000. Plot the results with (i) a linear vertical scale, and, on a second plot, (ii) also with a d B vertical scale. | Numerade (15)

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    For the following magnitude frequency response: |H(j ω)|=e^-k|ω|, where k is a positive real number, (a) Show that this function is square-integrable, (b) Show that there is no H(j ω) with the given magnitude frequency response that has a corresponding h( (2024)

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