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h(t) = 8met I[0,00) (t) The unit of time is 1 microsecond. (a) Find the transfer function H(f) and show that the maximum value of the amplitude gain |Ĥ(f)| occurs at f = 0. (b) Find the 3 dB cutoff frequency fo (in Hz). That is, find fo such that 10 log10 Ĥ (fo)|² Ĥ (0)|² -3. (c) What happens to the amplitude and phase of a sinusoid at 500 KHz when it is passed through the filter?

h(t) = 8met I[0,00) (t) The unit of time is 1 microsecond. (a) Find the transfer function H(f) and show that the maximum value of the amplitude gain |Ĥ(f)| occurs at f = 0. (b) Find the 3 dB cutoff frequency fo (in Hz). That is, find fo such that 10 log10 Ĥ (fo)|² Ĥ (0)|² -3. (c) What happens to the amplitude and phase of a sinusoid at 500 KHz when it is passed through the filter?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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 Consider a filter with impulse response

 

h(t) = 8πe^{-πt}[0,∞)(t) The unit of time is 1 microsecond. (a) Find the transfer function \( \hat{H}(f) \) and show that the maximum value of the amplitude gain \( |\hat{H}(f)| \) occurs at \( f = 0 \). (b) Find the 3 dB cutoff frequency \( f_0 \) (in Hz). That is, find \( f_0 \) such that \( 10 \log_{10} \frac{|\hat{H}(f_0)|^2}{|\hat{H}(0)|^2} = -3 \). (c) What happens to the amplitude and phase of a sinusoid at 500 KHz when it is passed through the filter? (d) What happens to the amplitude and phase of a sinusoid at 4 MHz when it is passed through the filter?
Transcribed Image Text:h(t) = 8πe^{-πt}[0,∞)(t) The unit of time is 1 microsecond. (a) Find the transfer function \( \hat{H}(f) \) and show that the maximum value of the amplitude gain \( |\hat{H}(f)| \) occurs at \( f = 0 \). (b) Find the 3 dB cutoff frequency \( f_0 \) (in Hz). That is, find \( f_0 \) such that \( 10 \log_{10} \frac{|\hat{H}(f_0)|^2}{|\hat{H}(0)|^2} = -3 \). (c) What happens to the amplitude and phase of a sinusoid at 500 KHz when it is passed through the filter? (d) What happens to the amplitude and phase of a sinusoid at 4 MHz when it is passed through the filter?
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