A siren is emitting a constant frequency in a noisy room, x(t) = cos(18t). There is a microphone he room measuring the signal, x(t), plus the background noise denoted as the signal, e(t). Let t hoise signal be g(t) = x(t) + e(t). The microphone signal is connected to an A/D converter wh amples the signal at a rate of 51 rad/sec. You take 148 samples from the A/D converter and alculate the DFT. Recall that r(t) = cos(Not) = ½ (einot + e-inot) What integer index, k, of the DFT, X[k], corresponds to the frequency closest to the complex -jnot Componente present in the input signal?
A siren is emitting a constant frequency in a noisy room, x(t) = cos(18t). There is a microphone he room measuring the signal, x(t), plus the background noise denoted as the signal, e(t). Let t hoise signal be g(t) = x(t) + e(t). The microphone signal is connected to an A/D converter wh amples the signal at a rate of 51 rad/sec. You take 148 samples from the A/D converter and alculate the DFT. Recall that r(t) = cos(Not) = ½ (einot + e-inot) What integer index, k, of the DFT, X[k], corresponds to the frequency closest to the complex -jnot Componente present in the input signal?
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![A siren is emitting a constant frequency in a noisy room, x(t) = cos(18t). There is a microphone in
the room measuring the signal, x(t), plus the background noise denoted as the signal, e(t). Let the
noise signal be g(t) = x(t) + e(t). The microphone signal is connected to an A/D converter which
samples the signal at a rate of 51 rad/sec. You take 148 samples from the A/D converter and
calculate the DFT. Recall that
x(t) = cos(Not) = ½ (einot + e¯¡Not)
What integer index, k, of the DFT, X[k], corresponds to the frequency closest to the complex
componente present in the input signal?
-jnot
Provide your answer as an integer value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9cefd9b-1e12-4ab9-bddf-7966a130d3b6%2F8f5a697e-2f47-4169-9964-96b85a51455d%2Fsmn2sb_processed.png&w=3840&q=75)
Transcribed Image Text:A siren is emitting a constant frequency in a noisy room, x(t) = cos(18t). There is a microphone in
the room measuring the signal, x(t), plus the background noise denoted as the signal, e(t). Let the
noise signal be g(t) = x(t) + e(t). The microphone signal is connected to an A/D converter which
samples the signal at a rate of 51 rad/sec. You take 148 samples from the A/D converter and
calculate the DFT. Recall that
x(t) = cos(Not) = ½ (einot + e¯¡Not)
What integer index, k, of the DFT, X[k], corresponds to the frequency closest to the complex
componente present in the input signal?
-jnot
Provide your answer as an integer value.
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