Suppose you analyzed the spectrum of an amplitude modulated two-tone message signal: m(t) = A₁m cos(@imt) + A2m cos(w₂mt). Write down the appropriate equation for the AM signal, given that the carrier wave has an amplitude Ac and frequency fc. What does the frequency spectrum look like? Assume w₁m < W2m.
Suppose you analyzed the spectrum of an amplitude modulated two-tone message signal: m(t) = A₁m cos(@imt) + A2m cos(w₂mt). Write down the appropriate equation for the AM signal, given that the carrier wave has an amplitude Ac and frequency fc. What does the frequency spectrum look like? Assume w₁m < W2m.
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![**Analysis of Amplitude Modulated Two-Tone Message Signal**
Consider the spectrum of an amplitude modulated two-tone message signal defined by the equation:
\[ m(t) = A_{1m} \cos(\omega_{1m}t) + A_{2m} \cos(\omega_{2m}t). \]
**Task:**
Derive the appropriate equation for the amplitude modulated (AM) signal, assuming the carrier wave has an amplitude \( A_C \) and frequency \( f_C \).
**Question:**
What does the frequency spectrum of the AM signal look like with the assumption that \( \omega_{1m} < \omega_{2m} \)?
**Explanation:**
In this context, the given signal is a combination of two cosine waves with different frequencies and amplitudes. The AM signal will involve modulating these cosine signals onto a carrier wave with specified amplitude and frequency. The frequency spectrum will reflect the combination of these signals and provide insights into how the carrier and message frequencies interact, considering \( \omega_{1m} < \omega_{2m} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53cd4567-e9c0-49bc-8f29-7fe4db37c68a%2Fc71c0dbc-d111-4a14-a583-63d1701e110d%2F50qjmcg_processed.png&w=3840&q=75)
Transcribed Image Text:**Analysis of Amplitude Modulated Two-Tone Message Signal**
Consider the spectrum of an amplitude modulated two-tone message signal defined by the equation:
\[ m(t) = A_{1m} \cos(\omega_{1m}t) + A_{2m} \cos(\omega_{2m}t). \]
**Task:**
Derive the appropriate equation for the amplitude modulated (AM) signal, assuming the carrier wave has an amplitude \( A_C \) and frequency \( f_C \).
**Question:**
What does the frequency spectrum of the AM signal look like with the assumption that \( \omega_{1m} < \omega_{2m} \)?
**Explanation:**
In this context, the given signal is a combination of two cosine waves with different frequencies and amplitudes. The AM signal will involve modulating these cosine signals onto a carrier wave with specified amplitude and frequency. The frequency spectrum will reflect the combination of these signals and provide insights into how the carrier and message frequencies interact, considering \( \omega_{1m} < \omega_{2m} \).
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