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The bandwidth of a DSBSC signal is twice that of the highest modulating frequency. So, for a single tone message of 100Hz, the DSBSC bandwidth is 200Hz. But the bandwidth of the envelope is many times this ..
So the lowpass filter will need to have a bandwidth wide enough to pass at least the first few odd harmonics of the 100Hz signal; say a passband extending to at least 1 kHz should be enough ..
2kHz seems to be to high as it will overlap the F(carrier)-F(message) product ..