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The underlying philosophy of both time domain and frequency domain equalizers are the same - to equalize the channel frequency response, but the latter achieves the job in the frequency domain.
In a frequency domain equalized system the reference signal (pilot) is usually sent in the frequency domain and is used to estimate the channel frequency response, which in turn will be used to equalize the received data.
But, in a Time domain equalized system the pilot will be sent in the time domain and the Channel Impulse response will be estimated and used to equalize the received data
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