If a system takes input as the time domain signal and outputs the frequency domain signal, is such a system an LTI system? For if the input time domain signal can be represented as a linear combination of sinusoids, then since the operation is transformation to the frequency domain, the outputs will also be the same Linear Combinations of the individual outputs (frequency domain representation of the individual sinusoids).. right? so we can say it's Linear? Since the system performs the same operation independent of time, it would be Time-Invariant too right?
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