Hello, I have some issues with the following problem (below), I don\'t get how t

Question

Hello, I have some issues with the following problem (below), I don't get how the overall system being LTI depends on the input signal. Shouldn't LTI system be a LTI for all possible input signal (otherwise they are not LTI)? The problem is the problem 7.22 of the Discrete-Time Signal Processing (3rd Edition) by Oppenheim and Schafer.

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In the system shown in Figure P7.22, the discrete-time system is a linear-phase FIR lowpass filter designed by the Parks-McClellan algorithm with 1-001, 2 = 0.001, ap = 0.4m, and as = 0.6 . The length of the impulse response is 28 samples. The sampling rate for the ideal C/D and D/C converters is 1/T= 10000 samples/sec Converter Converter Figure P7.22 (a) What property should the input signal have so that the overall system behaves as an LTI system with Ydjs2) = Heff(jS2)Xc(jQI

Explanation / Answer

Fourier transform of the signal must be exist,so that input signal must follow the dirichlet conditions.

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