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The Fourier series for the signal x(n)=cos√2πn exists.(a) True(b) FalseThe question was asked in semester exam.The origin of the question is Frequency Analysis of Discrete Time Signal in section Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer»

The CORRECT OPTION is (b) False

For explanation I would say: For ω0=√2π, we have f0=1/√2. Since f0 is not a rational NUMBER, the SIGNAL is not PERIODIC. Consequently, this signal cannot be expanded in a Fourier series.



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