If x(n) is a real signal, then x(n)=\(\frac{1}{π}\int_0^π\)[XR(ω) cosωn- XI(ω) sinωn] dω.(a) True(b) FalseI had been asked this question during a job interview.I need to ask this question from Properties of Fourier Transformfor Discrete Time Signals topic in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

If x(n) is a real signal, then x(n)=\(\frac{1}{π}\int_0^π\)[XR(ω) c

1.	If x(n) is a real signal, then x(n)=\(\frac{1}{π}\int_0^π\)[XR(ω) cosωn- XI(ω) sinωn] dω.(a) True(b) FalseI had been asked this question during a job interview.I need to ask this question from Properties of Fourier Transformfor Discrete Time Signals topic in portion Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» Right answer is (a) True To explain I WOULD say: We know that if x(n) is a REAL signal, then XI(n)=0 and xR(n)=x(n) We know that, xR(n)=x(n)=\(\FRAC{1}{2π}\int_0^{2π}\)[XR(ω) cosωn- XI(ω) sinωn] dω Since both XR(ω) cosωn and XI(ω) sinωn are even, x(n) is also even => x(n)=\(\frac{1}{π} \int_0^π\)[XR(ω) cosωn- XI(ω) sinωn] dω

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