1. Let r(t) be a seismic trace (a continuous time signal) which essentially provides a measure...

 

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1. Let r(t) be a seismic trace (a continuous time signal) which essentially provides a measure of activities inside carth's surface. Further, it is known that useful signal information in r(t) lies in the frequency range between 1.5 Hz to 450 Hz. In order to analyze r(t) digitally, we sample it at 4 kHz to get a discrete time signal r[n]. The signal r[n] is now read into a software program. However, due to an error in indexing, the said program is faulty and reads every 4-th sample (i.e. instead of r[n] it will read r[4n]). Explain, with technical justifications, how the faulty program will affect analysis of useful signal information present in r(t). 2. Determine the value of the integration (dt. 3. Consider a continuous-time periodic signal r(t) with period T such that its Fourier Series coefficients ak = 0 for non-zero even integer k. Show that r(t) = -r (t + 7). M 1. Let r(t) be a seismic trace (a continuous time signal) which essentially provides a measure of activities inside carth's surface. Further, it is known that useful signal information in r(t) lies in the frequency range between 1.5 Hz to 450 Hz. In order to analyze r(t) digitally, we sample it at 4 kHz to get a discrete time signal r[n]. The signal r[n] is now read into a software program. However, due to an error in indexing, the said program is faulty and reads every 4-th sample (i.e. instead of r[n] it will read r[4n]). Explain, with technical justifications, how the faulty program will affect analysis of useful signal information present in r(t). 2. Determine the value of the integration (dt. 3. Consider a continuous-time periodic signal r(t) with period T such that its Fourier Series coefficients ak = 0 for non-zero even integer k. Show that r(t) = -r (t + 7). M

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