Question
Download Solution PDFThe sampling frequency of the signal g(t) = sinc2 (200 t) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Nyquist Sampling interval is defined as the maximum time that:
1) is between regularly spaced samples that will permit the signal waveform to be completely determined.
2) and is equal to reciprocal to twice of the highest frequency in the sampling signal.
i.e., if signal frequency is fm then :
Nyquist rate fs ≥ 2fm
And Nyquist interval:
\({T_s} \le \frac{1}{{2{f_m}}}\)
sinc function: It is the Fourier transform of rectangular function with no scaling.
\(\sin c\left( x \right) = \frac{{\sin \left( x \right)}}{x}\)
\(\sin c\left( x \right) = \left\{ {\begin{array}{*{20}{c}} 1&{x = 0}\\ {\frac{{\sin x}}{x}}&{otherwise} \end{array}} \right.\)
Analysis:
If two or more than two signals are added with signal frequency then sampling frequency will be:
\({f_s} = 2 \left( {{f_{{m_1}}}+\;{f_{{m_2}}}+\;{f_m}}+.... \right)\)
And \({T_s} = \frac{1}{{{F_s}}}\)
Calculation:
ωm = 2 × (200 + 200) π = 800 π rad/sec
fm = ωm/2π = 400 Hz
Last updated on May 28, 2025
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