Question
Download Solution PDFHow many minimum number of samples are required to exactly describe the following signal?
x(t) = 10 cos(6πt) + 4 sin(8πt)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFSampling Theorem:
A continuous-time signal can be represented in its samples and can be recovered back when sampling frequency (fs)is greater than or equal to twice the highest frequency component of the message signal (fm).
The sampling frequency is given by:
\(f_s=2\times max(f_{m1},f_{m2})\)
Calculation:
Given, x(t) = 10 cos(6πt) + 4 sin(8πt)
6π = 2πfm1
fm1 = 3 Hz
8π = 2πfm2
fm2 = 4 Hz
\(f_s=2\times max(3,4)\)
fs = 8 Hz
fs = 8 samples per second
Last updated on Jul 2, 2025
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