Question

1. (a) A signal \(x(t)\) is defined by: \(x(t) = 10\cos(2\pi \times 1000t) + 20\cos(2\pi \times 3500t)\) It is sampled at \(1/0.4375\) times the Nyquist rate. Find the first 4 sample values. An FFT is obtained on 1000 samples of \(x(t)\). Draw an approximate sketch of the spectrum obtained. What is the resolution of the FFT? [16 marks]

          1.
(a) A signal \(x(t)\) is defined by:
\(x(t) = 10\cos(2\pi \times 1000t) + 20\cos(2\pi \times 3500t)\)
It is sampled at \(1/0.4375\) times the Nyquist rate. Find the first 4 sample values. An FFT
is obtained on 1000 samples of \(x(t)\). Draw an approximate sketch of the spectrum
obtained. What is the resolution of the FFT?
[16 marks]

1.
(a) A signal x(t) is defined by:
x(t) = 10cos(2π× 1000t) + 20cos(2π× 3500t)
It is sampled at 1/0.4375 times the Nyquist rate. Find the first 4 sample values. An FFT
is obtained on 1000 samples of x(t). Draw an approximate sketch of the spectrum
obtained. What is the resolution of the FFT?
[16 marks]

Added by Andrew C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Yatu Khandelwal

Step 1

Sampling rate: The Nyquist rate is twice the highest frequency component in the signal. In this case, the highest frequency component is 3500 Hz. Therefore, the Nyquist rate is 2 * 3500 = 7000 Hz. The sampling rate is 1/0.4375 times the Nyquist rate. Therefore, Show more…

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A signal xt is defined by xt = 10cos(2Ï€1000t) + 20cos(2Ï€3500t) It is sampled at 1/0.4375 times the Nyquist rate. Find the first 4 sample values. An FFT is obtained on 1000 samples of x(t). Draw an approximate sketch of the spectrum obtained. What is the resolution of the FFT? [16 marks]