Question

In 1024-point DFT of a signal sampled at 8192 Hz, \( k = 8 \) corresponds to a frequency of

• A. 64 Hz
• B. 32 Hz
• C. 16 Hz
• D. 8 Hz

Hint:

To find the frequency in DFT, use the formula \( f = \frac{k \cdot f_s}{N} \).

Answer 1

The Correct Option is B

- The frequency corresponding to \( k \) in a DFT is given by \[ f = \frac{k \cdot f_s}{N} \] where \( f_s = 8192 \, \text{Hz} \) and \( N = 1024 \). - Substituting the given values: \[ f = \frac{8 \times 8192}{1024} = 32 \, \text{Hz} \]
Conclusion: The frequency is 32 Hz, as given by option (b).