Digital signal and image processing
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Guess: what sampling rate does a 4 kHz signal need?
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Lesson notes
Explain how a continuous signal becomes a discrete sequence and state the Nyquist sampling criterion
Key points
- The Nyquist rate is twice the highest frequency, so 8 kHz, but the criterion demands a sampling frequency strictly greater than that.
- At exactly 8 kHz you can land every sample on the sine's zero crossings and record nothing at all, so examiners want fs above 8 kHz.
Takeaway: Sample strictly faster than twice the highest frequency.
Quick check: A signal's highest frequency is 4 kHz. Which sampling frequency satisfies the Nyquist criterion?
- Exactly 4 kHz
- Exactly 8 kHz
- Anything above 8 kHz
State fs > 2fmax: strictly greater than the Nyquist rate.
sampling frequencyNyquist ratediscrete-time signalfs > 2fmaxStrictly more
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