1. What is Sampling Frequency?

Sampling frequency (f_s) is the number of samples taken per second from a continuous signal to make a discrete signal. It is the reciprocal of the sampling period (T) and is measured in Hertz (Hz).

2. How Does the Calculator Work?

The calculator uses the sampling frequency formula:

Where:

• \( f_s \) — Sampling frequency (Hz)
• \( T \) — Sampling period (seconds)

Explanation: The sampling frequency is inversely proportional to the sampling period. A shorter sampling period results in a higher sampling frequency.

3. Importance of Sampling Frequency

Details: Proper sampling frequency is crucial in digital signal processing to avoid aliasing and accurately reconstruct the original signal. According to the Nyquist theorem, the sampling frequency must be at least twice the highest frequency component of the signal.

4. Using the Calculator

Tips: Enter the sampling period in seconds. The value must be greater than zero. The calculator will compute the corresponding sampling frequency in Hertz (Hz).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between sampling frequency and Nyquist rate?
A: The Nyquist rate is twice the highest frequency in the signal. The sampling frequency must be greater than or equal to the Nyquist rate to avoid aliasing.

Q2: What happens if the sampling frequency is too low?
A: If the sampling frequency is below the Nyquist rate, aliasing occurs where higher frequencies are misrepresented as lower frequencies in the sampled signal.

Q3: Can sampling frequency be too high?
A: While higher sampling frequencies prevent aliasing, they require more storage space and processing power. There's usually an optimal sampling frequency for each application.

Q4: How is sampling frequency related to bandwidth?
A: The maximum frequency that can be accurately represented is half the sampling frequency (Nyquist frequency). The bandwidth of the signal must be less than or equal to this value.

Q5: What are typical sampling frequencies used in practice?
A: Common sampling frequencies include 44.1 kHz for audio CD quality, 48 kHz for professional audio, and various rates from kHz to GHz in different signal processing applications.