Final answer:
The highest detectable frequency in a discrete Fourier analysis for a pressure transducer sampling at 1000 Hz is 500 Hz, calculated using the Nyquist theorem which states that the maximum frequency is half the sampling rate.
Step-by-step explanation:
If an experiment uses a pressure transducer that collects samples at 1000 Hz, the highest detectable frequency in a discrete Fourier analysis would be half of the sampling rate, according to the Nyquist theorem. This is known as the Nyquist frequency. Therefore, the maximum frequency that can be accurately detected without aliasing is 500 Hz.
To calculate this, we use the formula given by the Nyquist theorem:
- The Nyquist frequency (fN) is half the sampling rate (fs).
- fN = fs / 2
- fN = 1000 Hz / 2
- fN = 500 Hz
The importance of the Nyquist frequency lies in the fact that it represents the limit for the range of frequencies that can be properly sampled without introducing errors in the signal reconstruction process known as aliasing. In general, if frequencies higher than the Nyquist frequency are present in the signal, they must be filtered out before sampling to prevent distortion.