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The sampling frequency or sampling rate, , is the average number of samples obtained in one second, thus = /, with the unit samples per second, sometimes referred to as hertz, for example 48 kHz is 48,000 samples per second.
Rate reduction by an integer factor M can be explained as a two-step process, with an equivalent implementation that is more efficient: [5] Reduce high-frequency signal components with a digital lowpass filter. Decimate the filtered signal by M; that is, keep only every M th sample.
Sample-rate conversion prevents changes in speed and pitch that would otherwise occur when transferring recorded material between such systems. More specific types of resampling include: upsampling or upscaling; downsampling, downscaling, or decimation; and interpolation. The term multi-rate digital signal processing is sometimes used to refer ...
When the sample-rate is pre-determined by other considerations (such as an industry standard), () is usually filtered to reduce its high frequencies to acceptable levels before it is sampled. The type of filter required is a lowpass filter , and in this application it is called an anti-aliasing filter .
High PRF is limited to systems that require close-in performance, like proximity fuses and law enforcement radar. For example, if 30 samples are taken during the quiescent phase between transmit pulses using a 30 kHz PRF, then true range can be determined to a maximum of 150 km using 1 microsecond samples (30 x C / 30,000 km/s).
Similarly, the accuracy of the sampling timing, or aperture uncertainty of the sampler, frequently the analog-to-digital converter, must be appropriate for the frequencies being sampled 108MHz, not the lower sample rate. If the sampling theorem is interpreted as requiring twice the highest frequency, then the required sampling rate would be ...
In this example, f s is the sampling rate, and 0.5 cycle/sample × f s is the corresponding Nyquist frequency. The black dot plotted at 0.6 f s represents the amplitude and frequency of a sinusoidal function whose frequency is 60% of the sample rate. The other three dots indicate the frequencies and amplitudes of three other sinusoids that ...
The sampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at four times that rate requires a sampling frequency of 800 Hz. This gives the anti-aliasing filter a transition band of 300 Hz ((f s /2) − B = (800 Hz/2) − 100 Hz = 300 Hz) instead of 0 Hz if the sampling frequency was 200 Hz. Achieving an ...