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That paper includes an example of frequency aliasing dating back to 1922. The first published use of the term "aliasing" in this context is due to Blackman and Tukey in 1958. [ 5 ] In their preface to the Dover reprint [ 6 ] of this paper, they point out that the idea of aliasing had been illustrated graphically by Stumpf [ 7 ] ten years prior.
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 bandwidth, B, in this example is just small enough that the slower sampling does not cause overlap (aliasing). Sometimes, a sampled function is resampled at a lower rate by keeping only every M th sample and discarding the others, commonly called "decimation". Potential aliasing is prevented by lowpass-filtering the samples before decimation.
Effects of aliasing, blurring, and sharpening may be adjusted with digital filtering implemented in software, which necessarily follows the theoretical principles. A family of sinusoids at the critical frequency, all having the same sample sequences of alternating +1 and –1.
An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruction of the signal from its samples is possible when the power of frequencies above the Nyquist frequency is ...
When instead, the frequency range is (A, A+B), for some A > B, it is called bandpass, and a common desire (for various reasons) is to convert it to baseband. One way to do that is frequency-mixing the bandpass function down to the frequency range (0, B). One of the possible reasons is to reduce the Nyquist rate for more efficient storage.
The frequency axis has units of FFT "bins" when the window of length N is applied to data and a transform of length N is computed. For instance, the value at frequency 1 / 2 "bin" is the response that would be measured in bins k and k + 1 to a sinusoidal signal at frequency k + 1 / 2 . It is relative to the maximum possible ...
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 ...