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The first statistical use of the term "aliasing" in print is the 1945 paper by Finney, [67] which dealt with regular fractions with 2 or 3 levels. The term was imported into signal processing theory a few years later, possibly influenced by its use in factorial experiments; the history of that usage is described in the article on aliasing in ...
A graph of amplitude vs frequency (not time) for a single sinusoid at frequency 0.6 f s and some of its aliases at 0.4 f s, 1.4 f s, and 1.6 f s would look like the 4 black dots in Fig.3. The red lines depict the paths ( loci ) of the 4 dots if we were to adjust the frequency and amplitude of the sinusoid along the solid red segment (between f ...
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.
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 Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949.
Step 2 alone creates undesirable aliasing (i.e. high-frequency signal components will copy into the lower frequency band and be mistaken for lower frequencies). Step 1, when necessary, suppresses aliasing to an acceptable level. In this application, the filter is called an anti-aliasing filter, and its design is
Per Shannon's sampling theorem, the sampling rate must be at least twice the highest frequency of the desired signal in order to preclude spectral aliasing. Because the beam pattern (or array factor ) of a linear array is the Fourier transform of the element pattern, [ 2 ] the sampling theorem directly applies, but in the spatial instead of ...
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 ...