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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
The function is defined by the three poles in the left half of the complex frequency plane. Log density plot of the transfer function () in complex frequency space for the third-order Butterworth filter with =1. The three poles lie on a circle of unit radius in the left half-plane.
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 figure on the left shows a function (in gray/black) being sampled and reconstructed (in gold) at steadily increasing sample-densities, while the figure on the right shows the frequency spectrum of the gray/black function, which does not change. The highest frequency in the spectrum is half the width of the entire spectrum.
The Goertzel algorithm is a technique in digital signal processing (DSP) for efficient evaluation of the individual terms of the discrete Fourier transform (DFT). It is useful in certain practical applications, such as recognition of dual-tone multi-frequency signaling (DTMF) tones produced by the push buttons of the keypad of a traditional analog telephone.
The individual frequency-shifted copies of the original transform are called aliases. The frequency offset between adjacent aliases is the sampling-rate, denoted by f s. When the aliases are mutually exclusive (spectrally), the original transform and the original continuous function, or a frequency-shifted version of it (if desired), can be ...
Range aliasing occurs when reflections arrive from distances that exceed the distance between transmit pulses at a specific pulse repetition frequency (PRF). Range ambiguity resolution is required to obtain the true range when the measurements are made using a system where the following inequality is true.
The goal of an anti-aliasing filter is to greatly reduce frequencies above a certain limit, known as the Nyquist frequency, so that the signal will be accurately represented by its samples, or nearly so, in accordance with the sampling theorem; there are many different choices of detailed algorithm, with different filter transfer functions.