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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
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 of the 4 dots if we were to adjust the frequency and amplitude of the sinusoid along the solid red segment (between f s /2 and ...
For a given sampling rate (samples per second), the Nyquist frequency (cycles per second) is the frequency whose cycle-length (or period) is twice the interval between samples, thus 0.5 cycle/sample. For example, audio CDs have a sampling rate of 44100 samples/second. At 0.5 cycle/sample, the corresponding Nyquist frequency is 22050 cycles/second .
For example, in order to sample FM radio signals in the frequency range of 100–102 MHz, it is not necessary to sample at 204 MHz (twice the upper frequency), but rather it is sufficient to sample at 4 MHz (twice the width of the frequency interval).
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 ...
Lanczos windows for a = 1, 2, 3. Lanczos kernels for the cases a = 1, 2, and 3, with their frequency spectra. A sinc filter would have a cutoff at frequency 0.5. The effect of each input sample on the interpolated values is defined by the filter's reconstruction kernel L(x), called the Lanczos kernel.
Recall that decimation of sampled data in one domain (time or frequency) produces overlap (sometimes known as aliasing) in the other, and vice versa. Compared to an L {\displaystyle L} -length DFT, the s N {\displaystyle s_{_{N}}} summation/overlap causes decimation in frequency, [ 1 ] : p.558 leaving only DTFT samples least affected by ...
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 ...