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In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. Both downsampling and decimation can be synonymous with compression , or they can describe an entire process of bandwidth reduction ( filtering ) and sample-rate reduction.
Sample-rate conversion, sampling-frequency conversion or resampling is the process of changing the sampling rate or sampling frequency of a discrete signal to obtain a new discrete representation of the underlying continuous signal. [1]
Responses of the filter (dashed), and its discrete-time approximation (solid), for nominal cutoff frequency of 1 Hz, sample rate 1/T = 10 Hz. The discrete-time filter does not reproduce the Chebyshev equiripple property in the stopband due to the interference from cyclic copies of the response.
In digital signal processing, a digital down-converter (DDC) converts a digitized, band-limited signal to a lower frequency signal at a lower sampling rate in order to simplify the subsequent radio stages. The process can preserve all the information in the frequency band of interest of the original signal.
The highest frequency in the spectrum is half the width of the entire spectrum. The width of the steadily-increasing pink shading is equal to the sample-rate. When it encompasses the entire frequency spectrum it is twice as large as the highest frequency, and that is when the reconstructed waveform matches the sampled one.
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 -length DFT, the summation/overlap causes decimation in frequency, [1]: p.558 leaving only DTFT samples least affected by spectral leakage.
Sinc N filters are commonly used with delta-sigma modulation ADCs just prior to downsampling to the desired output data rate (ODR) of . A sinc N filter's frequency response will lie under a –20·N dB per decade envelope, so higher orders have steeper roll off for cutting out more high frequency noise, but will also have a lower -3 dB frequency .
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex valued frequency-domain (the z-domain or z-plane) representation. [1] [2] It can be considered a discrete-time equivalent of the Laplace transform (the s-domain or s-plane). [3]