Consider a sampled sequence with zero values between sampling instants. Replace it by taking every N-th value of the sampled sequence. The original and sampled sequences are equal at integer multiples of N. Decimation extracts every N-th sample from a sequence, making the new sequence more efficient. The Fourier transform of the decimated sequence is a combination of scaled and shifted versions of the original spectrum. This transform simplifies analysis by focusing on non-zero intervals. The final relationship shows the Fourier transform of the decimated sequence is a scaled version of the original's transform. This scaling emphasizes the periodic nature introduced by decimation, with spectra differing only in frequency scaling. If the original spectrum is band-limited with no aliasing, decimation spreads the spectrum over a larger frequency band. Decimating a sequence from a continuous-time signal reduces the sampling rate by a factor of N, avoiding aliasing if the original signal is oversampled. When interpreting the original sequence as samples from a continuous-time signal, decimation is called downsampling.