sinusoidal component at exactly frequency or that must be strictly less than ½ the sample rate. The threshold is called the Nyquist rate and is an attribute of the continuous-time input to be sampled. The sample rate must exceed the Nyquist rate for the samples to suffice to represent The threshold is called the Nyquist frequency and is an attribute of the sampling equipment. All meaningful frequency components of the properly sampled exist below the Nyquist frequency. The condition described by these inequalities is called the Nyquist criterion, or sometimes the Raabe condition. The theorem is also applicable to functions of other domains, such as space, in the case of a digitized image. The only change, in the case of other domains, is the units of measure attributed to and The symbol is customarily used to represent the interval between samples and is called the sample period or sampling interval. The samples of function are commonly denoted by (alternatively in older signal processing literature), for all integer values of Another convenient definition is which preserves the energy of the signal as varies. A mathematically ideal way to interpolate the sequence involves the use of sinc functions. Each sample in the sequence is replaced by a sinc function, centered on the time axis at the original location of the sample with the amplitude of the sinc function scaled to the sample value, Subsequently, the sinc functions are summed into a continuous function. A mathematically equivalent method uses the Dirac comb and proceeds by convolving one sinc function with a series of Dirac delta pulses, weighted by the sample values. Neither method is numerically practical. Instead, some type of approximation of the sinc functions, finite in length, is used. The imperfections attributable to the approximation are known as interpolation error. Practical digital-to-analog converters produce neither scaled and delayed sinc functions, nor ideal Dirac pulses. Instead they produce a piecewise-constant sequence of scaled and delayed rectangular pulses (the zero-order hold), usually followed by a lowpass filter (called an "anti-imaging filter") to remove spurious high-frequency replicas (images) of the original baseband signal. Aliasing When is a function with a Fourier transform : the Poisson summation formula indicates that the samples, , of are sufficient to create a periodic summation of . The result is: () which is a periodic function and its equivalent representation as a Fourier series, whose coefficients are This function is