filterorder

Filter order is a measure of the complexity and memory of a digital or analog filter. Note that the term is commonly written as "filter order"; some software and sources use the compound form "filterorder." In continuous-time (analog) filters, the order equals the highest power of s in the transfer function, and in discrete-time (digital) filters it corresponds to the degree of the difference equation or the number of delayed samples used by the filter. In FIR filters, the order is typically equal to the number of taps minus one. In IIR filters, the order is related to the number of poles (and sometimes zeros) in the transfer function.

A higher filter order generally yields a sharper transition between passband and stopband, increasing attenuation in the stopband and reducing passband leakage. However, it also increases computational cost and, for IIR, can introduce more phase distortion and potential stability concerns. In FIR implementations, increasing order increases impulse response length and group delay, typically about N/2 samples for symmetric FIR.

Design considerations include meeting specified stopband attenuation and edge frequencies, acceptable passband ripple, and allowed latency or computational budget. Common design approaches include selecting a target order based on these specifications and then choosing a prototype family such as Butterworth, Chebyshev, or Elliptic for the desired magnitude response.

Common examples: a first-order RC filter is a single energy-storage element; a 4th-order filter may be implemented as four cascaded biquads or as a 5-tap FIR, each with its own implications for delay and stability.

In practice, the filter order is chosen to satisfy the desired frequency response while balancing resources and latency.