Editing Filter design (section)

=== The impulse response ===
{{Main|Impulse response}}
There is a direct correspondence between the filter's frequency function and its impulse response: the former is the [[Fourier transform]] of the latter. That means that any requirement on the frequency function is a requirement on the impulse response, and vice versa.

However, in certain applications it may be the filter's impulse response that is explicit and the design process then aims at producing as close an approximation as possible to the requested impulse response given all other requirements.

In some cases it may even be relevant to consider a frequency function and impulse response of the filter which are chosen independently from each other. For example, we may want both a specific frequency function of the filter ''and'' that the resulting filter have a small effective width in the signal domain as possible. The latter condition can be realized by considering a very narrow function as the wanted impulse response of the filter even though this function has no relation to the desired frequency function. The goal of the design process is then to realize a filter which tries to meet both these contradicting design goals as much as possible. An example is for [[high-resolution audio]] in which the frequency response (magnitude and phase) for [[steady state]] signals (sum of sinusoids) is the primary filter requirement, while an unconstrained impulse response may cause unexpected degradation due to time spreading of [[Transient (acoustics)|transient]] signals.<ref>{{cite web|last1=Story|first1=Mike|title=A Suggested Explanation For (Some Of) The Audible Differences Between High Sample Rate And Conventional Sample Rate Audio Material |date=September 1997|url=http://sdg-master.com:80/lesestoff/aes97ny.pdf |publisher=dCS Ltd|archive-date=28 November 2009|archive-url=https://web.archive.org/web/20091128021651/http://sdg-master.com:80/lesestoff/aes97ny.pdf|url-status=live}}</ref><ref>{{cite web|last1=Robjohns|first1=Hugh|title= MQA Time-domain Accuracy & Digital Audio Quality|url= https://www.soundonsound.com/techniques/mqa-time-domain-accuracy-digital-audio-quality|website=soundonsound.com|date=August 2016|publisher= Sound On Sound|archive-date=10 March 2023|archive-url= https://web.archive.org/web/20230310175409/https://www.soundonsound.com/techniques/mqa-time-domain-accuracy-digital-audio-quality|url-status=live}}</ref>