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. 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. 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. 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. 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. That means that any requirement on the frequency function is a requirement on the impulse response, and vice versa. There is a direct correspondence between the filter's frequency function and its impulse response: the former is the Fourier transform of the latter. A peak EQ filter makes a peak or a dip in the frequency response, commonly used in parametric equalizers.A high-shelf filter passes all frequencies, but increases or reduces frequencies above the shelf frequency by specified amount.A low-shelf filter passes all frequencies, but increases or reduces frequencies below the shelf frequency by specified amount.A differentiator has an amplitude response proportional to the frequency.A very narrow band-stop filter is known as a notch filter. A band-stop filter passes frequencies above and below a certain range.A band-pass filter passes a limited range of frequencies.A high-pass filter passes high frequencies fairly well it is helpful as a filter to cut any unwanted low-frequency components.A low-pass filter is used to cut unwanted high-frequency signals.Typical examples of frequency function are: The larger weight, the more important is a close approximation. In relation to the desired frequency function, there may also be an accompanying weighting function, which describes, for each frequency, how important it is that the resulting frequency function approximates the desired one. To achieve steeper slopes, higher-order filters are required. For many purposes, this is not sufficient. This means that the slope of the frequency response is limited to 6 dB per octave. In particular, the steepness and complexity of the response curve is a deciding factor for the filter order and feasibility.Ī first-order recursive filter will only have a single frequency-dependent component.
The filter should be implemented in particular hardware or softwareĪn important parameter is the required frequency response.The computational complexity of the filter should be low.The filter should be localized (pulse or step inputs should result in finite time outputs).The filter should have a specific impulse response.The filter should have a specific phase shift or group delay.
The purpose is to find a realization of the filter that meets each of the requirements to a sufficient degree to make it useful. ( December 2012) ( Learn how and when to remove this template message)įilter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which are contradictory. Please help to improve this article by introducing more precise citations. This article includes a list of general references, but it remains largely unverified because it lacks sufficient corresponding inline citations.