In this article, an example of such a filter using finite impulse response is discussed and an application of the filter into real world data is shown.
This is an advantage over recursive filters such as IIR filter (Infinite Impulse Response) in applications that require a linear phase response because it will pass the input without phase distortion.
) is a transfer function of an impulse response to the input.
The convolution allows the filter to only be activated when the input recorded a signal at the same time value.
This filter returns the input values (x(t)) if k falls into the support region of function h. This is the reason why this filter is called finite response.
If k is outside of the support region, the impulse response is zero which makes output zero.
[2] According to Huang (1981)[3] Using this mathematical model, there are four methods of designing non-recursive linear filters with various concurrent filter designs: Define the input signal:
adds a random number from 1 to 200 to the sinusoidal function which serves to distort the data.
Use an exponential function as the impulse response for the support region of positive values.
Use an exponential function as the impulse response for the support region of positive values as before.
The opposite in signs of the powers of the exponent is to maintain the non-infinite results when computing the exponential functions.
This requires the data to be known in advance which makes it a challenge for these filters to function well in situations where signals cannot be known ahead of time such as radio signal processing.
Some examples are image enhancement, restoration and pre-whitening for spectral analysis.
[4] Additionally, linear non-recursive filters are always stable and usually produce a purely real output which makes them more favorable.
They are also computationally easy which usually creates a big advantage for using this FIR linear filter.