Many the system which only allows signals

Many external
causes in transmission system and other environmental factors are the sources
of noise produced (Nalin, 2014). For example, the increased use of industrial
equipment such as fans, engines, ventilators and compressors has causes the
problem of noise in industrial environments (Kang, Moon, and Lim, 2014). Most
manufacturing noise is variable or intermittent (Canadian Centre for
Occupational Health and Safety CCOHS, 2015). According to CCOHS (2015), noise
is irregular when the environment is mixed with noisy and quiet periods. For
instances, impact noise produced from the car collision in a quiet environment
produces a short period of loud noise (Pulsar, 2005).

In
signal processing, a filter is a device or process that removes unwanted
components or features from a signal (Revolvy Discuss, n.d.). Filtering is a
class of signal processing with the complete or partial suppression of some
aspect of the signal (Douglas, 2017). In other words, Douglas’s statement means
that filtering can be used suppress and reduce background noise by removing
certain frequencies in the signal. Filters are widely used in electronics and
telecommunications (Chang, Zhang, and Huang, 2011). For examples, filters are
used in television, radar, control system, radio, music synthesis, image
processing, audio recording and computer graphics.

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           Ideal filtering system is the system which
only allows signals within certain range of frequencies to pass through while
blocking the others (Kelsey and Aschliman, 1994). Ideal filter can be
categorized into low-pass, high-pass, band-pass and band-stop. The selectivity
of filtering technique used is based on the desire output of the application
since different filtering technique produce different output.

Low-pass
filter is a filter that passes signals with the low frequency than the cut-off
frequency and blocks signals with frequencies higher than the cut-off frequency
(Makandar and Halalli, 2015). The cut-off frequency is depended on the
applications. There are different types of low-pass filter, which include,
ideal low-pass filter, Butterworth low-pass filter and Gaussian low-pass filter
(Shi, 2011). According to Shi (2011), an ideal low-pass filter is the simplest
low-pass filter which blocks all high frequency signals with greater distance
than the specified distance from the origin. The transfer function of an ideal
low-pass filter is:

 

where D(u, v)
is the distance from point (u, v) to the center of the frequency.

 

According
to (Kevan, 2004), Butterworth low-pass filter is a design of frequency-domain
filter to remove high-frequency noise with minimal loss of signal components in
the specified pass-band with order n;

 

For
the Gaussian low-pass filter, the transfer function is as follows (Kevan, 2014):

 

For
high-pass filter, signals with the frequency above the cut-off frequency is to
allowed to pass through while signals with frequency lower than that will be
blocked. High-pass filter can be expressed in terms of low-pass filter where  is the high-pass
filter while  is the low-pass
filter:

Furthermore,
band-pass filter is a filter that passes signals within the range of the
cut-off frequencies set (Vigneshwaran, Santhoshkumar, and Srikanth, 2016). To
achieve band-pass filter, a signal should processed through high-pass filter,
amplifier and low-pass filter as shown in Figure 2.1 below.