The acquire knowledge, to make it understandable and to

The
first recorded EEG frequencies were alpha rhythms of about 10 Hz, which were
recorded by Berger (1929) and later in the beta. The beta value is now used to
define the frequency range of about 12 Hz to 30 Hz. The range of Gamma
frequency oscillations found by Adrian (1942) is between 30 and 80 Hz. The
frequency ranges are not precisely defined, and the intervals are used
differently in different articles 28.The purpose of signal processing methods is to
acquire knowledge, to make it understandable and to interpret it for this using
EEG signals may be appropriate. Our brain gives different reactions at
different times, but our first target is the reactions that the brain gives
about the heart and the effects that those reactions have on the signals. The
brain signals will be used for this purpose to examine the functioning of the
brain with the best and most understandable signals produced, processed and interpreted as it is possible. This
method is called brain signal processing. 29

Normally there are many things or data that do
not work in the obtained signals and when the signals are received, the signal
is distorted due to some negative factors in the environment. So, by filtering
the signal, we can get signal processing at the desired frequency range. For
various purposes, brain functioning is based on well-processed signals 30.
In Figure 6, an EEG signal of a schizophrenia
patient which plotted in MATLAB.EEG
records have been obtained from patients such as epilepsy, schizophrenia, etc.,
through the appropriate registration conditions prepared by the experts of the
Department of Neurology. Since EEG signals below 3 Hz and above 40 Hz are
unreliable due to the low signal-to-noise ratio, all of EEG data is bandpass
filtered to between 3-40 Hz 31. Numerical filters are one of the methods that convert input
signals into desired output signals. Separating the cluttered signals, the
noises in the signals and increasing the quality of the signal are some of the
purposes of this filter (Figure 7). Digital filters, usually identified by the before mentioned
differences, allow the components of the determined signal frequencies and
their coefficients to be selected correctly 32.  Finite Impulse Response (FIR) and
Infinite Impulse Response (IIR) are two main digital filters commonly used in
digital signal processing 33.

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The main purpose of the filters to be designed in this work
is to reduce the noise in the EEG signal. For this purpose, it will be applied
to brain signals with FIR (Finite Impulse Response) and IIR (Infinite Pulse
Response) filter designs to be designed in MATLAB program. The EEG signal
operating frequency range is 0.5 to 38 Hz. For this reason, the cutoff
frequencies of the FIR and IIR filters are designed to be 0.5 to 45 Hz to
design the filter. A bandpass filter was used in the design. For filter design,
MATLAB Filter Design and Analysis Department which is run by
“fdatool” command is used. Once the designed filters are applied to
the EEG signal, the characteristics are removed from the filtered EEG signal 34.The Parks-McClellan algorithm is used to design the most
appropriate filters between the real and desired frequency responses. Filters
are ideal for the reduction of the maximum error between the desired frequency
response and the actual frequency response. The filters designed in this way
exhibit an equal behavior in the frequency response and are sometimes referred
to as equiripple filters 37.Least Squares The
linear-phase FIR filter is used to minimize the weighted, integrated square
error between the ideal partial linear function and the magnitude response of
filter the preferred frequency bands 38.Designing FIR filters using the windowing method can be
simple and fast. One of the simplest window methods is the rectangular window
method 39.Constrained Least Squares (CLS) FIR filter design functions
are one of the techniques that enable FIR filters to be designed without having
to clearly define passbands for magnitude response 40.

Filter designs were made using some of these methods, and it
was applied to signal.IIR filters can be the best efficient of the digital signal
processing(DSP) methods 41.  As the input
is bound to its current and past values, which is also connected to the past
values, that is feedback filtered. The relationship between inputs and outputs
of an IIR Filter is showing in the Equation 2.A Butterworth filter is a type of signal processing filter
that has a straight frequency response as possible as within the passband 42.