Exp No: 3 Date:15/11/23
FIR FILTER DESIGN USING WINDOWING TECHNIQUES
1. DESIGN A HIGH PASS FILTER USING RECTANGULAR WINDOW:
AIM:
To design a high pass filter using rectangular window.
APPARATUS REQUIRED:
MATLAB
THEORY: (ABOUT WINDOWS AND FILTERS WITH FORMULA)
HIGH PASS FILTER:
A high-pass filter is an EQ curve that is used to remove low-frequency sounds
from an audio signal. It is called a high-pass filter because it allows high-
frequency signals to pass through, while attenuating (reducing the amplitude
of) lower-frequency signals.
For high pass filter:
Hd={-sinw(n-alpha)/(pi*(n-alpha)) ;n!= alpha
1-(w/pi) ;n=alpha
1)RECTANGULAR WINDOW:
RECTANGULAR is a window function that is applied to a signal to modify its
frequency spectrum.
The window calculated by RECTANGULAR is basically the
MATLAB PROGRAM WITH OUTPUTS (MAGNITUDE AND PHASE RESPONSE):
1)HIGH PASS FILTER USING RECTANGULAR WINDOW:
OUTPUT:
………
Simulink Program with outputs (Magnitude and Phase response):
1)RECTANGULAR WINDOW:
Inference:
RESULT:
Thus a high pass filter is designed using rectangular window.
Exp No: 4 Date:15/11/23
FIR FILTER DESIGN USING WINDOWING TECHNIQUES
2.DESIGN A HIGH PASS FILTER USING BLACKMANN
WINDOW:
AIM:
To design a high pass filter using blackmann window.
APPARATUS REQUIRED:
MATLAB
THEORY: (ABOUT WINDOWS AND FILTERS WITH FORMULA)
HIGH PASS FILTER:
A high-pass filter is an EQ curve that is used to remove low-frequency sounds
from an audio signal. It is called a high-pass filter because it allows high-
frequency signals to pass through, while attenuating (reducing the amplitude
of) lower-frequency signals.
For high pass filter:
Hd={-sinw(n-alpha)/(pi*(n-alpha)) ;n!= alpha
1-(w/pi) ;n=alpha
BLACKMAN WINDOW:
The Blackman window is a taper formed by using the first three terms of a
summation of cosines.
It was designed to have close to the minimal leakage possible.
w={0.42+0.5(cos(2*pi*n)/(N-1))+0.08(cos(4*pi*n)/(N-1) ; for –((N-1)/2)<=n<=(N-1)/2
0 ;othrwise
MATLAB PROGRAM (MAGNITUDE AND PHASE RESPONSE):
OUTPUT:
………….
SIMULINK PROGRAM (MAGNITUDE AND PHASE RESPONSE):
Inference:
It is designed to reduce spectral leakage similar to the Hanning window but provides a
different trade-off between main lobe width and side lobe suppression.
The Blackman window is known for providing better side lobe suppression compared
to the Hanning window but has a wider main lobe.
The Blackman window is often chosen when side lobe suppression is critical
RESULT:
Thus a high pass filter is designed using blackman window.
Exp No: 5 Date:15/11/23
FIR FILTER DESIGN USING WINDOWING TECHNIQUES
3.DESIGN A HIGH PASS FILTER USING HAMMING WINDOW
BY FINDING THE N VALUE:
AIM:
To design a high pass filter using hamming window.
APPARATUS REQUIRED:
MATLAB
THEORY: (ABOUT WINDOWS AND FILTERS WITH FORMULA)
HIGH PASS FILTER:
A high-pass filter is an EQ curve that is used to remove low-frequency sounds
from an audio signal. It is called a high-pass filter because it allows high-
frequency signals to pass through, while attenuating (reducing the amplitude
of) lower-frequency signals.
For high pass filter:
Hd={-sinw(n-alpha)/(pi*(n-alpha)) ;n!= alpha
1-(w/pi) ;n=alpha
HAMMING WINDOW:
Hamming Window is here to minimize the signal side lobe (unwanted
radiation).
Thus improving the quality or harmonics of the sound.
W={0.5+0.46(cos(2*pi*n)/(N-1)) ; for 0<=n<=N-1
0 ; otherwise
MATLAB PROGRAM (MAGNITUDE AND PHASE RESPONSE
INFERENCE:
The Hamming window is a type of window function commonly used in signal
processing and various applications, including filtering and spectral analysis.
It is designed to minimize the side lobes in the frequency domain when applying the
window to a signal.
This operation helps to reduce spectral leakage and improves the accuracy of
frequency analysis.
By applying the Hamming window to your signal, you are essentially emphasizing the
central portion of the signal while attenuating the edges.
This is particularly useful when performing Fourier analysis or other frequency
domain operations on the signal.
RESULT:
Thus N value is found and a high pass filter is designed using hamming window.
